TWI489400B - Adaptive computation method and framework thereof - Google Patents
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Description
本發明係相關於一種計算方法及其架構。尤指一種可適性計算方法與架構。The present invention is related to a computing method and its architecture. Especially a method and architecture for adaptability.
第一圖為傳統數值模式之開發流程，一般而言可分為4個階段：The first picture shows the development process of the traditional numerical model, which can be divided into four stages:
1.概念模式階段(Conceptual model)：對於所探討問題、自然現象或是系統，定義其所涵蓋範圍(如模擬區域，邊界條件，初始條件等)，以及對發生於其中的基本行為進行描述。1. Conceptual model: Define the scope (such as simulation area, boundary conditions, initial conditions, etc.) of the problem, natural phenomenon or system in question, and describe the basic behaviors that occur in it.
2.數學定義階段(Mathematical formulation)：在數學定義上，通常包含兩個步驟：2. Mathematical formulation: In mathematical definition, there are usually two steps:
a. 對於問題中之各種物理或化學基本行為以一個或多個數學量化的法則(變數及方程式)描述之。a. Describe the various physical or chemical basic behaviors in the problem as one or more mathematically quantified rules (variables and equations).
b. 將前述多個變數及方程式以數學技巧推導整合為數目較少之變數及控制方程式(通常為偏微分方程式(PDE)的型態)。b. Integrate the aforementioned variables and equations into mathematically derived variables into a smaller number of variables and governing equations (usually the form of partial differential equations (PDE)).
3.數值離散階段(Numerical discretization)：定義空間格點，將原時空上連續之解函數以時空上不連續之離散型變數近似，再選用適當的數值方法，如有限差分法(FDM)，有限元素法(FEM)，有限體積法(FVM)，邊界元素法(BEM)及有限解析法(FAM)等，將前述之控制方程式(組)，進行空間及時間上之數值積分推導，而將原來之控制方程式(組)表達成空間格點上之離散型代數方程式。3. Numerical discretization: Define the spatial lattice point, approximate the continuous solution function in the original space-time with discrete variables in time and space, and then select appropriate numerical methods, such as finite difference method (FDM), finite. Element method (FEM), finite volume method (FVM), boundary element method (BEM) and finite analytical method (FAM), etc., the above-mentioned control equations (groups) are deduced by numerical integration in space and time, and the original The governing equations (groups) are expressed as discrete algebraic equations on the spatial lattice points.
4.程式開發階段(Program development)：前述離散型變數之數值，常以電腦程式計算，因此需進行相關程式的開發，主要有兩大部份；先將所有空間格點上之離散型代數方程式，組合成矩陣方程式，此矩陣方程式描述了所有空間格點上離散變數彼此間之時空關係。前述之矩陣方程式，仍需再以適當之矩陣解法求解各變數之數值。4. Program development: The value of the above discrete variables is often calculated by computer program. Therefore, the development of related programs is required. There are two main parts; firstly, the discrete algebraic equations on all spatial lattice points. , combined into a matrix equation, which describes the spatio-temporal relationship between discrete variables on all spatial lattice points. For the aforementioned matrix equations, the values of the variables need to be solved by an appropriate matrix solution.
第一圖之傳統數值模式開發流程乃環環相扣，惟若欲加入一原模式未考量之變量或現象，則須加入描述此行為之規則(方程式)，如此則須重新推導並修正原問題之控制方程式、數值解及矩陣方程式，相關電腦程式亦需要重新修改，修改工作往往相當繁複，也因此限制了原模式擴充或修正的彈性。The traditional numerical model development process in the first figure is interlocking. However, if you want to add a variable or phenomenon that is not considered in the original mode, you must add a rule (equation) describing the behavior, so you must re-derive and correct the original problem. The control equations, numerical solutions and matrix equations, the related computer programs also need to be re-modified, the modification work is often quite complicated, and thus limits the flexibility of the original mode expansion or correction.
傳統數值模式由於缺乏彈性而無法與人工智慧方法緊密的結合。因此，傳統數值模式，只能模擬其控制方程式所描述之現象，無自我學習進而擴充本身之模擬功能，亦無依環境的不同而自行改變模擬內容等類「智慧」的能力。Traditional numerical models cannot be tightly integrated with artificial intelligence methods due to lack of flexibility. Therefore, the traditional numerical model can only simulate the phenomenon described by its control equation, without self-learning to expand its own simulation function, and it does not have the ability to change the "smart" such as analog content according to the environment.
近年來，細胞自動機(Cellular Automata)的架構雖可對於問題進行相當之化簡，惟該架構亦對Cellular Automata本身造成相當之限制，例如應用於三維未飽和地下水模式時，若需使用到問題中某區域之總進出流量，則Cellular Automata本身之架構無法提供此種資訊，且Cellular Automata之各個細胞僅能依據t時刻的狀態進行t+1時刻之計算(亦即顯示法)。In recent years, the Cellular Automata architecture has been able to simplify the problem considerably, but the architecture also imposes considerable limitations on Cellular Automata itself, such as when applied to 3D unsaturated groundwater mode. The total inflow and outflow of a certain area in the region, Cellular Automata's own structure can not provide such information, and each cell of Cellular Automata can only calculate the t+1 time according to the state of time t (ie, display method).
綜上所述，可知習知技術具有下述缺點：(1)開發計算模擬軟體費時費力的問題；(2)難以更新、擴充及累積計算功能；以及(3)難以整合各種人工智慧方法，進而自我學習與演進。In summary, it is known that the prior art has the following disadvantages: (1) development of computational simulation software is time consuming and laborious; (2) difficulty in updating, expanding, and accumulating computational functions; and (3) difficulty in integrating various artificial intelligence methods, and further Self-learning and evolution.
職是之故，申請人鑑於習知技術中所產生之缺失，經過悉心試驗與研究，並一本鍥而不捨之精神，終構思出本案「可適性計算方法與架構」，能夠克服上述缺點，以下為本案之簡要說明。For the sake of the job, the applicant has been able to overcome the above shortcomings by carefully testing and researching, and with a spirit of perseverance, and finally conceiving the "compatibility calculation method and structure" of the case. A brief description of the case.
本發明提出一種可適性計算方法與架構，以解決傳統數值建模費時費力與所開發之計算模擬軟體，難以更新、擴充及累積計算功能的問題，並將數值模式進一步發展成具備自我學習及演進的智慧型計算模擬系統。應用本發明的方法，模式可分兩階段發展，並各具有階段性的效益，第一階段的完成，研究者可從一個已開發完成的模式，彈性的藉由增減方程式而擴充或改變原模式所能模擬的問題，而不須如傳統數值模式般，進行繁瑣且複雜之程式修改及再開發流程。此將幫助研究人員有更多的時間回歸問題本質面的探討，而不需如過去般將大量時間耗費在開發或修正程式以求解欲探討的問題。第二階段可進一步深度結合人工智慧方法，使模式進一步發展成具備自我學習及演進的智慧型計算模擬系統，可藉由「群體智慧」效應，使所發展的模擬模式能整體展現出驚人的功能與彈性。The invention proposes an adaptability calculation method and architecture, which solves the problem that the traditional numerical modeling is time-consuming and laborious and the developed simulation software is difficult to update, expand and accumulate the calculation function, and further develops the numerical model into self-learning and evolution. Intelligent computing simulation system. By applying the method of the present invention, the model can be developed in two stages, and each has a phased benefit. Upon completion of the first stage, the researcher can expand or change the original from a developed mode, elastically by increasing or decreasing the equation. The problems that the model can simulate do not require complicated and complex program modification and re-development processes as in the traditional numerical model. This will help researchers have more time to go back to the nature of the problem without having to spend a lot of time developing or revising the program to solve the problem to be explored. The second phase can further integrate the artificial intelligence method to further develop the model into a self-learning and evolving intelligent computing simulation system. The "group wisdom" effect can make the developed simulation mode show amazing functions as a whole. With elasticity.
根據本發明的第一構想，提出一種可適性計算方法，包含以下步驟：(a)提供一方程式集合具有至少一方程式與至少一變數；(b)對該方程式集合進行一一致性分析，以檢驗該至少一方程式與該至少一變數之一致性，並得一求解順序，且定義多個空間網格與多個節點，並依該等節點將該方程式集合與該至少一變數，離散化成為一離散方程組；以及(c)依據該求解順序，求解該離散方程組。According to a first aspect of the present invention, an adaptive computing method is provided, comprising the steps of: (a) providing a set of programs having at least one program and at least one variable; (b) performing a consistency analysis on the set of equations, Verifying the consistency of the at least one program with the at least one variable, and obtaining a solution order, and defining a plurality of spatial meshes and a plurality of nodes, and discretizing the set of equations and the at least one variable according to the nodes a discrete system of equations; and (c) solving the set of discrete equations according to the solution sequence.
較佳地，本發明所提供的方法，其中步驟(b)包括一步驟：(b1)使用人工智慧方法補齊該方程式集合中所缺乏的一或多個未知方程式，以完成該一致性分析，其中該或該等未知方程式對應於該方程式集合所缺乏的一或多個應變數。Preferably, the method provided by the present invention, wherein the step (b) comprises a step of: (b1) using an artificial intelligence method to complete one or more unknown equations lacking in the set of equations to complete the consistency analysis, Where the or the unknown equations correspond to one or more strain numbers that are lacking in the set of equations.
較佳地，本發明所提供的方法，其中步驟(b1)包括一步驟：(b11)建立一類神經網路，以找出該或該等未知方程式。Preferably, the method provided by the present invention, wherein step (b1) comprises a step of: (b11) establishing a neural network to find the or the unknown equation.
較佳地，本發明所提供的方法，其中步驟(b11)包括一步驟：(b111)以一主成份分析找出與該或該等應變數相關的一或多個自變數，以建立該類神經網路。Preferably, the method provided by the present invention, wherein the step (b11) comprises a step of: (b111) analyzing, by a principal component analysis, one or more independent variables associated with the or the number of strains to establish the class Neural network.
較佳地，本發明所提供的方法，其中步驟(b)包括下列步驟：(b2)於該離散方程組所欲探討的變數所在的一空間劃分該等節點，其中該等節點係可依凡諾依圖定義；以及(b3)使用一簡單差分法將該方程式集合離散化成為該離散方程組。Preferably, the method provided by the present invention, wherein the step (b) comprises the following steps: (b2) dividing the nodes in a space in which the variables to be discussed by the discrete equations are located, wherein the nodes are The Noi diagram definition; and (b3) discretize the set of equations into the system of discrete equations using a simple difference method.
較佳地，本發明所提供的方法，其中步驟(c)包括一步驟使用一疊代法來求解該離散方程組的一待解變數在該等節點中的一任意節點的值。Preferably, the method provided by the present invention, wherein the step (c) comprises a step of using an iterative method to solve the value of an arbitrary node of the discrete equations in the nodes.
較佳地，本發明所提供的方法，其中該疊代法包括一內疊代與一外疊代。Preferably, the method of the present invention, wherein the iterative method comprises an inner iteration and an outer iteration.
較佳地，本發明所提供的方法，其中該內疊代係使用一最佳化方法來求解該待解變數在該任意節點的值。Preferably, the method provided by the present invention, wherein the inner iteration uses an optimization method to solve the value of the variable to be solved at the arbitrary node.
較佳地，本發明所提供的方法，其中該外疊代包括以下步驟：(c1)若該任意節點的一鄰近節點之該待解變數更新時，判斷該任意節點是否重啟該內疊代；以及(c2)重複步驟(c1)直到該等節點皆不需重啟該內疊代。Preferably, the method provided by the present invention, wherein the outer iteration comprises the following steps: (c1) determining whether the arbitrary node restarts the inner iteration if the to-be-solved variable of a neighboring node of the arbitrary node is updated; And (c2) repeating step (c1) until the nodes do not need to restart the inner iteration.
較佳地，本發明所提供的方法，其中該等步驟可由電腦語言實現。Preferably, the method provided by the present invention, wherein the steps are implemented by a computer language.
較佳地，本發明所提供的方法，更包括一步驟(d)調整該方程式集合，以描述所欲解決之問題定義與問題中基本行為或現象。Preferably, the method provided by the present invention further comprises a step (d) of adjusting the set of equations to describe the definition of the problem to be solved and the basic behavior or phenomenon in the problem.
根據本發明的第二構想，提出一種可適性計算方法，包括以下步驟：(a)提供一方程式集合；(b)對該方程式集合進行一一致性分析以獲得一求解順序，且將該方程式集合離散化成為一離散方程組；以及(c)依據該求解順序，求解該離散方程組。According to a second aspect of the present invention, an adaptive calculation method is provided, comprising the steps of: (a) providing a set of programs; (b) performing a consistency analysis on the set of equations to obtain a solution order, and formulating the equation The set discretization becomes a discrete system of equations; and (c) the set of discrete equations is solved according to the solution order.
根據本發明的第三構想，提出一種資訊架構「可適性計算架構」以實作第一構想，包含：一計算層，其將描述問題特性之一方程式集合所欲探討的變數所在的一空間劃分多個節點，並計算該方程式集合的一待解變數在該等節點上的值。According to a third aspect of the present invention, an information architecture "adaptability computing architecture" is proposed to implement a first concept, comprising: a computing layer, which will describe a spatial partition in which a variable of a set of equations is to be explored. A plurality of nodes and calculating a value of a set of equations of the set of equations on the nodes.
較佳地，本發明所提供的架構，其中該計算層包括多個計算元，該等計算元中的一任意計算元對應該等節點中一任意節點，並計算該待解變數在該任意節點上之值，且該等計算元係獨立計算。Preferably, the architecture provided by the present invention, wherein the computing layer comprises a plurality of computing elements, an arbitrary computing element of the computing elements corresponds to an arbitrary node in the node, and the variable to be solved is calculated at the arbitrary node. The above values, and the calculation elements are calculated independently.
較佳地，本發明所提供的架構，其中該等計算元包括一核心平台與一應用模組。Preferably, the architecture provided by the present invention, wherein the computing elements comprise a core platform and an application module.
較佳地，本發明所提供的架構，其中該等計算元分別執行一內疊代並以最佳化方法計算該待解變數。Preferably, the present invention provides an architecture in which the computing elements respectively perform an inner iteration and calculate the variable to be solved in an optimized manner.
較佳地，本發明所提供的架構，更包括：一主控協調層，用以執行一外疊代並協調該等計算元間的資料交換。Preferably, the architecture provided by the present invention further includes: a master coordination layer for performing an iteration and coordinating data exchange between the computing cells.
較佳地，本發明所提供的架構，其中該主控協調層偵測到該任意計算元之一鄰近計算元的該待解變數更新時，判斷該任意計算元是否重啟該內疊代，且持續偵測直到該等計算元皆不需重啟該內疊代。Preferably, the architecture provided by the present invention, wherein the master coordination layer detects that the one of the arbitrary computing elements is updated adjacent to the computing element, and determines whether the arbitrary computing element restarts the inner iteration, and Continuous detection until the computational elements do not need to restart the inner iteration.
較佳地，本發明所提供的架構，其中該計算層與該主控協調層具有人工智慧演算法。Preferably, the architecture provided by the present invention, wherein the computing layer and the master coordination layer have an artificial intelligence algorithm.
較佳地，本發明所提供的架構，其中該等計算元對該方程式集合進行一致性分析，以驗證該方程式集合有無矛盾與是否有解，並得出該方程式集合中各方程式求解順序。Preferably, the architecture provided by the present invention, wherein the computing elements perform a consistency analysis on the set of equations to verify whether the set of equations has a contradiction and whether there is a solution, and obtain a solution order of the equations in the set of equations.
本案將可由以下的實施例說明而得到充分瞭解，使得熟習本技藝之人士可以據以完成之，然本案之實施並非可由下列實施案例而被限制其實施型態。其中相同的標號始終代表相同的組件。The present invention will be fully understood by the following examples, so that those skilled in the art can do so. However, the implementation of the present invention may not be limited by the following embodiments. Where the same reference numerals always represent the same components.
第二圖為本發明所提出之「可適性計算方法」流程示意圖，第三圖為「可適性計算方法」與傳統數值模式建構流程之差異比較，由第三圖可看出本發明與傳統方式差異甚大，是整個開發流程的改變，由第二圖與第三圖可進一步說明各階段之差異如下：The second figure is a schematic diagram of the flow of the "compatibility calculation method" proposed by the present invention, and the third figure is a comparison of the difference between the "suitability calculation method" and the traditional numerical model construction process. The third figure shows the present invention and the conventional manner. The difference is very big, which is the change of the whole development process. The difference between the stages is further illustrated by the second and third figures:
(1)概念模式(Conceptual model)，如第三圖步驟S31：(1) Conceptual model, as shown in the third step, step S31:
此階段乃在定義問題及其中之基行為描述，因此兩者必須相同，如第二圖之步驟S21。This stage is to define the problem and its base behavior description, so the two must be the same, as in step S21 of the second figure.
(2)數學定義(Mathematical formulation)，如第三圖步驟S32：(2) Mathematical formulation, as in the third step, step S32:
此階段又可分為兩大步驟，首先為以各種基本方程式描述第一階段所定義問題中的各種變量之變化行為，此為正確量化描述問題所必需，因此本發明與傳統方式皆相同。惟接下來之步驟本發明將與傳統方法不同，本發明將保留前述之基本方程式組，並以其做為後續計算的基礎而並不採用如傳統方式般，將前述所得之多條方程式進行人為的整合推導，以盡量減少方程式及變數之數目。傳統方法的好處為最後待解的方程式與變數數目較少。傳統上認為方程式及變數愈少對後續解題將愈有利，惟以本發明的觀點而言，此種推導與簡化需以人力為之而無法自動化或程序化，因此若欲考慮新的現象或變量而需新增或修改前述之基本方程式時，則需人為重新推導，而這點將先天上限制了後續所開發出來的模式擴充模擬功能的可能。本發明為維持後續增減方程式的彈性，將不再對前述多條基本方程式進行進一步整合。如此本發明後續將需處理較多的方程式與變數，惟由於各方程式並未再經人為整合推導，將可維持其原先較基本而簡單的型式，而不像傳統方式般，雖然最後面對的方程式數目較少，惟這些方程式已經人為整合後所得，其型式將比較複雜。This stage can be further divided into two major steps. Firstly, the change behavior of various variables in the problem defined in the first stage is described by various basic equations, which is necessary for correctly quantifying the description problem, and thus the present invention is the same as the conventional method. However, the next step of the present invention will be different from the conventional method, and the present invention will retain the aforementioned basic equation set and use it as a basis for subsequent calculations without using the conventional equations as described above. The integration of derivation to minimize the number of equations and variables. The advantage of the traditional method is that the number of equations and variables to be solved is small. Traditionally, the less the equations and variables are, the better it will be for subsequent problems. However, from the point of view of the present invention, such derivation and simplification need to be automated or programmed, so if you want to consider new phenomena or variables. When the basic equations mentioned above need to be added or modified, they need to be re-derived artificially, and this will limit the possibility of the subsequent development of the model expansion simulation function. In order to maintain the elasticity of the subsequent increase and decrease equations, the present invention will no longer further integrate the aforementioned plurality of basic equations. Therefore, the present invention will need to deal with more equations and variables, but since the programs are not artificially integrated, they will be able to maintain their original basic and simple style, unlike the traditional way, although the final face The number of equations is small, but these equations have been artificially integrated, and their patterns will be more complicated.
傳統方法常需面對二階以上之微分方程式，惟本發明的方法，所處理的方程式絕少高於一階微分方程式。方程式的複雜度亦將直接影響下一步驟數值離散之難易，一階微分以下之方程式可以很簡單的方式進行離散，若是二階微分以上之方程式則其數值離散之難度將大為提高。除了不進行方程式整合外，為維持將來增減方程式的彈性，這些基本方程式將來亦不採同時聯立求解，而是依變數間之相互關係循序逐條求解，如未來若有方程式的增減，則只需重新定義方程式計算順序即可。因此本發明在此亦提出方程式一致性的實作方式，以檢驗方程式與變數關係的一致性，同時決定方程式之計算順序，如第二圖之步驟S22。Traditional methods often need to face second-order differential equations. However, the method of the present invention processes equations that are rarely higher than first-order differential equations. The complexity of the equation will also directly affect the difficulty of numerical dispersion in the next step. The equation below the first-order differential can be discretized in a very simple way. If the equation is above the second-order differential, the difficulty of numerical dispersion will be greatly improved. In addition to not integrating the equations, in order to maintain the flexibility of the equations in the future, these basic equations will not be solved simultaneously in the future, but will be solved sequentially according to the relationship between the variables. For example, if there is an increase or decrease of the equation in the future, Simply redefine the equation calculation order. Therefore, the present invention also proposes an implementation of equation consistency to verify the consistency of the relationship between the equation and the variable, and at the same time determine the order of calculation of the equation, as in step S22 of the second figure.
(3) 數值離散(Numerical discretization)，如第三圖步驟S33：(3) Numerical discretization, as in the third step, step S33:
在此步驟傳統方法由於常需面對較高階的微分方程式，因此需要複雜的數值離散方法，如有限元素法(Finite Element Method,FEM)，有限差分法(Finite Difference Method,FDM)等皆是。本發明由於絕少面對一階以上之微分式，因此只需簡單的一階差分，即可對原方程組進行離散化。另外，為維持增減方程式的彈性，本發明為了更易於進行離散化，並建議了較佳以凡諾依多邊形進行空間格綱之定義，如第二圖之步驟S23。In this step, traditional methods often need to face higher-order differential equations, so complex numerical discrete methods, such as Finite Element Method (FEM) and Finite Difference Method (FDM), are required. Since the invention rarely faces the differential equation of the first order or more, the original equation group can be discretized by a simple first-order difference. In addition, in order to maintain the elasticity of the equation of increase and decrease, the present invention is more convenient for discretization, and it is suggested that the definition of the space lattice is preferably performed by the Vanoyoi polygon, as in step S23 of the second figure.
(4) 程式開發(Program development)，如第三圖步驟S34：(4) Program development, as in the third step, step S34:
延續前述數值離散，傳統方式為照顧各節點間之互相影響，必需將所有節點上之離散方程式與變數，再組合成矩陣方程式，接著發展各種不同矩陣解法之計算程式，對所組成的矩陣方程式，計算其數值解。本發明將不如傳統數值方法般，組合所有節點上的變數而成矩陣方程式。相反的，本發明將以單一計算節點上之離散方程式為主進行計算，再以各計算節點互相交換資訊配合疊代計算方式，求得整個問題所有節點的解，如第二圖之步驟S24。Continuing the aforementioned numerical discretization, the traditional way is to take care of the mutual influence between the nodes. It is necessary to combine the discrete equations and variables on all nodes into a matrix equation, and then develop a calculation formula of various matrix solutions for the matrix equations. Calculate its numerical solution. The present invention will not combine the variables on all nodes into a matrix equation as in the conventional numerical method. On the contrary, the present invention calculates the discrete equations on a single computing node, and then exchanges information with each computing node to calculate the solution of all nodes of the whole problem, as in step S24 of the second figure.
由前述說明應用第二圖所開發之數值模式具有可彈性增減方程式之特點，因此應前述開發流程，經適當規劃可實作如目前瀏覽器上常應用之***(Plug In)型的數值模式建構系統此亦為大幅超出傳統數值建模方法之處。如第四圖所示，數值模式建構系統包含可適性數值計算平台41與方程式擴充介面42，方程式A~X可因應所欲解決之問題而彈性調整與擴充。The numerical model developed by the above description using the second figure has the characteristics of the elastic increase and decrease equation. Therefore, according to the foregoing development process, the plug-in numerical model which is commonly used in browsers can be implemented by appropriate planning. Constructing the system is also a significant departure from traditional numerical modeling methods. As shown in the fourth figure, the numerical model construction system includes an adaptive numerical calculation platform 41 and an equation expansion interface 42, and the equations A to X can be elastically adjusted and expanded according to the problem to be solved.
以下說明本發明之一系統架構：The following describes a system architecture of the present invention:
傳統上數值計算皆需在待求變量(變數)所在的空間上，畫分網格，且將各變數的值表達在各格點上，惟最後仍以矩陣的方式整體計算，換句話說，各格點的意義主要是空間上的座標及其對應的變數而已。而本發明主要的計算皆在格點上，因此可將格點代表的意義擴充如第五圖所示，各格點23不僅具有空間座標及變數，而可視為一個具有獨立運算能力的個體，本發明將其暫名為「計算元」。而完整的架構則以此為基礎擴充至二個層次，即分別如第五圖中所示的計算層21與主控協調層22，其進一步說明如下：Traditionally, numerical calculations need to draw a grid on the space where the variable (variable) is to be obtained, and express the values of each variable on each grid point, but finally calculate it as a matrix as a whole, in other words, The meaning of each grid point is mainly the coordinates of the space and its corresponding variables. The main calculations of the present invention are all on the grid points, so the meaning of the lattice points can be expanded as shown in the fifth figure. Each grid point 23 not only has space coordinates and variables, but can be regarded as an individual with independent computing power. The present invention temporarily names it as "computation element". The complete architecture is extended to two levels based on this, namely, the computing layer 21 and the master coordination layer 22, respectively, as shown in the fifth figure, which are further described as follows:
a.計算元2111 -211n ：本發明計算層21由計算元2111 -211n 組成，計算元2111 -211n 與其鄰近計算元的相鄰關係，亦如以往由網格24定義，計算元2111 -211n 的功能為最底層的數值計算，其計算方式，發展之初由開發者依問題而定義，惟若能結合專家系統與機惟若能結合專家系統與機器學習等人工智慧方法25，各計算元將可容易的以人工輔助的方式增加或改變計算功能，或是經由自我學習演化增加本身的計算能力。a computing elements 211 1 -211 n:. layer was calculated by the calculating element 21 of the present invention 211 1 -211 n composition, calculates the element 1 -211 n computing elements adjacent thereto adjacent relationship, and as conventionally defined by the grid 24 211 The function of the calculation unit 211 1 -211 n is the lowest level numerical calculation. The calculation method is defined by the developer according to the problem at the beginning of development. However, if the expert system and the machine can be combined with the expert system and machine learning, etc. Wisdom Method 25, each computational unit will be able to easily add or change computational functions in a human-assisted manner, or increase its computational power through self-learning evolution.
b.主控協調層22：前述計算元2111 -211n 所關心及涵蓋的範圍為本身及與其緊鄰的計算元，惟難以避免的，某些計算與考量必須就部份或全體計算元整體考量，因此必須在各別的計算層之上設置主控協調層22，可依需求調整計算元的計算行為。主控協調層22亦可結合專家系統與機器學習等人工智慧方法25增強其功能。b. Master coordination layer 22: The above-mentioned calculation elements 211 1 - 211 n are concerned with and cover the range of themselves and the computing elements immediately adjacent thereto, but it is difficult to avoid, some calculations and considerations must be partial or total computing elements as a whole Considering, it is necessary to set the master coordination layer 22 on top of the respective computing layers, and the calculation behavior of the computing cells can be adjusted according to requirements. The master coordination layer 22 can also enhance its functionality in conjunction with an artificial intelligence method 25 such as expert systems and machine learning.
●計算元獨立運算●Computed element independent operation
為使系統的運算能力可彈性的變化及擴充，而具有與人工智慧方法25進行深度結合的可能，計算元2111 -211n 必需可獨立運算，而不可如以往數值模式一般，將所有格點23上的變數以矩陣方程式一起求解。因此，為維持計算元2111 -211n 獨立計算的同時，亦兼顧計算元2111 -211n 與其鄰近計算元的互動關係，某種形式的疊代運算將是不可避免。計算元2111 -211n 獨立運算的特性，使發展的計算軟體，可容易的進行大量平行化計算或分散式計算。In order to make the computing power of the system elastically change and expand, and have the possibility of deep integration with the artificial intelligence method 25, the computing elements 211 1 - 211 n must be independently operable, and not all the lattice points as in the previous numerical mode. The variables on 23 are solved together in a matrix equation. Therefore, in order to maintain the calculation of the computational elements 211 1 - 211 n independently, and also the interaction between the computational elements 211 1 - 211 n and their neighboring computational elements, some form of iterative operation will be inevitable. Computational features of the 211 1 -211 n independent operations enable the development of computational software to easily perform a large number of parallelization calculations or decentralized calculations.
●單一類型(均質架構)或多類型(非均質架構)的計算元●Computed elements of a single type (homogeneous architecture) or multiple types (non-homogeneous architecture)
第五圖所示為系統主要計算架構示意圖，惟系統實作上，計算元2111 -211n 可依需求或底層平台而有不同的型態如：(1)單一類型計算元(均質架構)：此即每一計算元皆具有強大而相同的計算功能，各計算元皆可處理所有的底層計算需求。(2)多類型計算元(非均質架構)：計算元依計算功能分成幾種類型，每一類型的計算元具有部份底層運算的能力，不同類型計算元間必須交換資訊，以完成所有的底層計算需求。The fifth figure shows the main computing architecture of the system. However, in the system implementation, the computing elements 211 1 -211 n can have different types according to the requirements or the underlying platform, such as: (1) single type of computing elements (homogeneous architecture) : This means that each computational unit has powerful and identical computational functions, and each computational element can handle all of the underlying computational requirements. (2) Multi-type computing elements (non-homogeneous architecture): Computational elements are divided into several types according to the calculation function. Each type of computational element has the ability of partial underlying operations. Information must be exchanged between different types of computational elements to complete all The underlying computing needs.
如第五圖所示為系統架構，就系統開發的步驟而言，可以兩步大階段的方式進行發展，以使系統的效益能及早展現，降低整體開發風險，第六圖所示即為本發明建議的系統開發兩大階段，其中第一階段乃是先不內嵌人工智慧方法，惟仍需遵守前述開發原則，維持系統擴充功能的彈性，並為未來與人工智慧方法的結合預留空間，此階段完成的系統雖未具自我學習及擴充功能等特質，惟已是個全新而良好的新型態數值模式，可更新及累積相關模擬能力，前述第一階段本發明稱為可適性計算(Adaptive Computation,AC)。As shown in the fifth figure, the system architecture can be developed in a two-step and large-stage manner in terms of system development steps, so that the benefits of the system can be displayed early and the overall development risk can be reduced. The two phases of system development proposed by the invention, the first phase is to not embed artificial intelligence methods, but still need to abide by the aforementioned development principles, maintain the flexibility of the system expansion function, and reserve space for the combination of future and artificial intelligence methods. Although the system completed at this stage does not have the characteristics of self-learning and expansion functions, it is a new and good new state numerical model that can update and accumulate relevant simulation capabilities. The first phase of the present invention is called adaptability calculation ( Adaptive Computation, AC).
第二階段則再整合及建置適當的人工智慧方法進一步增加模式的功能，甚至具有自我學習演化的能力，當資料或模擬之案例增加後可改善各項參數準確度、增加新的參數與變數或甚至增加規則等。此人工智慧部份可包括如類神經網路(ANN)、專家系統(Expert System)或其他機器學習(Machine Learning)方法等。前述整個兩階段系統的概念，本發明稱為智慧型可適性計算(Intelligently Adaptive Computation,LAC)。In the second phase, the integration and establishment of appropriate artificial intelligence methods will further increase the function of the model, and even have the ability to self-learn and evolve. When the data or simulation case is increased, the accuracy of each parameter can be improved, and new parameters and variables can be added. Or even increase the rules and so on. This artificial intelligence component may include, for example, an analog neural network (ANN), an expert system (Expert System), or other methods of machine learning (Machine Learning). The foregoing concept of the entire two-stage system, the present invention is referred to as Intelligently Adaptive Computation (LAC).
以上主要說明在「可適性計算」階段各計算節點之實作方式，各節點間需再以疊代方式求解整個問題，而不以求解全域矩陣方程式之方式求解，依此再選用適當之程式語言進行程式之撰寫，即可完成依「可適性計算」概念開發之模擬模式，其中「方程式集合一致性分析演算法」、變數空間上之離散化及疊代求解等細部實作方式，將在後續之實作案例進一步說明。前述各計算節點若再結合人工智慧方法，則升級為「工作元」此時整個系統將晉升至「智慧型可適性計算架構」之層次。The above mainly explains the implementation of each computing node in the "adaptability calculation" stage. The nodes need to solve the whole problem in an iterative manner instead of solving the global matrix equation, and then select the appropriate programming language. By writing the program, you can complete the simulation mode developed according to the concept of "compatibility calculation". The detailed implementation of "equal set consistency analysis algorithm", discretization in variable space and iterative solution will be followed. The actual case is further explained. If the above-mentioned computing nodes are combined with the artificial intelligence method, they will be upgraded to "work elements" and the entire system will be promoted to the level of "smart adaptive computing architecture".
以下說明本案一較佳實施例，其系統架構示意圖為如前述第五圖所示之可適性計算架構，其包含工作元2111 -211n 、協調委員會221、主控者222與背後的人工智慧系統25，而如說明書第六圖所示在尚未整合人工智慧前為可適性計算(Adaptive Computation,AC)，以下將以地下水模擬的具體例子，說明至此階段的可能具體實作方式之一，此例將說明各工作元如何進行數值計算，及工作元與工作元之間的溝通方法。此實作案例稱為「新型態地下水模擬模式」。The following description of a preferred embodiment case, which is a system architecture diagram of FIG preceding shown in the fifth adaptive computing architecture, comprising a working element 211 1 -211 n, AI Coordinating Committee 221, and 222 are behind the master System 25, and as shown in the sixth figure of the specification, before the artificial intelligence has been integrated (Adaptive Computation (AC)), the following concrete example of groundwater simulation will be used to illustrate one of the possible implementations at this stage. The example will explain how each work element performs numerical calculations and how to communicate between work elements and work elements. This implementation case is called the “new state groundwater simulation model”.
新型態地下水模擬模式之說明：Description of the new state groundwater simulation model:
1.空間網格與節點定義：1. Spatial grid and node definition:
本案例採用凡諾依圖(Voronoi Diagram)作為空間網格與節點之定義，因此可以配置規則或不規則分佈之運算節點，透過凡諾依圖空間分割，可定義運算節點間之相鄰關係。本發明提出之可適性計算(AC)之應用並不限制網格之定義方式，惟採用凡諾依圖網格較有彈性。In this case, the Voronoi Diagram is used as the definition of the space grid and the nodes. Therefore, the rules or irregularly distributed operation nodes can be configured. The spatial relationship between the computational nodes can be defined through the partition of the Vanoyoi diagram. The application of the adaptability calculation (AC) proposed by the present invention does not limit the definition of the grid, but the use of the Fanoyi grid is more flexible.
2.地下水方程式集合定義：2. Definition of the set of groundwater equations:
以下將列出地下水模擬模式所需之所有方程式及其說明。All equations required for the groundwater simulation mode and their descriptions are listed below.
上式為最重要而基本之質量守恆方程式，其中孔隙率(n )為水文地質參數，穿越面積()與控制體積(Vol )則與空間切割方式有關，因此在實際模擬運算時，水文地質參數與空間切割均已經訂定，因此可視為已知參數。流體密度(ρ f )、飽和度(S d )與水流流速()，為式(a)之變數。而此三個變數需藉由後續之方程式進一步定義，密度(ρ f )可由密度變化方程式式(b)推估，此方程式為Rana A. Fine等人所建議(1973)，可定義不同溫度與不同壓力下的地下水流密度；飽和度(S d )則需透過特性曲線(式c與d)定義，在此採用Van Genuchten經驗式(1980)，其為土壤中不同壓力狀態的水分含量關係；地下水流速()可由達西定律式(e)定義，其乃利用水力坡降來估算水流流速。The above formula is the most important and basic mass conservation equation, in which the porosity ( n ) is a hydrogeological parameter and the crossing area ( ) and the control volume ( Vol ) is related to the space cutting method. Therefore, in the actual simulation operation, hydrogeological parameters and spatial cutting have been fixed, so it can be regarded as a known parameter. Fluid density (ρ f ), saturation ( S d ) and water flow rate ( ) is a variable of the formula (a). The three variables need to be further defined by the subsequent equations. The density (ρ f ) can be estimated from the density variation equation (b), which is recommended by Rana A. Fine et al. (1973), and can define different temperatures and groundwater flow density at different pressures; saturation (S d) is required transmission characteristic (formula c and d) is defined, using this empirical formula Van Genuchten (1980), a moisture content of soil in relation to the different pressure conditions; Groundwater flow rate ( It can be defined by Darcy's law (e), which uses hydraulic gradient to estimate the water flow rate.
上式中P 為壓力水頭、T 為溫度，B 、A 1 、A 2 與V 0 均為溫度(T )之函數，θ r 為殘餘含水量，θ e 為有效含水量，為質量流率，為達西流速，為實際流速，K (P )為未飽和水力傳導係數，h 為總水頭，代表流線方向，α、β、γ為van Genuchten經驗式之相關參數，n 為土壤孔隙率。In the above formula, P is the pressure head, T is the temperature, B , A 1 , A 2 and V 0 are functions of temperature ( T ), θ r is the residual water content, and θ e is the effective water content. For mass flow rate, For the Darcy flow rate, For the actual flow rate, K ( P ) is the unsaturated hydraulic conductivity and h is the total head. Representing the direction of the streamline, α, β, γ are the relevant parameters of the van Genuchten empirical formula, and n is the soil porosity.
式e為達西公式，其中水力傳導係數(K (P ))與總水頭(h )，則是新出現的未知變數，後續將由式f與g進一步定義之。未飽和層中，水力傳導係數(K (P ))隨壓力變化而變化，在此亦採用van Genuchten經驗式(式f)計算。另外，總水頭(h )則定義為壓力水頭與位置水頭之和(式g)，式h為控制體積內部蓄水質量式，以該時刻之孔隙率、水流密度與飽和度求得該時刻之蓄水質量。Equation e is the Darcy formula, where the hydraulic conductivity coefficient ( K ( P )) and the total head ( h ) are new and unknown variables, which will be further defined by the equations f and g. In the unsaturated layer, the hydraulic conductivity ( K ( P )) varies with pressure and is also calculated using the van Genuchten empirical formula (formula f). In addition, the total head ( h ) is defined as the sum of the pressure head and the position head (formula g), and the formula h is the internal volume of the control volume, and the time is obtained by the porosity, water flow density and saturation at that moment. Water storage quality.
另外，根據地下水理論，拘限含水層之水量進出與壓力變化關係，係受到水的壓縮性與土的壓縮性所造成，亦即土壤孔隙率會隨壓力變化。式i為土壤孔隙率隨壓力變化方程式。In addition, according to the groundwater theory, the relationship between the water inlet and outlet of the aquifer and the pressure change is caused by the compressibility of the water and the compressibility of the soil, that is, the soil porosity changes with the pressure. Equation i is the equation of soil porosity as a function of pressure.
gh =P +z g h = P + z
h.S t =(ρ f nS d ) t Vol h. S t =(ρ f nS d ) t Vol
其中K s 為飽和水力傳導係數、K r (P )為相關水力傳導係數，其數值隨壓力變化而在0至1之間變化，z 為高程，S t 代表控制體積內於時刻t 的蓄水質量。Where K s is the saturated hydraulic conductivity coefficient and K r ( P ) is the relevant hydraulic conductivity coefficient, the value of which varies from 0 to 1 with the change of pressure, z is the elevation, and S t represents the water storage at the time t in the control volume. quality.
至此，在定溫情形下，由質量守恆方程式(式a)及其他八個方程式(式b~i)，合計共9個方程式定義了本問題；其變數為P 、θ e 、ρ f 、S d 、、K (P )、h 、n 、S ，共9個未知變數。若在變溫問題中，溫度(T )為變數，則必須引入另外之熱流相關方程式。So far, in the case of constant temperature, the mass conservation equation (formula a) and the other eight equations (formula b~i), a total of nine equations define the problem; the variables are P , θ e , ρ f , S d , , K ( P ), h , n , S , a total of 9 unknown variables. If the temperature ( T ) is a variable in the temperature change problem, then another heat flow correlation equation must be introduced.
3.方程式集合一致性分析：3. Equation set consistency analysis:
方程式集合一致性分析是以演算法分析方程式集合是否充分可解，即是確認方程式的數目必須與變數數目一致，並進一步訂定方程式集合的求解順序，後續則可依據此訂定的求解順序進行求解。The consistency analysis of the equation set is based on the algorithm to analyze whether the set of equations is fully solvable, that is, the number of equations must be consistent with the number of variables, and the order of solving the set of equations is further determined, and subsequent steps can be performed according to the set solution order. Solve.
若下式(1)為方程式集合：If the following formula (1) is a set of equations:
f i (c i ,1 x 1 ,c i ,2 x 2 ,c i ,3 x 3 ......c i , n x n )=0i =1,2,3...m (1) f i ( c i ,1 x 1 , c i ,2 x 2 , c i ,3 x 3 ...... c i , n x n )=0 i =1,2,3... m ( 1)
其中，f i 代表第i個方程式，共有m個方程式存在方程式集合中，x j 代表此議題的第j個變數，合計共有n個變數在此議題內，c i , j 為方程式變數係數，其為0或1的布林值，若方程式i並不存在變數j，其方程式變數係數應為0；反之，則為1。接著將上述之地下水方程式集合整理為變數係數第一表，再以此表進行方程式一致性分析。Where f i represents the i-th equation, a total of m equations exist in the set of equations, x j represents the j-th variable of the subject, a total of n variables are in this topic, c i , j are the equation variable coefficients, For a Boolean value of 0 or 1, if the equation i does not have a variable j, the equation variable coefficient should be 0; otherwise, it is 1. Then the above set of groundwater equations is organized into the first table of variable coefficients, and then the equation consistency analysis is performed by this table.
本方法是採用疊代運算求解方程組，透過最佳化的計算方法疊代求解，即表示會針對問題內的待解變數給予一起始猜值，此問題中，待解變數為壓力水頭(P )，配合前述之疊代求解起始時可以將第一表內水頭(P )一欄的係數更改為0(修改後如第二表)。由第二表可得知更新後式b,f、g、i此四條方程式均只有一個未知變數K (P )、h 、ρ f 與n ，其可從此四條方程式求得。因此可再將第二表上各欄內此四個變數欄位的數值更改為0，修改後如第三表，修改後之表上，式d、e兩式也僅剩一個未知變數，θ e ，其亦可由此兩式求得，再更改此兩變數欄位的數值為0(修改後如第四表)，由第四表可得以式c可對S d 進行求解，執行上述同樣的步驟，可在第五表得到式h可對S 進行求解，此時已僅剩式a，即守恆方程式，即為此問題內最後一條需要求解的方程式。The method uses the iterative operation to solve the equations and solves them by the optimized calculation method, that is, it gives a starting guess for the variables to be solved in the problem. In this problem, the variable to be solved is the pressure head ( P ), in conjunction with the aforementioned iterative solution, the coefficient of the head ( P ) column in the first table can be changed to 0 (as modified in the second table). It can be seen from the second table that the updated equations b, f, g, and i have only one unknown variable K ( P ), h , ρ f and n , which can be obtained from the four equations. Therefore, the values of the four variable fields in the columns on the second table can be changed to 0. After the modification, as in the third table, on the modified table, only one unknown variable remains in the equations d and e. , θ e , which can also be obtained by the two equations, and then change the value of the two variable fields to 0 (as modified as the fourth table), and the fourth table can be used to solve the S d by the formula c, and the above In the same step, the equation h can be used to solve S in the fifth table. At this time, only the equation a, that is, the conservation equation, is the last equation to be solved in this problem.
由上述的處理過程，可以看出方程組的處理上是有一定順序的，在此問題內可分成五個處理階段，各階段所處理的方程式與變數整理如第七表：From the above process, it can be seen that there is a certain order in the processing of the equations. In this problem, it can be divided into five processing stages, and the equations and variables processed in each stage are organized as the seventh table:
第七表內表示的處理階段即代表了此數值方法內方程式的處理順序，各階段內的方程式處理順序並無規定，而階段與階段間的處理顺序則必須一定。以第二階段與第三階段舉例，第二階段內的式d與e兩方程式的順序沒有固定，任何一條優先處理都是可行的，但是在進行第三階段之前，必須完成此兩條方程式的求解。The processing stage represented in the seventh table represents the processing order of the equations in the numerical method. The order of the equation processing in each stage is not specified, and the processing order between the stages and the stages must be fixed. Taking the second and third stages as an example, the order of the equations d and e in the second stage is not fixed, and any one of the priority treatments is feasible, but before the third stage, the two equations must be completed. Solve.
方程式一致性分析的過程中，若最後可求到欄位全為0的表，表示此方程組是可以解的，並且同時也可定出方程式處理的順序。通過方程式一致性分析的方程組，即可作為下一階段，各節點內之內疊代的運算目標。In the process of equation consistency analysis, if the table with the field all 0 is finally found, it means that the system of equations can be solved, and the order of equation processing can also be determined. The equations that pass the equation consistency analysis can be used as the next stage, the operation target of the inner iteration within each node.
4.計算元(節點)運算：由上述一致性分析結果可知，方程式中之變數數目決定方程式求解順序，因此變數數目最多的方程式往往是最後求解，在此例中最後求解的方程式為守恆方程式。惟此最後求解之方程式與之前的方程式有所不同，在求解該方程式時，該方程式之所有變數皆已由順序較前之方程式求得，故此方程式之實質意義已不在於求解變數，而在於利用此方程式評估等號左右兩邊之數值是否已經趨於相近，進而檢驗所有的變數解是否恰可滿足所有方程式，若等號兩邊數值之差不為零則存在一誤差，再經由第七圖中之疊代計算可將此誤差最小化，而得所有變數之解，本發明稱此一步驟為「內疊代」(第七圖)。此內疊代計算旨在獨立計算每個節點之變數值，底下將針對「內疊代」做進一步說明。4. Computational element (node) operation: From the above consistency analysis results, the number of variables in the equation determines the order of equation solving, so the equation with the largest number of variables is often the last solution. In this case, the last solved equation is the conservation equation. However, the equation for the last solution is different from the previous equation. When solving the equation, all the variables of the equation are obtained from the earlier equations. Therefore, the essence of the equation is not to solve the variables, but to use This equation evaluates whether the values on the left and right sides of the equal sign have become similar, and then test whether all the variables can satisfy all the equations. If the difference between the two sides of the equal sign is not zero, there is an error, and then through the seventh figure. The iterative calculation minimizes this error, and the solution to all the variables is referred to herein as "internal iteration" (seventh image). This inner iteration calculation is designed to calculate the variable value of each node independently, and the "internal iteration" will be further explained below.
每個節點內疊代計算時鄰近節點之待解變數乃取其當下之值，在此條件下各節點之待解變數值則可透過如最陡坡降法等最佳化方法進行求解，如第七圖。第七圖為以最陡坡降法為例之內疊代計算流程圖，在前述之地下水流問題中，壓力水頭為待解變數，由於最陡坡降法需要給予初始解並以其開始搜尋，在此必須給予初始壓力水頭，代入方程式集合中，以鄰近及本身結點之壓力水頭進一步計算出代表變量(在此為地下水)之穿越流量，代入連續方程式中，控制表面的總穿越量應與控制體積內的變化量相等，若非如此則為守恆誤差。透過差分方式可以求得壓力水頭值對守恆誤差之微分近似值，應用此微分近似值，可以逐步往最佳解收斂。當守恆誤差趨近於零時，代表控制表面的總穿越量與控制體積內的變化量相等，意即已求得結點本身之壓力水頭。本案稱此一步驟為「內疊代」，此「內疊代」計算即為第五圖中計算元2111 -211n 之計算工作。The number of nodes to be solved in the iterative calculation of each node is taken as the current value. Under this condition, the values to be solved of each node can be solved by the optimization method such as the steepest slope method, such as Seven maps. The seventh picture shows the flow chart of the internal iteration calculation with the steepest slope method. In the above groundwater flow problem, the pressure head is the variable to be solved. Because the steepest slope method needs to give the initial solution and start searching with it, This must be given to the initial pressure head, substituted into the equation set, and further calculate the cross-flow of the representative variable (here, groundwater) from the pressure head of the adjacent and its own nodes. Substituting into the continuous equation, the total crossing amount of the control surface should be controlled. The amount of change within the volume is equal, and otherwise it is a conservation error. By using the differential method, the differential approximation of the pressure head value to the conservation error can be obtained. By applying this differential approximation, the optimal solution can be gradually converge. When the conservation error approaches zero, the total amount of crossing representing the control surface is equal to the amount of change in the control volume, meaning that the pressure head of the node itself has been obtained. This case refers to this step as "internal iteration". This "internal iteration" calculation is the calculation of the calculation elements 211 1 -211 n in the fifth figure.
5.外疊代處理方法5. Outer generation processing method
前述內疊代計算，每個節點皆獨立計算其變數值，計算時鄰近節點僅考慮其當下之值，惟鄰近節點之值可能因其本身之節點計算而更新，因此須有一上位的程序重覆啟動各節點之計算直至收斂為止，本案稱此為「外疊代」。此乃不同於傳統方法透過矩陣解法同時求解整體區域所有節點之值，以維持各節點計算之獨立性與隨之而來的彈性。茲說明如下：當一節點進行上述內疊代計算時，部分方程式需運用到相鄰節點資訊，而本案提出的方法中各節點均為獨立運算，各節點所取得之相鄰節點資訊，為各相鄰節點當下之資訊，而其可能因各相鄰節點本身之內疊代計算而更新，因此每次各節點之內疊代收斂結束後，則尚需確認其相鄰節點是否有更新資訊，若有，則需判斷該節點是否需要再啟動內疊代計算，其判斷標準可根據該節點有資料更新之相鄰節點數及各相鄰節點之資料更新幅度，決定是否須再重新啟動該節點之內疊代計算，若所有節點皆無需再重新進行內疊代計算，則整個計算可收斂結束。上述判斷各節點是否須重新啟動內疊代計算以及是否整體達到收歛之過程，本案稱之為「外疊代」，其如第八圖所示，外疊代結束後則進入下一時刻之計算。In the above-mentioned inner iteration calculation, each node calculates its variable value independently. When calculating, the neighboring node only considers its current value, but the value of the neighboring node may be updated by its own node calculation, so it must be repeated with a higher level program. Start the calculation of each node until it converges. This case is called "outer generation". This is different from the traditional method of solving all the values of all nodes in the whole region through the matrix solution, in order to maintain the independence of each node and the consequent elasticity. It is explained as follows: When a node performs the above-mentioned internal iterative calculation, some equations need to be applied to the adjacent node information, and each node in the method proposed in the present case is an independent operation, and the information of the adjacent nodes obtained by each node is The information of the neighboring node is currently updated, and it may be updated by the iterative calculation of each adjacent node itself. Therefore, each time the iterative convergence of each node ends, it is necessary to confirm whether the neighboring node has updated information. If yes, it is necessary to determine whether the node needs to restart the inner iteration calculation. The criterion can determine whether the node needs to be restarted again according to the number of neighboring nodes with data update and the data update range of each adjacent node. In the iterative calculation, if all nodes do not need to re-internal iterative calculation, the entire calculation can end. The above-mentioned process of judging whether each node needs to restart the inner iteration calculation and whether or not the convergence is achieved as a whole is referred to as "overlap generation". As shown in the eighth figure, the calculation of the next moment is performed after the outer generation is over. .
6整體數值模擬流程6 overall numerical simulation process
整體數值模擬流程如第九圖，首先依據模式設定檔，讀入空間切割相關資訊、水文地質參數、邊界條件與方程式集合等資訊，接著則依據模擬之模擬型態、起始時刻、結束時刻與模擬間距，開始進行模擬，流程中當外疊代收斂後，則進行下一時刻之模擬，並依時刻判斷是否結束計算。若為穩態模擬，則僅執行外疊代流程一次；若為非穩態模擬，則依據起始時刻、結束時刻與模擬時刻等資訊進行判斷。整體數值模擬流程之控制包含外疊代之計算及時刻之前進等乃屬於第五圖中主控協調層22負責。The overall numerical simulation process, as shown in the ninth figure, first reads the information related to spatial cutting, hydrogeological parameters, boundary conditions and equation sets according to the mode setting file, and then according to the simulated simulation type, starting time, ending time and Simulate the spacing and start the simulation. After the outer iterations converge in the process, the simulation at the next moment is performed, and the calculation is terminated according to the time. If it is a steady-state simulation, only the outer generation process is performed once; if it is an unsteady simulation, it is judged based on information such as the start time, the end time, and the simulation time. The control of the overall numerical simulation process, including the calculation of the outer generation and the advancement of the time, is the responsibility of the master coordination layer 22 in the fifth figure.
7.智慧型可適性計算方法實作7. Intelligent adaptability calculation method
前述可適性計算方法為本發明之模擬方法，而近一步的結合人工智慧後，方成為智慧型可適性計算方法(IAC)。目前學者專家於人工智慧領域的研究發展快速，且種類繁多，諸如類神經網路(Annual Neural Network)、專家系統(Expert system)、模糊理論(Fuzzy Theory)等等，唯基於各種人工智慧之特性，應用於本發明智慧型計算之部分亦不盡相同，以下實施例將說明本發明與類神經網路結合之應用。對於許多問題而言，其變化之物理機制尚未明白，但可以藉由大量採集之觀測資料，透過機器學習(Machine learning)或資料採礦(Data mining)相關之人工智慧演算法，建立變數與變數之相對關係。對於未知的問題，雖有部分機制已可用量化之數學方程式描述，但是尚有部分關係尚未能完整描述，因此其變化機制的控制方程組並不完備，為了補齊不足的方程式，本發明可利用現地觀測資料與資料採礦等人工智慧技術補足缺少的方程式。其中本發明所使用的工具是採用類神經網路(A.N.N.)，步驟如下：The foregoing applicability calculation method is the simulation method of the present invention, and the next step is to combine the artificial intelligence to become the intelligent adaptive calculation method (IAC). At present, scholars and experts in the field of artificial intelligence research and development are fast and diverse, such as the Analog Neural Network, the Expert System, the Fuzzy Theory, etc., based on the characteristics of various artificial intelligences. The parts applied to the intelligent calculation of the present invention are also different. The following embodiments will illustrate the application of the present invention in combination with a neural network. For many problems, the physical mechanism of change has not been understood, but variables and variables can be established through a large number of collected observations through artificial learning algorithms related to Machine Learning or Data Mining. Relative relationship. For some unknown problems, although some mechanisms have been described by quantitative mathematical equations, some of the relationships have not yet been fully described, so the governing equations of the changing mechanisms are not complete. In order to fill the insufficient equations, the present invention can Make up the missing equations using artificial intelligence techniques such as in-situ observations and data mining. The tool used in the present invention uses a neural network (A.N.N.), and the steps are as follows:
I.以方程式一致性分析檢驗既存方程式集合，如果無法找到足夠的方程式來定義基本變數與對應的守恆物理量間的關係，顯示部分關係定義尚未完備。統計各變數於各方程式中的應變數數量，如果其數字為0，則表示該變數無法求解，以此方法即能找出目前問題範疇中所有無法求解之應變數。I. Test the existing set of equations by equation consistency analysis. If enough equations cannot be found to define the relationship between the basic variables and the corresponding conservation physics, the partial relationship definition is not yet complete. Count the number of strains of each variable in each program. If the number is 0, it means that the variable cannot be solved. In this way, all the strains that cannot be solved in the current problem category can be found.
II.假設待補齊函數之變數有n個自變數與m個應變數，自變數與應變數皆由目前問題範疇已知之變數，其中m個應變數即前述之應變數數量為0者，其數量已經決定，但是自變數的數量n則尚未決定。因此將n值由小至大改變，遞迴地任意挑選n個變數，在此藉由外界採集的大量觀測資料，並配合主成分分析等，藉由主成分分析與觀測資料決定最佳的自變數數量與選定之自變數。II. Assume that the variable of the function to be complemented has n self-variables and m strain numbers, and the number of independent variables and strains are known from the current problem domain, wherein m strain numbers, that is, the number of strains mentioned above is zero, The number has been determined, but the number n of independent variables has not yet been determined. Therefore, the value of n is changed from small to large, and n variables are randomly selected in a recursive manner. Here, the majority of observation data collected by the outside world, together with principal component analysis, etc., determine the best self by principal component analysis and observation data. The number of variables and the selected arguments.
III. 依據前述選定之自變數與應變數組合建立類神經網路。III. Establish a neural network based on the combination of the selected independent variables and strain numbers.
IV. 完成神經網路，即可在IAC中呼叫計算。IV. Completing the neural network, you can call the calculation in the IAC.
8.應用可適性計算架構於地下水模擬模式成果說明：8. Application of adaptive computing architecture to groundwater simulation model results description:
本發明將可適性計算架構實作概念應用於不規則網格之暫態飽和侷限含水層模擬，底下將以兩個案例說明模擬成果。此兩案例之模擬區域為11公尺乘上13公尺之垂向二維方形薄板，在邊界條件的設定上，左右邊界之總水頭均設定為80(m)，上下邊界則設定為無流量邊界(No Flow Boundary)。在材質設定方面，孔隙率為0.38、水力傳導係數為0.01(m/day)。在初始條件上，所有位置之初始總水頭為80(m)，意即初始水位代表未經抽水時狀態，處於靜水壓分佈。於點位(5,5)處配置抽水井，並以500(kg/day)之抽水量進行抽水，模擬間距為0.01天(約14.4分鐘)，總模擬時刻數為6個時刻。因此單一時刻之抽水量為5(kg)。在網格切割上，案例一其網格配置為0.33m見方的方形網格，如第十圖所示。案例二僅在抽水井周遭配置較細網格，在外圍區域仍以1m見方之較粗網格為主，以節省計算量，如第十一圖所示，如此可在一定的精度需求下，維持低計算量。The invention applies the adaptive computing architecture implementation concept to the transient saturation limited aquifer simulation of the irregular grid, and the simulation results are illustrated in two cases. The simulated area of the two cases is a vertical two-dimensional square sheet of 11 meters by 13 meters. In the boundary condition setting, the total head of the left and right borders is set to 80 (m), and the upper and lower boundaries are set to no flow. No Flow Boundary. In terms of material setting, the porosity was 0.38 and the hydraulic conductivity was 0.01 (m/day). In the initial conditions, the initial total head of all locations is 80 (m), meaning that the initial water level represents the state of unpumped water and is in a hydrostatic pressure distribution. Pumping wells were placed at points (5, 5) and pumped at a pumping capacity of 500 (kg/day). The simulated spacing was 0.01 days (about 14.4 minutes) and the total number of simulated hours was six. Therefore, the pumping amount at a single moment is 5 (kg). In the grid cutting, the case 1 has a grid configuration of a square grid of 0.33 m square, as shown in the tenth figure. Case 2 only has a fine mesh around the pumping well, and the coarser mesh is still 1m square in the peripheral area to save the calculation amount, as shown in the eleventh figure, so that under certain precision requirements, Maintain low calculations.
第十二圖為兩案例之邊界流量變化圖，不同網格尺寸均可得到相同的邊界流量。第八表為兩案例之相對系統守恆誤差表，兩案例之相對系統守恆誤差均極小，表示各時刻之邊界流量、抽水量與系統蓄水變化量均符合質量守恆定律。這表示在不同網格尺寸案例中，模擬結果雖均可符合質量守恆定律，但在水位的呈現上可能會有不同的結果。由於抽水井附近水位變化較為劇烈，傳統模擬技巧多會建議配置較細之網格方可精確掌握水位變化，因此可認定案例一之模擬結果較接近真值。The twelfth image shows the boundary flow variation of the two cases. The same boundary flow can be obtained for different mesh sizes. The eighth table is the relative system conservation error table of the two cases. The relative system conservation error of the two cases is extremely small, indicating that the boundary flow, pumping quantity and system water storage variation at each moment are in accordance with the law of mass conservation. This means that in the case of different grid sizes, the simulation results can all conform to the law of conservation of mass, but there may be different results in the presentation of the water level. Because the water level change near the pumping well is more severe, traditional simulation techniques will suggest that a finer grid can be used to accurately grasp the water level change. Therefore, the simulation result of Case 1 can be determined to be closer to the true value.
案例二所建立之加密網格在計算節點方面255個計算節點，在計算時間方面則分別為315秒，其洩降錐與案例一差距為0.21米深。由上述數據顯示，若在關鍵區域加強配置一定比例之計算節點，並透過Voronoi Diagram的空間切割方法，可以在一定的增加成本下，有效提升計算精度，以案例二而言，其計算誤差僅約0.21米深，計算時間則不到案例一的十分之一。The encrypted grid established in Case 2 has 255 computing nodes in terms of computing nodes, and the calculation time is 315 seconds respectively. The gap between the leakage cone and the case is 0.21 meters deep. According to the above data, if a certain proportion of computing nodes are strengthened in key areas and the space cutting method of Voronoi Diagram is used, the calculation accuracy can be effectively improved under a certain increase cost. In the second case, the calculation error is only about 0.21 meters deep, the calculation time is less than one tenth of case one.
而在第二圖的開發流程中，可套用如第十三圖的架構型式，包含核心平台111與應用模組112，其中核心平台111包含基本必要功能，如Voronoi Digram空間離散模組、通用數值模組與方程式一致性分析模組，其分別用於劃分網格、求解方程式、以及分析方程式的合理性與求解順序。本領域技術人士可以理解的是，上述模組可由能夠達到相同效果的演算法模組所取代，而不限於上述舉出的模組。而應用模組112包含地下水流模組、熱流傳輸模組與溶質傳輸模組，或因應其他研究問題所定義的控制方程式或數學模型等(未顯示於圖中)，該等模組可依研究需求增減或替換，因此第十三圖的架構建構完成後可具有強大的彈性，而異於傳統數值方法。In the development flow of the second figure, the architecture type as shown in the thirteenth figure may be applied, including the core platform 111 and the application module 112, wherein the core platform 111 includes basic necessary functions, such as a discrete system of Voronoi Digram space, and a universal value. The module and equation consistency analysis module is used to divide the grid, solve the equation, and analyze the rationality and solution order of the equation. It can be understood by those skilled in the art that the above modules can be replaced by an algorithm module capable of achieving the same effect, and are not limited to the above-mentioned modules. The application module 112 includes a groundwater flow module, a heat flow transmission module and a solute transport module, or a control equation or a mathematical model defined by other research problems (not shown), and the modules can be studied according to the research. The demand is increased or decreased or replaced, so the frame construction of the thirteenth figure can have strong elasticity after completion, which is different from the traditional numerical method.
因此本發明的開發流程可擴充如第十四圖，先建構「可適性計算架構」核心模組，該建構過程可由其架構開發者完成，如步驟S51。核心模組包含如前述內疊代、外疊代與劃分網格等基本必須功能。而步驟S52與S53建構延伸模組及驗證的流程與第二圖流程類似，唯其僅需依照所欲解決之問題建構其控制方程式，而無須重複建構內疊代與外疊代等基本必須功能。因而保留大量彈性並節省開發成本。Therefore, the development process of the present invention can be expanded as shown in FIG. 14 to construct a core module of the "adaptability computing architecture", which can be completed by its architecture developer, such as step S51. The core module contains basic essential functions such as the above-mentioned inner iteration, outer iteration and meshing. The process of constructing the extension module and the verification process in steps S52 and S53 is similar to the process of the second figure, except that it only needs to construct the control equation according to the problem to be solved, and does not need to repeatedly construct the basic necessary functions such as the inner iteration and the outer iteration. . Therefore, a large amount of flexibility is retained and development costs are saved.
總結而言，本案實為一難得一見，值得珍惜的難得發明，惟以上所述者，僅為本發明之最佳實施例而已，當不能以之限定本發明所實施之範圍。即大凡依本發明申請專利範圍所作之均等變化與修飾，皆應仍屬於本發明專利涵蓋之範圍內，謹請貴審查委員明鑑，並祈惠准，是所至禱。In summary, the present invention is a rare and incomprehensible invention, but the above is only the preferred embodiment of the present invention, and the scope of the present invention is not limited thereto. That is to say, the equivalent changes and modifications made by the applicants in accordance with the scope of the patent application of the present invention should still fall within the scope covered by the patent of the present invention. I would like to ask your review committee to give a clear explanation and pray for the best.
21‧‧‧計算層21‧‧‧ calculation layer
2111 -211n ‧‧‧計算元211 1 -211 n ‧‧‧Computational elements
22‧‧‧主控協調層22‧‧‧Master Coordination Layer
23‧‧‧格點23‧‧ ‧ grid points
24‧‧‧網格24‧‧‧Grid
25‧‧‧人工智慧25‧‧‧Artificial wisdom
S21-S24‧‧‧步驟S21-S24‧‧‧Steps
S31-S34‧‧‧步驟S31-S34‧‧‧Steps
41‧‧‧可適性數值計算平台41‧‧‧Adaptability Numerical Computing Platform
42‧‧‧方程式擴充介面42‧‧‧ equation expansion interface
111‧‧‧核心平台111‧‧‧ Core Platform
112‧‧‧應用模組112‧‧‧Application Module
S51-S53‧‧‧步驟S51-S53‧‧‧Steps
第一圖為習知技術的傳統數值模式之開發流程。The first picture shows the development process of the traditional numerical model of the prior art.
第二圖為本發明之流程示意圖。The second figure is a schematic flow chart of the present invention.
第三圖為本發明與傳統數值方法建構流程之差異。The third figure is the difference between the invention and the traditional numerical method construction process.
第四圖為***型數值模式建構系統之示意圖。The fourth figure is a schematic diagram of the plug-in numerical model construction system.
第五圖為本發明之架構示意圖。The fifth figure is a schematic diagram of the architecture of the present invention.
第六圖為本發明之系統開發階段示意圖The sixth figure is a schematic diagram of the development stage of the system of the present invention.
第七圖為內疊代流程。The seventh picture shows the inner iteration process.
第八圖為外疊代流程。The eighth picture is the outer generation process.
第九圖為本發明模擬流程圖。The ninth figure is a simulation flow chart of the present invention.
第十圖為本發明案例一的網格配置示意圖。The tenth figure is a schematic diagram of the grid configuration of Case 1 of the present invention.
第十一圖為本發明案例二的網格配置示意圖。The eleventh figure is a schematic diagram of the grid configuration of Case 2 of the present invention.
第十二圖為本發明邊界流量變化圖。Figure 12 is a graph showing changes in boundary flow of the present invention.
第十三圖為本發明之一架構示意圖。Figure 13 is a schematic diagram of one of the structures of the present invention.
第十四圖為本發明之一流程圖。Figure 14 is a flow chart of the present invention.
S21-S22．．．步驟S21-S22. . . step
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