Complex dynamic system modeling method, application method and related device

Abstract

The invention discloses a complex dynamic system modeling method, an application method and a related device, and relates to the field of automation, and the modeling method comprises the steps: constructing an actual physical complex dynamic system; determining a solver of an actual physical complex dynamic system; performing time discretization on an actual physical complex dynamic system; constructing a deep neural network based on the solver and the discretized actual physical complex dynamic system; the residual error of the deep neural network and the ordinary differential equation is fused, and a physical equation and data fusion driven deep neural network model is constructed; obtaining an actual data set, constructing a data residual error loss function and an ordinary differential equation residual error loss function, and obtaining a total loss function through weighted summation calculation; and by minimizing the total loss function, determining an optimal shared parameter between the deep neural network and the residual error of the ordinary differential equation, and obtaining an optimal physical equation and data fusion driven deep neural network model. According to the invention, deep fusion and complementation of the mechanism model and the data model can be realized.

Description

Technical Field

[0001] The present invention relates to the field of automation technology, and in particular to a complex dynamic system modeling method, an application method and related devices. Background Art

[0002] Accurate modeling of complex dynamic systems is the key to simulating and analyzing the evolution of complex physical systems, and is the premise for achieving accurate prediction, optimal control, and efficient optimization of complex physical systems in the field of automation. At present, the modeling methods of complex dynamic systems mainly include mechanism modeling methods driven by physical knowledge and data-driven deep learning modeling methods. Mechanism models essentially reveal the laws of actual physical systems and have the advantages of high reliability, good generalization performance, and strong interpretability. However, mechanism models are usually composed of complex, high-order nonlinear equations, which are difficult to solve and have a large amount of calculations. Online calculations and applications are difficult, and their model parameters are difficult to identify. In contrast, deep learning models are mainly driven by pure data, such as DNN, CNN, RNN, LSTM, Transformer, etc., which directly establish the mapping relationship between input data and output data, without analyzing the physical mechanism of the process object, and have good real-time online calculation. However, the disadvantages of such data models are poor generalization ability, easy overfitting, insufficient interpretability, and dependence on the completeness and accuracy of training set data.

[0003] Therefore, how to overcome the respective defects of the mechanism model and data model of complex dynamic systems and achieve the effect of leveraging each other's strengths and making up for each other's weaknesses has become a technical problem that needs to be urgently solved in this field. Summary of the invention

[0004] The purpose of the present invention is to provide a complex dynamic system modeling method, application method and related devices, which can realize the deep integration and complementarity of mechanism model and data model, and provide a physically reasonable, mathematically accurate and computationally efficient complex dynamic system model for the prediction, control and optimization of complex physical systems in the field of automation.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] In a first aspect, the present invention provides a complex dynamic system modeling method, the complex dynamic system modeling method comprising:

[0007] Construct an actual physical complex dynamic system; the actual physical complex dynamic system is a nonlinear steady-state state space model.

[0008] Determine the solution operator of the actual physical complex dynamic system; the solution operator of the actual physical complex dynamic system includes: control variables and initial state values.

[0009] The actual physical complex dynamic system is time discretized to obtain a discretized actual physical complex dynamic system.

[0010] Based on the solution operator of the actual physical complex dynamic system and the discretized actual physical complex dynamic system, a deep neural network is constructed; the deep neural network approximates the solution operator of the actual physical complex dynamic system within each time interval.

[0011] The deep neural network is fused with the residual of the ordinary differential equation to construct a deep neural network model driven by the fusion of physical equations and data.

[0012] An actual data set is obtained, and a data residual loss function and an ordinary differential equation residual loss function are constructed; the actual data set is data measured in an actual production process.

[0013] The total loss function is calculated by weighted summing the data residual loss function and the ordinary differential equation residual loss function.

[0014] By minimizing the total loss function, the optimal shared parameters between the residuals of the deep neural network and the ordinary differential equations are determined, and the optimal deep neural network model driven by the fusion of physical equations and data is obtained.

[0015] In a second aspect, the present invention provides a complex dynamic system application method, the complex dynamic system application method comprising:

[0016] According to the deep neural network model driven by the optimal physical equation and data fusion, the deep neural network used for prediction is determined; the deep neural network model driven by the optimal physical equation and data fusion is a model trained based on the complex dynamic system modeling method described above.

[0017] Obtain the data to be predicted; the data to be predicted includes: time variables, control variables and the initial state of the system at the first time interval.

[0018] The data to be predicted is input into the deep neural network used for the prediction to obtain a prediction result.

[0019] In a third aspect, the present invention provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any of the complex dynamic system modeling methods or the complex dynamic system application methods described above.

[0020] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the complex dynamic system modeling methods or the complex dynamic system application methods described above.

[0021] In a fifth aspect, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements any of the complex dynamic system modeling methods or the complex dynamic system application methods described above.

[0022] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0023] The present invention provides a complex dynamic system modeling method, application method and related devices. First, an actual physical complex dynamic system is constructed to determine the solution operator of the actual physical complex dynamic system, and the actual physical complex dynamic system is time-discretized to obtain the discretized actual physical complex dynamic system. Based on the solution operator of the actual physical complex dynamic system and the discretized actual physical complex dynamic system, a deep neural network is constructed, and the residuals of the deep neural network and ordinary differential equations are fused to construct a deep neural network model driven by physical equations and data fusion; secondly, an actual data set is obtained, and a data residual loss function and an ordinary differential equation residual loss function are constructed, and a total loss function is calculated by weighted summation of the data residual loss function and the ordinary differential equation residual loss function; finally, the optimal shared parameters between the deep neural network and the residuals of the ordinary differential equation are determined by minimizing the total loss function, so as to obtain the optimal deep neural network model driven by physical equations and data fusion. The deep neural network framework (PDFD-DNN) driven by the fusion of physical equations and data proposed in the present invention designs the loss function of the deep neural network by using the most basic idea of ​​the neural network model of physical information (Physics-informed Neural Networks, PINN), constructs the residual of the ordinary differential equation through the automatic differentiation technology widely used in the deep neural network, and integrates it into the loss function design process of the deep neural network. It can be regarded as a process of embedding the physical laws represented by the ordinary differential equation into the deep neural network, thereby obtaining a deep neural network with physical equation constraints (differential form constraints formed by the ordinary differential equation), and obtaining a deep neural network model driven by the fusion of physical equations and data, realizing the deep fusion and complementarity of the mechanism model and the data model, thereby obtaining a physically reasonable, mathematically accurate, and computationally efficient complex dynamic system model. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0025] Figure 1 A flowchart of a complex dynamic system modeling method provided by an embodiment of the present invention.

[0026] Figure 2 A schematic diagram of the structure of a deep neural network model driven by physical equations and data fusion provided in one embodiment of the present invention.

[0027] Figure 3 A flowchart of a complex dynamic system application method provided by an embodiment of the present invention.

[0028] Figure 4 A schematic diagram of the evolution of a self-loop prediction model over time provided by an embodiment of the present invention.

[0029] Figure 5 A schematic diagram of the structure of a double-link manipulator provided in one embodiment of the present invention.

[0030] Figure 6 A schematic diagram of how the PDFD-DNN prediction effect of the generalized coordinate angle α provided by an embodiment of the present invention changes with the number of samples in the actual data set.

[0031] Figure 7 A schematic diagram of how the PDFD-DNN prediction effect of the generalized coordinate angle β provided by an embodiment of the present invention changes with the number of samples in the actual data set.

[0032] Figure 8 A schematic diagram of how the PDFD-DNN prediction effect of the generalized coordinate angle α varies with the number of configuration point set samples provided by an embodiment of the present invention.

[0033] Fig. 9 A schematic diagram of how the PDFD-DNN prediction effect of the generalized coordinate angle β provided by an embodiment of the present invention changes with the number of configuration point set samples.

[0034] Fig.10 A schematic diagram comparing the prediction effects of PDFD-DNN and DNN for the generalized coordinate angle α provided in one embodiment of the present invention.

[0035] Fig.11 A schematic diagram comparing the prediction effects of PDFD-DNN and DNN for the generalized coordinate angle β provided in one embodiment of the present invention.

[0036] Fig.12 A schematic diagram of the structure of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] At present, in the field of automated complex dynamic system modeling, there are two main modeling methods driven by physical knowledge and data hybrid. One is to use the mechanism model as the main method and identify and modify the mechanism model based on data; the other is to use the two methods in parallel and obtain the final result based on the combined evaluation of the results of the two methods. However, both methods lack deeper integration and optimization. In 2017, Raissi proposed a neural network model based on physical information, which realized the construction of a deep neural network model driven by the fusion of physical equations and data. In recent years, PINN has gradually become a research hotspot in the interdisciplinary field of machine learning and computational mathematics, and has made great progress in both theory and application. However, the above PINN model and its variants are only suitable for simulation and analysis design in the fields of fluid mechanics, material mechanics, and biomedicine, and cannot be applied to the field of automated complex system modeling such as prediction, control, and optimization of complex physical systems. The main reason is that the PINN model and its variants assume that the physical field boundary conditions are fixed. Therefore, in order to be applicable to the field of automated control (real-time changes in physical field boundary conditions are a common feature), it is necessary to specifically study modeling methods driven by the fusion of physical equations and data for automated complex dynamic systems, construct deep neural network models driven by the fusion of physical equations and data, and achieve deep fusion and complementarity between mechanism models and data models, providing physically reasonable, mathematically accurate, and computationally efficient complex dynamic system models for the prediction, control, and optimization of complex physical systems in the field of automation.

[0040] In an exemplary embodiment, Figure 1 As shown, a complex dynamic system modeling method is provided, the method comprising the following steps:

[0041] S1: Construct an actual physical complex dynamic system; the actual physical complex dynamic system is a nonlinear steady-state state space model.

[0042] S2: Determine a solution operator of the actual physical complex dynamic system; the solution operator of the actual physical complex dynamic system includes: control variables and initial state values.

[0043] S3: Time discretizing the actual physical complex dynamic system to obtain a discretized actual physical complex dynamic system.

[0044] S4: Based on the solution operator of the actual physical complex dynamic system and the discretized actual physical complex dynamic system, a deep neural network is constructed; the deep neural network approximates the solution operator of the actual physical complex dynamic system within each time interval.

[0045] S5: Fuse the residual of the deep neural network with the ordinary differential equation to construct a deep neural network model driven by physical equation and data fusion.

[0046] S6: Obtain an actual data set, and construct a data residual loss function and an ordinary differential equation residual loss function; the actual data set is data measured in an actual production process.

[0047] S7: Calculate the total loss function by weighted summing the data residual loss function and the ordinary differential equation residual loss function.

[0048] S8: By minimizing the total loss function, the optimal shared parameters between the residuals of the deep neural network and the ordinary differential equation are determined, and the optimal deep neural network model driven by the fusion of physical equations and data is obtained.

[0049] Implementing the above steps S1 to S8 has the following technical effects:

[0050] (1) By incorporating the residual of ordinary differential equations into the loss function design process of the deep neural network, the trained deep neural network can not only approximate the observed data, but also automatically satisfy the physical laws such as symmetry, invariance, conservation, etc. followed by ordinary differential equations, thereby improving the physical interpretability of the deep neural network model.

[0051] (2) The residual term of the ordinary differential equation plays a regularization role, which can enhance the generalization ability of the deep neural network and avoid the occurrence of overfitting. At the same time, it reduces the dependence on training data and solves the bottleneck that deep neural networks are difficult to apply to small sample scenarios in the industrial field.

[0052] (3) The PDFD-DNN framework divides the entire simulation process into multiple equidistant control time intervals, each of which is τ seconds. The solution x(t) in each time interval is repeatedly iteratively calculated by a single PDFD-DNN network, which significantly alleviates the problem of rapid degradation of the prediction performance of traditional PINN after exceeding the time training range.

[0053] (4) Different from the traditional PINN whose initial state is fixed, the PDFD-DNN framework adds the initial state to the input space of the deep neural network, enabling it to handle complex dynamic system solutions with changing initial states and can be applied in the field of automation.

[0054] (5) The deep neural network with ordinary differential equation residual loss (i.e., the deep neural network model driven by the fusion of physical equations and data) has better complex dynamic system modeling and prediction effect than the deep neural network without ordinary differential equation residual loss (i.e., the conventional pure data-driven deep neural network, DNN).

[0055] In an exemplary embodiment, the steps of the complex dynamic system modeling solution driven by physical equation and data fusion are as follows:

[0056] A1: The actual physical complex dynamic system is represented by the following nonlinear steady-state state space model (composed of ordinary differential equations):

[0057]

[0058] in, Represents the time variable, x: Indicates the system status. Indicates the initial state of the system, u: represents the system control variable, t0 represents the initial time, t N represents the termination time, and N() represents the nonlinear function. Assume that the nonlinear function N() is continuous and locally Lipschitz continuous with respect to the state x, so that the initial value problem of the actual physical complex dynamic system (1) is has a unique (weak) solution.

[0059] A2: Define the solution operator corresponding to the actual physical complex dynamic system, that is, map the control variables and initial state values ​​to the current solution of the system. The expression is as follows:

[0060]

[0061] A3: Considering the practical application of controllers in digital control of physical systems, the actual physical complex dynamic system (1) is time discretized and the following time grid is introduced:

[0062] t0<t1<t2<...<t N (3);

[0063] Choose an equidistant time grid, i.e., t k =t0+kτ, τ>0 is a constant sampling period, corresponding to the sampling period of the discrete time control system. The setting of τ usually depends on the specific dynamic characteristics of the actual physical system.

[0064] A4: Introducing transfer input u k :=u(t0+kτ), k=0,1,2,...,N-1, we can get the following expression:

[0065]

[0066] where x k =x(t k ). If the control input satisfies the zero-order hold assumption, that is, Then formula (4) is similar to a discrete-time control system.

[0067] A5: Building a Deep Neural Network N (t,u,x0;w) approximate system solution operator in each time interval The input of the deep neural network includes: time variable t, control variable u, and the initial state x0 of the system at each time interval. Assuming that the control input remains constant in the time interval t∈[0,τ], similar to the zero-order holder, the expression is as follows:

[0068] x(t)=f N (t,u,x0;w),t∈[0,τ] (5);

[0069] Among them, f N Represents the mapping relationship of a deep neural network parameterized by w, where w is a set of trainable weight parameters and bias parameters. The nonlinear activation function of the deep neural network is the hyperbolic tangent activation function tanh(x) or the sine activation function sin(x).

[0070] A6: Fusion of Deep Neural Networks N The residual of (t,u,x0;w) and the ordinary differential equation constitutes a deep neural network model driven by the fusion of physical equations and data. The model structure is as follows Figure 2 As shown, the residual of the ordinary differential equation is defined as:

[0071]

[0072] Among them, F(t,u,x0;w) represents the residual of the ordinary differential equation, represents the time variable, u: represents the system control variable, X0 represents the initial state of the system at each time interval, w represents the set of trainable weight parameters and bias parameters, and f N (t,u,x0;w) represents a deep neural network, f N Represents the deep neural network mapping relationship parameterized by w, and N() represents a nonlinear function.

[0073] A7: Use automatic differentiation techniques to solve the differentials of function combinations by applying the chain rule to obtain

[0074] A8: The actual data set is composed of actual production process measurement data And construct the data residual loss function L data (w), as shown in Formula 7.

[0075]

[0076] Among them, L data (w) represents the data residual loss function, the data pair represents the i-th training data sample, X represents the actual state of the system, represents all inputs of the deep neural network (including time, control input, initial state), represents the time variable, u: represents the system control variable, X0 represents the initial state of the system at each time interval, represents the deep neural network of the i-th training data sample, f N represents the deep neural network mapping relationship parameterized by w, where w represents the set of trainable weight parameters and bias parameters, N data Indicates the number of samples in the actual dataset.

[0077] A9: Randomly sample the residual of the ordinary differential equation from the three dimensions (time, control input, initial state) from their respective specific intervals to form a configuration point set And construct the ordinary differential equation residual loss function L phys (w), as shown in Formula 8.

[0078]

[0079] Among them, L phys (w) represents the residual loss function of the ordinary differential equation, represents the residual of the ordinary differential equation of the jth training data sample, represents the time variable, u: represents the system control variable, X0 represents the initial state of the system at each time interval, w represents the set of trainable weight parameters and bias parameters, N phys Represents the number of collocation point set samples.

[0080] It should be noted that the interval range of time t is [0,τ].

[0081] A10: The total loss function L(w) is calculated by weighted summing of data residual loss and partial differential equation residual loss. The total loss function is defined as:

[0082] L(w)=λ data L data (w)+λ phys L phys (w) (9);

[0083] Among them, λ data represents the first weight coefficient used to balance the interaction between data residual loss and partial differential equation residual loss, λ phys Represents the second weight coefficient used to balance the interaction between the data residual loss and the partial differential equation residual loss, so that the magnitude of the two losses is on the same scale. These weight coefficients can be given by experience before neural network training, or they can be adaptively adjusted during training. Reasonable weight coefficient settings play an important role in improving the trainability and convergence speed of the PDFD-DNN model.

[0084] A11: When the PDFD-DNN network structure, actual data set, configuration point set and loss function are determined, the deep neural network f is learned by minimizing the total loss function L(w) N The shared parameter w between (t,u,x0;w) and the residual F(t,u,x0;w) of the ordinary differential equation is firstly iterated K1 times by the ADAM optimizer, and then the L-BFGS optimizer is used for K2 iterations to obtain the optimal physical equation and data fusion driven deep neural network model parameter w * .

[0085] In another exemplary embodiment of the present invention, Figure 3 As shown, the present invention also provides a complex dynamic system application method, the complex dynamic system application method comprising:

[0086] B1: Determine the deep neural network used for prediction based on the optimal physical equation and the deep neural network model driven by data fusion; the optimal physical equation and the deep neural network model driven by data fusion is a model trained based on the complex dynamic system modeling method described above.

[0087] B2: Obtain the data to be predicted; the data to be predicted includes: time variables, control variables and the initial state of the system at the first time interval.

[0088] B3: Inputting the data to be predicted into the deep neural network used for prediction to obtain a prediction result.

[0089] That is, in step A11, the optimal physical equation and data fusion driven deep neural network model parameter w are obtained. * After that, we get the deep neural network f used for prediction N (t,u,x0;w* ), given the input of the deep neural network, including: time variables, control variables and the initial state of the system in the first time interval, using the deep neural network f N (t,u,x0;w * ) can directly calculate the solution in the time interval t∈[0,τ]. The calculation result f of the deep neural network at time t=τ N (τ,u,x0;w * ) as the initial state of the time interval t∈[τ,2τ], and iteratively repeat the solution calculation process of formula (5) to form a self-loop prediction model, and then the solution of the system at all times when time t>τ can be obtained, as follows: Figure 4 shown.

[0090] Next, a dual-link manipulator dynamics simulation system is used to verify the effectiveness of the deep neural network framework driven by physical equations and data fusion proposed in the present invention.

[0091] The schematic diagram of the double-link manipulator and the inertial reference frame {e1, e2, e3} used for modeling are shown in Figure 2. Figure 5 The links are connected by revolute joints representing the rotational units. The system under consideration has two degrees of freedom. The kinematics of the two-link manipulator can be described by generalized coordinates q = [α, β] T , α, β represent the angles between two generalized coordinates. System parameters include mass m1 and m2, moment of inertia J1 and J2, connecting rod lengths l0, l1 and l2, etc.

[0092] The rigid two-link manipulator system under consideration is systematically modeled to obtain the minimum form of the nonlinear motion equation:

[0093]

[0094] The input vector consists of the motor currents of the first and second revolute joints u = [I1, I2] T The dynamic system in equation (10) is represented by the positive definite symmetric generalized mass matrix M(q), the vector consisting of the centrifugal force, the Coriolis force and the gyroscopic force Force Vector The input matrix D is represented as follows:

[0095]

[0096] Among them, T fr,1 、T fr,2 are the friction torques of the first and second revolute joints, R1 and R2 are the gear ratios of the first and second revolute joints, k1 and k2 are the motor constants of the first and second revolute joints.

[0097] Introduction The first-order nonlinear state space model expression of equation (10) is obtained:

[0098]

[0099] The deep neural network used in this simulation experiment consists of 4 fully connected layers, and the hyperbolic tangent activation function is used on the hidden layer neurons, including 32 neurons. For the data residual loss function L data Quantization of (w) using N data Initial state data pair Constitute the actual data samples, these data pairs are only a subset of all possible initial states. Therefore, for the ordinary differential equation residual loss function L phys Quantization of (w) randomly generates N in the allowed 7-dimensional input space domain phys Configuration Points The range is:

[0100]

[0101] All hyperparameters are the result of grid search, including the number of deep neural network layers, the number of neurons in the hidden layer, and the number of samples in the actual data set N. data , the number of configuration point set samples N phys For the training of the PDFD-DNN network, ADAM was first used to optimize the loss function for K1=10,000 iterations, and then L-BFGS was used to optimize the loss function for K2=20,000 iterations to enhance the stability of the training process.

[0102] In order to verify the effectiveness of the PDFD-DNN method proposed in this invention and its approximate prediction ability, PDFD-DNN was run in the self-loop mode (see Figure 4 ), the sampling time interval is set to τ = 0.2S, and there are 20 self-loop iterations in this experiment.

[0103] Figure 6 and Figure 7 The PDFD-DNN prediction effect is shown as the number of samples in the actual dataset changes (N phys Remain unchanged at 20000, N data 100, 500, and 1000, respectively). It can be seen from the figure that as the number of samples in the actual dataset increases, the prediction effect of PDFD-DNN becomes better (that is, the predicted values ​​α-pre, β-pre of the generalized coordinate angles α, β are closer to the actual values ​​α-rel, β-rel).

[0104] Figure 8 and Fig. 9 The PDFD-DNN prediction effect is shown as the number of configuration point set samples changes (Ndata Keep it unchanged at 1000, N phys 5000, 10000, and 20000 respectively). It can be seen from the figure that as the number of configuration point set samples increases, the prediction effect of PDFD-DNN becomes better (that is, the predicted values ​​α-pre, β-pre of the generalized coordinate angles α, β are closer to the actual values ​​α-rel, β-rel).

[0105] Fig.10 and Fig.11 The comparison of prediction effects between PDFD-DNN and DNN is shown. It can be seen from the figure that the prediction effect of the deep neural network driven by physical equations and data fusion (PDFD-DNN) is significantly better than that of the pure data-driven deep neural network (DNN). Even the prediction effect of PDFD-DNN with only 1000 samples in the actual data set is much better than that of DNN with 10000 samples in the actual data set. This is because PDFD-DNN embeds the physical laws represented by ordinary differential equations into the deep neural network, and the residual term of the ordinary differential equation plays a regularization role, which enhances the generalization ability of the deep neural network and reduces the dependence on training data. It can be applied to small sample scenarios in the industrial field.

[0106] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Fig.12 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store actual data sets. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a complex dynamic system modeling method or a complex dynamic system application method is implemented.

[0107] Those skilled in the art will understand that Fig.12The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0108] In an exemplary embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the above-mentioned method embodiments are implemented when the processor executes the computer program.

[0109] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the above-mentioned method embodiments are implemented.

[0110] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the above-mentioned method embodiments are implemented.

[0111] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in the present invention are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0112] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0113] The database involved in each embodiment provided by the present invention may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided by the present invention may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0114] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0115] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A complex dynamic system modeling method, characterized in that: The complex dynamic system modeling method comprises: Constructing an actual physical complex dynamic system; the actual physical complex dynamic system is a nonlinear steady-state state space model; Determine a solution operator of the actual physical complex dynamic system; the solution operator of the actual physical complex dynamic system includes: a control variable and an initial state value; Performing time discretization on the actual physical complex dynamic system to obtain a discretized actual physical complex dynamic system; Based on the solution operator of the actual physical complex dynamic system and the discretized actual physical complex dynamic system, a deep neural network is constructed; the deep neural network approximates the solution operator of the actual physical complex dynamic system in each time interval; Fusing the residual of the deep neural network with the ordinary differential equation to construct a deep neural network model driven by physical equation and data fusion; Obtaining an actual data set, and constructing a data residual loss function and an ordinary differential equation residual loss function; the actual data set is data measured in an actual production process; By weighted summing of the data residual loss function and the ordinary differential equation residual loss function, a total loss function is calculated; By minimizing the total loss function, the optimal shared parameters between the residuals of the deep neural network and the ordinary differential equations are determined, and the optimal deep neural network model driven by the fusion of physical equations and data is obtained.

2. The complex dynamic system modeling method according to claim 1, characterized in that: The expression of the actual physical complex dynamic system is: in, represents the time variable, Indicates the system status. Indicates the initial state of the system. represents the system control variable, t0 represents the initial time, t N represents the termination time, and N() represents a nonlinear function.

3. The complex dynamic system modeling method according to claim 1, characterized in that: The expression of the residual of the ordinary differential equation is: Among them, F(t,u,x0;w) represents the residual of the ordinary differential equation, represents the time variable, represents the system control variable, X0 represents the initial state of the system at each time interval, w represents the set of trainable weight parameters and bias parameters, and f N (t,u,x0;w) represents a deep neural network, f N Represents the deep neural network mapping relationship parameterized by w, and N() represents a nonlinear function.

4. The complex dynamic system modeling method according to claim 1, characterized in that: The expression of the data residual loss function is: Among them, L data (w) represents the data residual loss function, the data pair represents the i-th training data sample, X represents the actual state of the system, represents the time variable, represents the system control variable, x0 represents the initial state of the system at each time interval, represents the deep neural network of the i-th training data sample, f N represents the deep neural network mapping relationship parameterized by w, where w represents the set of trainable weight parameters and bias parameters, N data Indicates the number of samples in the actual dataset.

5. The complex dynamic system modeling method according to claim 1, characterized in that: The expression of the ordinary differential equation residual loss function is: Among them, L phys (w) represents the residual loss function of the ordinary differential equation, represents the residual of the ordinary differential equation of the jth training data sample, represents the time variable, represents the system control variable, x0 represents the initial state of the system at each time interval, w represents the set of trainable weight parameters and bias parameters, N phys Represents the number of collocation point set samples.

6. The complex dynamic system modeling method according to claim 1, characterized in that: The expression of the total loss function is: L(w)=λ data L data (w)+λ phys L phys (w); Among them, L(w) represents the total loss function, L data (w) represents the data residual loss function, L phys (w) represents the residual loss function of the ordinary differential equation, λ data represents the first weight coefficient used to balance the interaction between data residual loss and partial differential equation residual loss, λ phys Represents the second weight coefficient used to balance the interaction between the data residual loss and the partial differential equation residual loss.

7. A complex dynamic system application method, characterized in that: The complex dynamic system application method comprises: Determine the deep neural network used for prediction according to the deep neural network model driven by the optimal physical equation and data fusion; the deep neural network model driven by the optimal physical equation and data fusion is a model trained based on the complex dynamic system modeling method according to any one of claims 1 to 6; Acquire data to be predicted; the data to be predicted includes: time variables, control variables and the initial state of the system at the first time interval; The data to be predicted is input into the deep neural network used for the prediction to obtain a prediction result.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the complex dynamic system modeling method described in any one of claims 1 to 6 or the complex dynamic system application method described in claim 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the complex dynamic system modeling method described in any one of claims 1 to 6 or the complex dynamic system application method described in claim 7 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the complex dynamic system modeling method described in any one of claims 1 to 6 or the complex dynamic system application method described in claim 7 is implemented.

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