A method and system for solving an electrochemical model based on a physical information neural network

Abstract

The application discloses a method and system for solving an electrochemical model based on a physical information neural network, and the method comprises the following steps: establishing a physical information neural network according to a partial differential equation group in an electrochemical model to be trained; adjusting the weight and bias of the physical information neural network according to a loss function of the physical information neural network, so as to train the physical information neural network; obtaining the trained physical information neural network when the loss function is less than a preset value; obtaining a physical information neural network system by simultaneously connecting each partial differential equation group corresponding to the trained physical information neural network; iteratively solving the physical information neural network system according to a loss function of the physical information neural network system, so as to obtain a trained physical information neural network system; and solving the electrochemical model according to the trained physical information neural network system.

Description

Technical Field

[0001] This invention relates to the field of electrochemical solutions, and more specifically to a method for solving electrochemical models based on physical information neural networks. Background Technology

[0002] In recent years, the development of artificial intelligence has provided new ideas in many fields. In particular, the rapid development of deep learning technology has enabled the modeling and prediction of complex nonlinear systems through neural networks. However, traditional neural networks mainly rely on large amounts of data for training, which limits their application to systems like batteries, whose internal states are difficult to measure directly.

[0003] Physics-Informed Neural Networks (PINNs) offer a potential solution to this problem. PINNs are a special type of neural network characterized by incorporating prior knowledge of physics during training, such as physical laws (e.g., conservation laws) or physical properties (e.g., continuity, smoothness). This allows PINNs to guarantee the physical plausibility of the model output to a certain extent, especially when data is sparse or incomplete. Therefore, a PINN-based method is needed to solve the partial differential equations of a P2D model representing the internal physical processes of a battery. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method and system for solving electrochemical models based on physical information neural networks.

[0005] Specifically, the technical solution of the present invention is as follows:

[0006] In a first aspect, the present invention provides a method for solving electrochemical models based on a physical information neural network, comprising:

[0007] A physical information neural network is established based on the partial differential equations in the electrochemical model to be trained; the partial differential equations include: solid phase partial differential equations, liquid phase partial differential equations, and electric field partial differential equations.

[0008] The weights and biases of the physical information neural network are adjusted according to the loss function of the physical information neural network to train the physical information neural network; the loss function includes: equation residual loss function and boundary condition loss function;

[0009] When the loss function is less than a preset value, the trained physical information neural network is obtained;

[0010] By simultaneously solving the physical information neural network corresponding to each set of partial differential equations, the physical information neural network system is obtained;

[0011] Based on the loss function of the physical information neural network system, the physical information neural network system is iteratively solved to obtain the trained physical information neural network system;

[0012] The electrochemical model is obtained by solving the physical information neural network system after training.

[0013] This implementation method provides a physical information neural network established through the partial differential equations of an electrochemical model. Based on training the physical information neural network, a corresponding trained physical information neural network is obtained. The corresponding physical information neural network can solve for the electrochemical parameters of the corresponding partial differential equations. By combining the physical information neural networks, the entire electrochemical model can be solved iteratively and quickly.

[0014] In some methods for solving electrochemical models based on physical information neural networks, the establishment of a physical information neural network based on the partial differential equations in the electrochemical model to be trained includes:

[0015] The partial differential equations in the electrochemical model to be trained are converted into the partial differential equations in dimensionless form.

[0016] A physical information neural network is established based on the dimensionless partial differential equations described herein.

[0017] This implementation method provides a way to transform a system of partial differential equations into a dimensionless form, which facilitates processing and computation.

[0018] In some methods for solving electrochemical models based on physical information neural networks, the method of converting the partial differential equations in the electrochemical model to be trained into a dimensionless form includes:

[0019] Substituting the dimensionless time calculation formula, the dimensionless concentration calculation formula, and the dimensionless radius calculation formula into the partial differential equation system yields the partial differential equation system in dimensionless form.

[0020] This implementation method provides a specific way to calculate a system of dimensionless partial differential equations.

[0021] In some methods for solving electrochemical models based on physical information neural networks, before training the physical information neural network by adjusting its weights and biases according to its loss function, the method further includes:

[0022] The loss function includes: equation residual loss function and boundary condition loss function;

[0023] Dimensionless time and dimensionless radius are input into the physical information neural network to obtain dimensionless concentration;

[0024] By substituting the partial derivatives of the dimensionless concentration with respect to the dimensionless time and the dimensionless radius into the physical information neural network, the residual loss function of the equation is obtained;

[0025] The boundary condition loss function is obtained by using the difference between the output of the physical information neural network at the boundary of the partial differential equation system and the boundary conditions of the partial differential equation system.

[0026] The loss function is obtained based on the residual loss function of the equation and the boundary condition loss function.

[0027] This implementation provides a method for calculating the loss function used in training and debugging physical neural networks.

[0028] In some methods for solving electrochemical models based on physical information neural networks, the step of adjusting the weights and biases of the physical information neural network according to its loss function to train the network includes:

[0029] The weights and biases of the physical information neural network are adjusted using an optimization algorithm to train the physical information neural network until the loss function is less than the preset value; the optimization algorithm includes: stochastic gradient descent optimization algorithm.

[0030] This implementation provides a method for adjusting the weights and biases of a neural network.

[0031] Secondly, the present invention provides a system for solving electrochemical models based on a physical information neural network, comprising:

[0032] A neural network establishment module is used to establish a physical information neural network based on the partial differential equations in the electrochemical model to be trained; the partial differential equations include: solid phase partial differential equations, liquid phase partial differential equations, and electric field partial differential equations; the physical information neural network is sent to the neural network training module;

[0033] The neural network training module, connected to the neural network establishment module, is used to adjust the weights and biases of the physical information neural network according to the loss function of the physical information neural network, so as to train the physical information neural network; the loss function includes: equation residual loss function and boundary condition loss function;

[0034] The neural network training module is further configured to obtain the trained physical information neural network when the loss function is less than a preset value; and send the trained physical information neural network to the neural network system establishment module.

[0035] The neural network system establishment module is connected to the neural network training module and is used to obtain a physical information neural network system by simultaneously solving the physical information neural network corresponding to each set of partial differential equations; and to send the neural network system to the neural network training module.

[0036] The neural network training module is further configured to iteratively solve the physical information neural network system according to the loss function of the physical information neural network system to obtain the trained physical information neural network system; and send the trained physical information neural network system to the electrochemical model solving module.

[0037] The electrochemical model solving module is connected to the neural network training module and is also used to solve for the electrochemical model based on the trained physical information neural network system.

[0038] Implementation methods for some systems that solve electrochemical models based on physical information neural networks.

[0039] The neural network establishment module further includes a dimensionless submodule, which is used to convert the partial differential equations in the electrochemical model to be trained into a dimensionless form of the partial differential equations.

[0040] The neural network building module is used to build a physical information neural network based on the dimensionless partial differential equations.

[0041] Implementation methods for some systems that solve electrochemical models based on physical information neural networks.

[0042] The dimensionless submodule is used to substitute the dimensionless time calculation formula, the dimensionless concentration calculation formula, and the dimensionless radius calculation formula into the partial differential equation system to obtain the partial differential equation system in dimensionless form.

[0043] Implementation methods for some systems that solve electrochemical models based on physical information neural networks.

[0044] The loss function includes: equation residual loss function and boundary condition loss function;

[0045] The neural network training module further includes a residual loss calculation submodule, which is used to input dimensionless time and dimensionless radius into the physical information neural network to obtain dimensionless concentration; and to obtain the equation residual loss function by substituting the partial derivatives of the dimensionless concentration with respect to the dimensionless time and the dimensionless radius into the physical information neural network.

[0046] The neural network training module further includes a boundary loss calculation submodule, which obtains the boundary condition loss function by using the difference between the output of the physical information neural network at the boundary of the partial differential equation system and the boundary conditions of the partial differential equation system.

[0047] The neural network training module is further configured to obtain the loss function based on the equation residual loss function and the boundary condition loss function.

[0048] In some implementation methods of systems that solve electrochemical models based on physical information neural networks, the neural network training module is further used to adjust the weights and biases of the physical information neural network using an optimization algorithm to train the physical information neural network until the loss function is less than the preset value; the optimization algorithm includes: stochastic gradient descent optimization algorithm.

[0049] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0050] 1. This invention provides a physical information neural network established through a set of partial differential equations of an electrochemical model. Based on training the physical information neural network, a corresponding trained physical information neural network is obtained. The corresponding physical information neural network can solve for the electrochemical parameters of the corresponding set of partial differential equations. By combining the physical information neural networks and iterating, the entire electrochemical model can be solved iteratively.

[0051] 2. This invention provides a method for calculating the loss function used in training and debugging physical neural networks. Attached Figure Description

[0052] The preferred embodiments will now be described in a clear and easy-to-understand manner, in conjunction with the accompanying drawings, to further explain the above-mentioned characteristics, technical features, advantages, and implementation methods of the present invention.

[0053] Figure 1 This is a flowchart of a method for solving electrochemical models based on physical information neural networks provided by the present invention;

[0054] Figure 2 This is a system block diagram of a system for solving electrochemical models based on a physical information neural network, provided by the present invention.

[0055] The following are the icon numbers: 10--Neural network establishment module; 11--Dimensionless sub-module; 20--Neural network training module; 21--Residual loss calculation sub-module; 22--Boundary loss calculation sub-module; 30--Neural network system establishment module; 40--Electrochemical model solving module. Detailed Implementation

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0057] To keep the drawings concise, each figure only schematically shows the parts relevant to the invention, and these do not represent the actual structure of the product. Furthermore, to facilitate understanding, in some figures, only one of components with the same structure or function is schematically depicted, or only one is labeled. In this document, "one" not only means "only one," but can also mean "more than one."

[0058] It should also be further understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0059] In this document, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0060] Furthermore, in the description of this application, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0061] In one embodiment, refer to the appendix to the specification. Figure 1 The present invention provides a method for solving electrochemical models based on physical information neural networks, comprising:

[0062] S110, Based on the partial differential equations in the electrochemical model to be trained, establish a physical information neural network; the partial differential equations include: solid phase partial differential equations, liquid phase partial differential equations and electric field partial differential equations.

[0063] In step S110, initial and boundary conditions are set for the partial differential equations representing the solid phase, liquid phase, and electric field, respectively, and an independent physical information neural network is created for each set of partial differential equations. The neural network structure of the physical information neural network can be selected to suit the processing of partial differential equations, such as a fully connected neural network or a convolutional neural network.

[0064] S120, based on the loss function of the physical information neural network, adjust the weights and biases of the physical information neural network to train the physical information neural network; the loss function includes: equation residual loss function and boundary condition loss function.

[0065] S130: When the loss function is less than the preset value, the trained physical information neural network is obtained.

[0066] In steps S120 and S130, each physical information neural network is trained. The training objective of the physical information neural network is to minimize the residuals of the partial differential equation and the discrepancy between the predicted and observed solutions to the equation under given boundary and initial conditions.

[0067] S140, by simultaneously solving the training physical information neural network corresponding to each set of partial differential equations, a physical information neural network system is obtained.

[0068] In step S140, since the physical information neural network established by each single partial differential equation system lacks the coupling relationship between the partial differential equation systems, it is necessary to connect the physical information neural networks corresponding to each partial differential equation system to obtain the physical information neural network system.

[0069] S150, based on the loss function of the physical information neural network system, iteratively solve the physical information neural network system to obtain the trained physical information neural network system.

[0070] In step S150, in each iteration, the output of each physical information neural network system is used as the input of the next iteration until the difference between the solution obtained by the entire physical information neural network system and the observed data is within the allowable range. At this point, the iteration ends and the trained physical information neural network system is obtained.

[0071] S160, based on the trained physical information neural network system, solves to obtain the electrochemical model.

[0072] In step S160, all partial differential equations in the electrochemical model are solved quickly using a physical information neural network system.

[0073] This embodiment provides a physical information neural network established through the partial differential equations of an electrochemical model. Based on training the physical information neural network, a corresponding trained physical information neural network is obtained. The corresponding physical information neural network can solve for the electrochemical parameters of the corresponding partial differential equations. By combining the physical information neural networks, the entire electrochemical model can be solved iteratively and quickly.

[0074] This embodiment provides a method for solving electrochemical models based on physical information neural networks, based on the foregoing embodiments. Step S110 includes:

[0075] Substitute the dimensionless time calculation formula, dimensionless concentration calculation formula, and dimensionless radius calculation formula into the partial differential equation system in the electrochemical model to be trained, and convert it into a partial differential equation system in dimensionless form.

[0076] A physical information neural network is established based on a system of dimensionless partial differential equations.

[0077] For example, the partial differential equations for the solid phase in the electrochemical model to be trained are as follows:

[0078]

[0079] c = c0;

[0080] r = 0;

[0081] r = R p Where c is the ion concentration, t is the reaction time, and D is the reaction time. s Let be the solid-state diffusion coefficient of lithium ions, r be the radial dimension of lithium ions in the spherical coordinate system of the spherical particle, F be the Faraday constant, and i be the solid-state diffusion coefficient of lithium ions. s Let n be the solid-state current, n be the valence of the charged particle, Rp be the particle radius, and c0 be the initial concentration.

[0082] The dimensionless time calculation formula: Dimensionless concentration calculation formula: c'=c / c0; dimensionless radius calculation formula: r'=r / Rp. Substitute these into the above partial differential equations for the solid phase; where τ is the dimensionless time, c' is the dimensionless concentration, and r' is the dimensionless radius.

[0083] The dimensionless system of partial differential equations is obtained as follows:

[0084]

[0085] r' = 0;

[0086] r' = 1.

[0087] This embodiment provides steps for transforming a system of partial differential equations into a dimensionless form, so as to facilitate the processing and calculation of the system of partial differential equations.

[0088] This embodiment provides a method for solving electrochemical models based on physical information neural networks, building upon the aforementioned embodiments. Before step S120, the method further includes:

[0089] Loss functions include: equation residual loss function and boundary condition loss function;

[0090] Dimensionless time and dimensionless radius are input into a physical information neural network to obtain dimensionless concentration;

[0091] By substituting the partial derivatives of dimensionless concentration with respect to dimensionless time and dimensionless radius into the physical information neural network, the residual loss function of the equation is obtained.

[0092] The boundary condition loss function is obtained by using the difference between the output of the physical information neural network at the boundary of the partial differential equation system and the boundary conditions of the partial differential equation system.

[0093] The loss function is obtained based on the residual loss function and the boundary condition loss function of the equation.

[0094] In this embodiment, when training a physical information neural network, a loss function needs to be defined. This loss function consists of two parts: an equation residual loss function and a boundary condition loss function. The equation residual loss function can be obtained by automatically differentiating the partial derivatives of the dimensionless concentration c' of the neural network output with respect to the dimensionless time τ and the dimensionless radius r', and then substituting these partial derivatives into a system of dimensionless partial differential equations. The boundary condition part can be obtained by comparing the difference between the neural network's output at the boundary and the boundary conditions. The final loss function is obtained by adding these two losses together.

[0095] This embodiment provides a method for solving electrochemical models based on physical information neural networks, based on the foregoing embodiments. Step S120 includes:

[0096] The weights and biases of the physical information neural network are adjusted using optimization algorithms to train the physical information neural network until the loss function is less than a preset value; the optimization algorithms include: stochastic gradient descent optimization algorithm.

[0097] This embodiment employs optimization algorithms such as stochastic gradient descent to minimize the loss function, thereby training the physical information neural network. During training, the weights and biases of the neural network need to be continuously adjusted so that the value of the loss function gradually decreases.

[0098] In one embodiment, refer to the appendix to the specification. Figure 2The present invention provides a system for solving electrochemical models based on a physical information neural network, comprising:

[0099] The neural network establishment module 10 is used to establish a physical information neural network based on the partial differential equations in the electrochemical model to be trained; the partial differential equations include: solid phase partial differential equations, liquid phase partial differential equations and electric field partial differential equations; and the physical information neural network is sent to the neural network training module 20.

[0100] The neural network training module 20 is connected to the neural network establishment module and is used to adjust the weights and biases of the physical information neural network according to the loss function of the physical information neural network in order to train the physical information neural network; the loss function includes: equation residual loss function and boundary condition loss function.

[0101] The neural network training module 20 is also used to obtain the trained physical information neural network when the loss function is less than a preset value; and to send the trained physical information neural network to the neural network system establishment module 30.

[0102] The neural network system establishment module 30 is connected to the neural network training module 20. It is used to obtain the physical information neural network system by combining the trained physical information neural networks corresponding to each set of partial differential equations; and to send the neural network system to the neural network training module 20.

[0103] The neural network training module 20 is also used to iteratively solve the physical information neural network system according to the loss function of the physical information neural network system to obtain the trained physical information neural network system; and to send the trained physical information neural network system to the electrochemical model solving module 40.

[0104] The electrochemical model solving module 40 is connected to the neural network training module 20. The electrochemical model solving module 40 calls the physical information neural network system to perform iterative solving to obtain the electrochemical model.

[0105] This embodiment provides a neural network establishment module 10 that establishes a physical information neural network through the partial differential equations of the electrochemical model. The physical information neural network is trained by the neural network training module 20 to obtain the corresponding trained physical information neural network. The corresponding physical information neural network can solve the electrochemical parameters of the corresponding partial differential equations. After the neural network system establishment module 30 sets the physical information neural network together, the electrochemical model solving module 40 can quickly iteratively solve the entire electrochemical model.

[0106] This embodiment provides a system for solving electrochemical models based on a physical information neural network, building upon the foregoing embodiments.

[0107] The neural network building module 10 also includes: a dimensionless submodule 11, which is used to convert the partial differential equations in the electrochemical model to be trained into a dimensionless form of partial differential equations.

[0108] The neural network establishment module 10 is used to establish a physical information neural network based on a system of dimensionless partial differential equations.

[0109] In this embodiment, the partial differential equation system is transformed into a dimensionless form through the dimensionless transformation submodule 11, which facilitates processing and calculation.

[0110] This embodiment provides a system for solving electrochemical models based on a physical information neural network, building upon the foregoing embodiments.

[0111] The dimensionless submodule 11 is used to substitute the dimensionless time calculation formula, the dimensionless concentration calculation formula, and the dimensionless radius calculation formula into the partial differential equation system to obtain the partial differential equation system in dimensionless form.

[0112] In this embodiment, the dimensionless submodule 11 calculates the dimensionless time formula: Dimensionless concentration calculation formula: c'=c / c0; Dimensionless radius calculation formula: r'=r / Rp. Substituting these into a system of partial differential equations, such as the partial differential equations for a solid phase: c = c0; r = 0; r = R p Where c is the ion concentration, t is the reaction time, and D is the reaction time. s Let be the solid-state diffusion coefficient of lithium ions, r be the radial dimension of lithium ions in the spherical coordinate system of the spherical particle, F be the Faraday constant, and i be the solid-state diffusion coefficient of lithium ions. s Let τ be the solid-phase current, τ be the dimensionless time, c' be the dimensionless concentration, and r' be the dimensionless radius; then we obtain a set of partial differential equations for the solid phase in dimensionless form: r' = 0; r' = 1.

[0113] This embodiment provides a system for solving electrochemical models based on a physical information neural network, building upon the foregoing embodiments.

[0114] Loss functions include: equation residual loss function and boundary condition loss function;

[0115] The neural network training module 20 also includes a residual loss calculation submodule 21, which is used to input dimensionless time and dimensionless radius into the physical information neural network to obtain dimensionless concentration; and to obtain the equation residual loss function by substituting the partial derivatives of dimensionless concentration with respect to dimensionless time and dimensionless radius into the physical information neural network.

[0116] The neural network training module 20 also includes a boundary loss calculation submodule 22. The boundary loss calculation submodule obtains the boundary condition loss function by using the difference between the output of the physical information neural network at the boundary of the partial differential equation system and the boundary conditions of the partial differential equation system.

[0117] The neural network training module 20 is also used to obtain the loss function based on the equation residual loss function and the boundary condition loss function.

[0118] In this embodiment, the neural network training module 20 defines a loss function, which includes two parts: an equation residual loss function and a boundary condition loss function. The equation residual loss function is obtained by automatically differentiating the partial derivatives of the dimensionless concentration c' of the neural network output with respect to the dimensionless time τ and the dimensionless radius r', and then substituting these partial derivatives into a system of dimensionless partial differential equations. The boundary condition part is obtained by comparing the difference between the neural network output at the boundary and the boundary conditions. The final loss function is obtained by adding these two losses together.

[0119] This embodiment provides a system for solving electrochemical models based on a physical information neural network, building upon the foregoing embodiments.

[0120] The neural network training module 20 is also used to adjust the weights and biases of the physical information neural network using optimization algorithms to train the physical information neural network until the loss function is less than a preset value; the optimization algorithm includes: stochastic gradient descent optimization algorithm.

[0121] In this embodiment, the neural network training module 20 employs optimization algorithms such as stochastic gradient descent to minimize the loss function, thereby training the physical information neural network. During training, the weights and biases of the neural network need to be continuously adjusted so that the value of the loss function gradually decreases.

[0122] It should be noted that the above embodiments can be freely combined as needed. The above are merely preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for solving electrochemical models based on physical information neural networks, characterized in that, include: A physical information neural network is established based on the set of partial differential equations in the electrochemical model to be trained. The partial differential equations include: solid phase partial differential equations, liquid phase partial differential equations, and electric field partial differential equations. The weights and biases of the physical information neural network are adjusted according to the loss function of the physical information neural network to train the physical information neural network; the loss function includes: equation residual loss function and boundary condition loss function; When the loss function is less than a preset value, the trained physical information neural network is obtained; By simultaneously solving the physical information neural network corresponding to each set of partial differential equations, the physical information neural network system is obtained; Based on the loss function of the physical information neural network system, the physical information neural network system is iteratively solved to obtain the trained physical information neural network system; Based on the trained physical information neural network system, the electrochemical model is obtained; The step of establishing a physical information neural network based on the partial differential equations in the electrochemical model to be trained includes: The partial differential equations in the electrochemical model to be trained are converted into the partial differential equations in dimensionless form. A physical information neural network is established based on the dimensionless partial differential equations described above. The method of converting the partial differential equations in the electrochemical model to be trained into a dimensionless form is characterized by comprising: Substituting the dimensionless time calculation formula, the dimensionless concentration calculation formula, and the dimensionless radius calculation formula into the partial differential equation system, we obtain the partial differential equation system in dimensionless form. Before training the physical information neural network by adjusting its weights and biases according to the loss function of the physical information neural network, the method further includes: The loss function includes: equation residual loss function and boundary condition loss function; Dimensionless time and dimensionless radius are input into the physical information neural network to obtain dimensionless concentration; By substituting the partial derivatives of the dimensionless concentration with respect to the dimensionless time and the dimensionless radius into the physical information neural network, the residual loss function of the equation is obtained; The boundary condition loss function is obtained by using the difference between the output of the physical information neural network at the boundary of the partial differential equation system and the boundary conditions of the partial differential equation system. The loss function is obtained based on the residual loss function of the equation and the boundary condition loss function.

2. The method for solving electrochemical models based on physical information neural networks according to claim 1, characterized in that, The method of adjusting the weights and biases of the physical information neural network according to the loss function of the physical information neural network to train the physical information neural network includes: The weights and biases of the physical information neural network are adjusted using an optimization algorithm to train the physical information neural network until the loss function is less than the preset value; the optimization algorithm includes: stochastic gradient descent optimization algorithm.

3. A system for solving electrochemical models based on physical information neural networks, characterized in that, The system for solving electrochemical models based on physical information neural networks is used to perform the operations performed by the method for solving electrochemical models based on physical information neural networks as described in claim 1, including: A neural network establishment module is used to establish a physical information neural network based on the partial differential equations in the electrochemical model to be trained; the partial differential equations include: solid phase partial differential equations, liquid phase partial differential equations, and electric field partial differential equations; the physical information neural network is sent to the neural network training module; The neural network training module, connected to the neural network establishment module, is used to adjust the weights and biases of the physical information neural network according to the loss function of the physical information neural network, so as to train the physical information neural network; the loss function includes: equation residual loss function and boundary condition loss function; The neural network training module is further configured to obtain the trained physical information neural network when the loss function is less than a preset value; and send the trained physical information neural network to the neural network system establishment module. The neural network system establishment module is connected to the neural network training module and is used to obtain a physical information neural network system by simultaneously solving the physical information neural network corresponding to each set of partial differential equations; and to send the neural network system to the neural network training module. The neural network training module is further configured to optimize and solve the physical information neural network according to the loss function of the physical information neural network, obtain the trained physical information neural network, and send the trained physical information neural network to a preset electrochemical model solving module for iterative solution. The electrochemical model solving module is connected to the neural network training module and is also used to solve for the electrochemical model based on the trained physical information neural network system.

4. The system for solving electrochemical models based on physical information neural networks according to claim 3, characterized in that, The neural network establishment module further includes a dimensionless submodule, which is used to convert the partial differential equations in the electrochemical model to be trained into a dimensionless form of the partial differential equations. The neural network building module is used to build a physical information neural network based on the dimensionless partial differential equations.

5. The system for solving electrochemical models based on physical information neural networks according to claim 4, characterized in that, The dimensionless submodule is used to substitute the dimensionless time calculation formula, the dimensionless concentration calculation formula, and the dimensionless radius calculation formula into the partial differential equation system to obtain the partial differential equation system in dimensionless form.

6. The system for solving electrochemical models based on physical information neural networks according to claim 4, characterized in that, The loss function includes: equation residual loss function and boundary condition loss function; The neural network training module further includes a residual loss calculation submodule, which is used to input dimensionless time and dimensionless radius into the physical information neural network to obtain dimensionless concentration; and to obtain the equation residual loss function by substituting the partial derivatives of the dimensionless concentration with respect to the dimensionless time and the dimensionless radius into the physical information neural network. The neural network training module further includes a boundary loss calculation submodule, which obtains the boundary condition loss function by using the difference between the output of the physical information neural network at the boundary of the partial differential equation system and the boundary conditions of the partial differential equation system. The neural network training module is further configured to obtain the loss function based on the equation residual loss function and the boundary condition loss function.

7. The system for solving electrochemical models based on physical information neural networks according to claim 3, characterized in that, The neural network training module is further configured to use an optimization algorithm to adjust the weights and biases of the physical information neural network to train the physical information neural network until the loss function is less than the preset value; the optimization algorithm includes: stochastic gradient descent optimization algorithm.

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