Physics-informed neural network-based thermo-mechanical coupling analysis method for inertial microsystem

Abstract

Disclosed in the present invention is a physics-informed neural network-based thermo-mechanical coupling analysis method for an inertial microsystem, the method comprising: S1, configuring material parameters and boundary conditions of an inertial microsystem, and establishing a thermo-mechanical coupling analysis model; S2, performing electro-thermal coupling analysis to obtain a temperature distribution of the inertial microsystem; S3, performing thermo-mechanical coupling simulation analysis to obtain a thermal stress distribution of the microsystem; S4, predicting temperature fields of the microsystem by means of a physics-informed neural network; S5, using the temperature fields as boundary conditions for mechanical simulation of the microsystem, obtaining mechanical properties such as stress and strain of the microsystem; and S6, performing electromechanical coupling simulation analysis to analyze the impact of structural deformation on various parameters of electrical performance. The present invention improves the solution accuracy of the neural network by means of an improved adaptive weighting strategy, combines a complete polynomial basis function with the neural network, and introduces an expanded basis function to reduce the state dimensionality, thus reducing computational costs and time, achieving accurate prediction of temperature fields of microsystems at multiple moments, and allowing for computation of the performance of microsystems under electro-thermal-mechanical multi-physics coupling.

Description

A Thermo-Mechanical Coupling Analysis Method for Inertial Microsystems Based on Physics Information Neural Networks

[0001] This application claims priority to Chinese Patent Application No. 2024114175414, filed on October 11, 2024, entitled "A Thermo-Coupling Analysis Method for Inertial Microsystems Based on Physical Information Neural Networks", the entire contents of which are incorporated herein by reference. Technical Field

[0002] This invention relates to the field of inertial microsystems technology, and in particular to a thermo-mechanical coupling analysis method for inertial microsystems based on a physical information neural network. Background Technology

[0003] Inertial microsystems (IMS) are widely used in various fields due to their advantages such as miniaturization, integration, intelligence, low cost, high performance, and mass production. With the continuous development of IMS technology, reliability failure analysis has become a weak link in the further development of microsystem packaging technology. The increased integration of IMS packaging structures makes interconnection issues crucial. The reduction in interconnection size and the increase in the number of layers will lead to an increase in electromagnetic losses, which in turn will cause the internal temperature of the system to rise, causing structural reliability problems. Reliability characterization through traditional physical and experimental methods faces great difficulties, thus urgently requiring reliability analysis and evaluation methods. Therefore, how to accurately present the failure of IMS through simulation and combine it with failure analysis to provide feedback to engineering has always been a hot topic in IMS packaging failure analysis.

[0004] Inertial microsystems (IMS) are subjected to the combined effects of electrical, thermal, and mechanical physical fields during space service, with energy exchange between these fields, making them complex multi-field coupled systems. The multi-physics coupling exacerbates IMS errors and severely impacts performance. Chinese patent CN108920831A discloses a rapid calculation method for the impact of high-temperature ablation of a high-speed aircraft enclosure on antenna electrical performance, but this method only analyzes the thermal field. It fails to consider the engineering application environment of multi-load stress coupling or the mutual influence between thermal forces, leading to inaccurate results. Currently, there is a lack of analysis on the coupling of the three physical fields (electricity, heat, and force) in IMS. Furthermore, most IMS analyses only consider thermal or mechanical simulations, neglecting the harsh operating conditions of space service with multi-physics coupling and the mutual influence between heat, force, and electromagnetic fields. This fails to fully reflect actual operating conditions, resulting in inaccurate analysis results. Therefore, there is an urgent need for multi-physics coupling analysis of IMS to guide and verify IMS product design.

[0005] Summary of the Invention

[0006] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks. This method enables high-precision prediction of the temperature field of inertial microsystems at multiple time moments, calculates the performance of inertial microsystems under electro-thermal-mechanical multi-physics coupling, improves the accuracy and reliability of the solution, and ensures the reliability of inertial microsystems in space service.

[0007] The technical solution of this invention is: a method for thermo-mechanical coupling analysis of inertial microsystems based on physical information neural networks, comprising:

[0008] S1. Based on the space service conditions, set the material parameters and boundary conditions of the inertial microsystem, and establish a thermo-mechanical coupling analysis model of the inertial microsystem;

[0009] S2. Perform electrothermal coupling simulation analysis on the thermo-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each device in the inertial microsystem under working conditions;

[0010] S3. Using the temperature distribution and power loss of each device obtained in step S2 as heat sources, perform thermo-mechanical coupling simulation analysis to obtain the thermal stress distribution of the inertial microsystem.

[0011] S4. Based on the temperature distribution and thermal stress distribution obtained in steps S2 and S3, establish a physical information neural network with position and time as inputs and temperature field at various moments of the inertial microsystem as output. Use the physical information neural network to predict the temperature field of the inertial microsystem at different moments. Specific steps include:

[0012] S41. Experimentally measure the temperature at the point to be measured on the inertial microsystem;

[0013] S42. Using position x and time t as inputs, the complete polynomial coefficients β i As an extended parameter of the physical information neural network, it is related to the weights and biases of the physical information neural network parameters (w). i ,b i The physical information neural network is constructed by combining the physical information, including the temperature values ​​at the measurement points, the governing equations, and the boundary conditions, into its loss function. The Adam adaptive motion estimation algorithm and the inverse rank 2-quasi-Newton method (LBFGS) are used for training and optimization to minimize the loss function, resulting in the complete polynomial coefficients β. i and weights and biases (w) i ,b i );

[0014] S43, Combine the complete polynomial coefficients βi, weights, and biases (w) i ,b i Substituting this into a physical information neural network, we can accurately predict the temperature field of an inertial microsystem at different times.

[0015] S5. Using the temperature field of the inertial microsystem at different times obtained in step S4 as the boundary condition for the mechanical simulation of the inertial microsystem structure, perform mechanical analysis to obtain the mechanical properties of the inertial microsystem structure.

[0016] S6. Feed the mechanical properties obtained in step S5 into the electromagnetic simulation, perform electrical performance simulation based on mechanical properties, analyze the influence of mechanical properties on electrical performance, and obtain the electrical performance of the inertial microsystem.

[0017] Furthermore, the loss function of the physical information neural network is as follows:

[0018] In the formula: W F The heat conduction weighting coefficient, loss F W is the mean square error of the residuals of the governing equation. N This is the weighting coefficient for the heat flux term. W represents the mean square error of the residuals of the boundary heat flux. U N is the weighting coefficient for the temperature term. BCT N RC N represents the number of coordinates of the corresponding nodes. t N represents the number of time points. m The number of measurement points, loss BCT loss RC The loss is the sum of squared residuals at the boundary temperature and the initial temperature, respectively. m The mean square error of the temperature residual at the measuring point. For the predicted temperature value of the temperature field in the measurement point neural network, T m Γ represents the temperature corresponding to the measuring point. m For the boundary of the measuring point, t end This is the termination time of the transient calculation.

[0019] Furthermore, the temperature weighting coefficient W U and the weighting coefficient W of the heat flow term N First, the Adam solver is used for iterative calculation, updating the weight coefficients with each calculation. The weight coefficients obtained after multiple updates are used as the optimal weight coefficients for the inertial microsystem. Then, the LBFGS algorithm is used to optimize the parameters of the physical information neural network to minimize the loss function.

[0020] Furthermore, the temperature weighting coefficient W U and the weighting coefficient W of the heat flow term N The update method is as follows:

[0021] In the formula: l is the number of iterations, and α is the weight coefficient. and These are respectively the temperature weighting coefficients after the l-th iteration. This represents the average value of the temperature loss term during the l-th iteration. and These represent the weighting coefficients of the heat flux term after the l-th iteration. This represents the average value of the heat flow loss term during the l-th iteration.

[0022] Furthermore, in step S43, the complete polynomial coefficients β obtained in step S422 are... i Substituting this into a physical information neural network, specifically: using the complete polynomial coefficients β i The parameters of the temperature field heat source g(x,t) in the physical information neural network are updated using the following formula:

[0023] In the formula: λ is the scaling factor, φ i (x,t) represents the polynomial basis functions, s represents the number of basis functions, and i = 1, 2, ..., s.

[0024] Furthermore, in step S43, the weights and bias values ​​(w) obtained in step S422 are compared... i ,b i Substituting into the physical information neural network, specifically: Substituting into the following formula

[0025] In the formula: x1, x2, and x3 represent the x-axis, y-axis, and z-axis coordinates of the measuring point, respectively, w i b i The unknown parameters that need to be optimized in the neural network model are the weights and biases of the neural network, respectively, and k is the number of layers in the physical information neural network.

[0026] The following formula can be used to predict the temperature field of an inertial microsystem at different times:

[0027] T = L k (z k )oσoL k-1 (z k-1 )o…oσoL1(z1)

[0028] In the formula: o is a combination operator that varies according to the number of hidden layers and neurons; the above formula represents a physical information neural network with a depth of k layers; σ is the Softplus activation function; L k For layer k, z k Let be the parameters of the k-th hidden layer of the neural network.

[0029] Furthermore, in step S2, the electrothermal coupling simulation analysis uses the following heat conduction equation to solve for the temperature distribution of the inertial microsystem.

[0030] In the formula: ρ and c are the density and specific heat capacity of the device material, respectively; k(T1) is the conductivity of the device material as a function of temperature; P is the heating power of the device; T1 is the transient spatial temperature field distribution; h is the convective heat transfer coefficient; T is the temperature of the inertial microsystem; T0 is the initial temperature; t is the time of the measurement point; n is the spatial coordinate; and Γa is the convective heat transfer boundary.

[0031] Furthermore, the thermal stress distribution in the inertial microsystem during step S3 is as follows:

[0032] σ YL =Eε-β(T-T0)

[0033] In the formula, σ YL Let E be the thermal stress on the inertial microsystem, ε be the elastic coefficient, β be the strain of the inertial microsystem, T be the temperature of the inertial microsystem, and T0 be the initial temperature.

[0034] Furthermore, the mechanical properties in step S5 include thermal stress, elastoplastic strain, fatigue life, creep, deformation, fracture, and warpage.

[0035] The present invention also provides a computer program product, which, when executed by a processor, implements the steps of any of the methods described above.

[0036] This invention also provides a thermo-mechanical coupling analysis system for inertial microsystems based on a physical information neural network, comprising:

[0037] The model building module is used to set the material parameters and boundary conditions of the inertial microsystem according to the space service conditions, and to establish a thermo-mechanical coupling analysis model of the inertial microsystem.

[0038] The electrothermal coupling analysis module is used to perform electrothermal coupling simulation analysis on the thermo-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each device in the inertial microsystem under working conditions.

[0039] The thermo-coupling analysis module uses the temperature distribution and power loss of each device as heat sources to perform thermo-coupling simulation analysis and obtain the thermal stress distribution of the inertial microsystem.

[0040] The temperature field prediction module is used to establish a physical information neural network based on temperature and thermal stress distribution, taking position and time as inputs and outputting the temperature field of the inertial microsystem at various moments. It takes position x and time t as inputs and the complete polynomial coefficients β... i As an extended parameter of the physical information neural network, it is related to the weights and biases of the physical information neural network parameters (w). i ,b iThe loss function of the physical information neural network is constructed using these parameters as outputs, incorporating physical information, including temperature values ​​at measurement points of the inertial microsystem obtained through experimental measurements, as well as the governing equations and boundary conditions. The network is trained and optimized using the adaptive motion estimation algorithm Adam and the inverse rank two-quasi-Newton method (LBFGS) to minimize the loss function, resulting in complete polynomial coefficients βi and weights and biases (w). i ,b i The obtained complete polynomial coefficients βi, weights, and biases (w) i ,b i Substituting the data into a physical information neural network, we can accurately predict the temperature field of an inertial microsystem at different times using the physical information neural network.

[0041] The mechanical performance analysis module is used to take the temperature field of the inertial microsystem at different times as the boundary condition for the mechanical simulation of the inertial microsystem structure, perform mechanical analysis, and obtain the mechanical performance of the inertial microsystem structure.

[0042] The electrical performance analysis module is used to feed back the mechanical properties of the inertial microsystem structure to the electromagnetic simulation, perform electrical performance simulation based on mechanical properties, analyze the influence of mechanical properties on electrical performance, and obtain the electrical performance of the inertial microsystem.

[0043] The advantages of this invention compared to the prior art are:

[0044] This invention proposes a thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks. By improving the adaptive weighting strategy, the solution accuracy of the neural network is enhanced. The complete polynomial basis functions are combined with the neural network, and the expanded basis functions are introduced to reduce the state dimension, thereby achieving high-precision prediction of the temperature field of the microsystem at multiple time points. This enables accurate prediction of the microsystem performance under electro-thermal-mechanical multi-physics coupling, ensuring the reliability of the microsystem in space service. Attached Figure Description

[0045] Figure 1 is a flowchart of the thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to the present invention;

[0046] Figure 2 is a structural framework diagram of the physical information neural network of the present invention. Detailed Implementation

[0047] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0048] This invention provides a method for thermo-mechanical coupling analysis of inertial microsystems based on physical information neural networks, as shown in Figure 1. The steps include:

[0049] S1. Based on the space service conditions, set the material parameters and boundary conditions of the inertial microsystem, and establish a thermo-mechanical coupling analysis model of the inertial microsystem;

[0050] S2. Perform electrothermal coupling simulation analysis on the thermo-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each device in the inertial microsystem under working conditions;

[0051] In one possible implementation, the electrothermal coupling simulation analysis in step S2 solves for the temperature distribution of the microsystem using the following heat conduction equation.

[0052] In the formula: ρ and c are the density and specific heat capacity of the device material, respectively; k(T1) is the conductivity of the device material as a function of temperature; P is the heating power of the device; T1 is the transient spatial temperature field distribution; h is the convective heat transfer coefficient; T is the temperature of the inertial microsystem; T0 is the initial temperature; n is the spatial coordinate; and Γa is the convective heat transfer boundary.

[0053] S3. Using the temperature distribution and power loss of each device obtained in step S2 as heat sources, perform thermo-mechanical coupling simulation analysis to obtain the thermal stress distribution of the inertial microsystem.

[0054] In one possible implementation, the thermal stress distribution in the inertial microsystem during step S3 is as follows:

[0055] σ YL =Eε-β(T-T0)

[0056] In the formula, σ YL Let E be the thermal stress on the inertial microsystem, ε be the elastic coefficient, β be the strain of the inertial microsystem, T be the temperature of the inertial microsystem, and T0 be the initial temperature.

[0057] S4. Based on the temperature distribution and thermal stress distribution obtained in steps S2 and S3, establish a physical information neural network with position and time as inputs and temperature field at various moments of the inertial microsystem as output. The physical information neural network structure is shown in Figure 2. The physical information neural network is used to predict the temperature field of the inertial microsystem at different moments. Specific steps include:

[0058] S41. Experimentally measure the temperature at the point to be measured on the inertial microsystem;

[0059] S42. Calculate the coefficients β of the complete polynomial. i and weights and biases (w) i ,b i )

[0060] S421. Taking position x and time t as inputs, the complete polynomial coefficients β iAs an extended parameter of the physical information neural network, it is related to the weights and biases of the physical information neural network parameters (w). i ,b i These are used together as output; the loss function of the physical information neural network is constructed by incorporating physical information, including the temperature value of the measuring point, the governing equation, and the boundary conditions, into the loss function;

[0061] The loss function for a physical information neural network is as follows:

[0062] In the formula: W F The heat conduction weighting coefficient, loss F W is the mean square error of the residuals of the governing equation. N This is the weighting coefficient for the heat flux term. W represents the mean square error of the residuals of the boundary heat flux. U N is the weighting coefficient for the temperature term. BCT N RC N represents the number of coordinates of the corresponding nodes. t N represents the number of time points. m The number of measurement points, loss BCT loss RC The loss is the sum of squared residuals at the boundary temperature and the initial temperature, respectively. m The mean square error of the temperature residual at the measuring point. For the predicted temperature value of the temperature field in the measurement point neural network, T m Γ represents the temperature corresponding to the measuring point. m For the boundary of the measuring point, t end This is the termination time of the transient calculation.

[0063] S422. The Adam adaptive motion estimation algorithm and the inverse rank two-quasi-Newton method (LBFGS) are used for training and optimization to minimize the loss function, thereby obtaining the complete polynomial coefficients βi and the weights and biases (w). i ,b i );

[0064] In step S422, the temperature weight coefficient W is used in the weight coefficients of the neural network loss function. U and the weighting coefficient W of the heat flow term N The Adam solver performs iterative calculations, updating the weight coefficients with each calculation. The weight coefficients obtained after multiple updates are used as the optimal weight coefficients for the inertial microsystem. The LBFGS algorithm is then used to optimize the neural network parameters to minimize the loss function.

[0065] Temperature weighting coefficient W U and the weighting coefficient W of the heat flow term N The update method is as follows:

[0066] In the formula, l is the number of iterations, and α is the weight coefficient. and These are respectively the temperature weighting coefficients after the l-th iteration. This represents the average value of the temperature loss term during the l-th iteration. and These represent the weighting coefficients of the heat flux term after the l-th iteration. This represents the average value of the heat flow loss term during the l-th iteration.

[0067] S43, Combine the complete polynomial coefficients βi, weights, and biases (w) i ,b i Substituting this into a physical information neural network, we can accurately predict the temperature field of the microsystem at different times.

[0068] Using the complete polynomial coefficients β obtained in step S422 i Update the parameters of the temperature field heat source g(x,t) in the physical information neural network as follows:

[0069] In the formula: λ is the scaling factor, φ i (x,t) represents the polynomial basis functions, s represents the number of basis functions, and i = 1, 2, ..., s.

[0070] By introducing polynomial basis functions to reduce the dimensionality of the temperature field state in the neural network, high-precision prediction of the temperature field of the microsystem at multiple time points can be achieved.

[0071] The weights and biases (w) obtained in step S422 are compared. i ,b i Substitution formula:

[0072] In the formula: x1, x2, and x3 represent the x-axis, y-axis, and z-axis coordinates of the measuring point, respectively; t is the measuring time; w i b i The unknown parameters that need to be optimized in the neural network model are the weights and biases of the neural network, respectively, and k is the number of layers in the physical information neural network.

[0073] The following formula can be used to predict the temperature field of a microsystem at different times:

[0074] T = L k (z k )oσoL k-1 (z k-1 )o…oσoL1(z1)

[0075] In the formula, o is a combination operator that varies according to the number of hidden layers and neurons. The above formula represents a physical information neural network with a depth of k layers. σ is the Softplus activation function, and L... k For layer k, z k Let be the parameters of the k-th hidden layer of the neural network.

[0076] S5. Using the temperature field of the microsystem at different times obtained in step S4 as the boundary condition for the mechanical simulation of the inertial microsystem structure, perform mechanical analysis to obtain the mechanical properties of the microsystem structure.

[0077] The mechanical properties in step S5 include thermal stress, elastoplastic strain, fatigue life, creep, deformation, fracture, and warpage.

[0078] S6. Feed the mechanical properties obtained in step S5 into the electromagnetic simulation to perform electrical performance simulation based on the mechanical properties, analyze the influence of mechanical properties on electrical performance, and obtain the electrical performance of the microsystem.

[0079] The present invention also provides a computer program product, which, when executed by a processor, implements the steps of any of the methods described above.

[0080] This invention also provides a thermo-mechanical coupling analysis system for inertial microsystems based on a physical information neural network, comprising:

[0081] The model building module is used to set the material parameters and boundary conditions of the inertial microsystem according to the space service conditions, and to establish a thermo-mechanical coupling analysis model of the inertial microsystem.

[0082] The electrothermal coupling analysis module is used to perform electrothermal coupling simulation analysis on the thermo-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each device in the inertial microsystem under working conditions.

[0083] The thermo-coupling analysis module uses the temperature distribution and power loss of each device as heat sources to perform thermo-coupling simulation analysis and obtain the thermal stress distribution of the inertial microsystem.

[0084] The temperature field prediction module is used to establish a physical information neural network based on temperature and thermal stress distribution, taking position and time as inputs and outputting the temperature field of the inertial microsystem at various moments. It takes position x and time t as inputs and the complete polynomial coefficients β... i As an extended parameter of the physical information neural network, it is related to the weights and biases of the physical information neural network parameters (w). i ,b iThe loss function of the physical information neural network is constructed using these parameters as outputs, incorporating physical information, including temperature values ​​at measurement points of the inertial microsystem obtained through experimental measurements, as well as the governing equations and boundary conditions. The network is trained and optimized using the adaptive motion estimation algorithm Adam and the inverse rank two-quasi-Newton method (LBFGS) to minimize the loss function, resulting in complete polynomial coefficients βi and weights and biases (w). i ,b i The obtained complete polynomial coefficients βi, weights, and biases (w) i ,b i Substituting the data into a physical information neural network, we can accurately predict the temperature field of an inertial microsystem at different times using the physical information neural network.

[0085] The mechanical performance analysis module is used to take the temperature field of the inertial microsystem at different times as the boundary condition for the mechanical simulation of the inertial microsystem structure, perform mechanical analysis, and obtain the mechanical performance of the inertial microsystem structure.

[0086] The electrical performance analysis module is used to feed back the mechanical properties of the inertial microsystem structure to the electromagnetic simulation, perform electrical performance simulation based on mechanical properties, analyze the influence of mechanical properties on electrical performance, and obtain the electrical performance of the inertial microsystem.

[0087] The specific functions of each module are implemented according to the methods described above.

[0088] It is understood that this invention has been described through embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of this invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific circumstances without departing from the spirit and scope of this invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are protected by this invention.

[0089] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for thermo-mechanical coupling analysis of inertial microsystems based on physical information neural networks, characterized in that, include: S1. Based on the space service conditions, set the material parameters and boundary conditions of the inertial microsystem, and establish a thermo-mechanical coupling analysis model of the inertial microsystem; S2. Perform electrothermal coupling simulation analysis on the thermo-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each device in the inertial microsystem under working conditions; S3. Using the temperature distribution and power loss of each device as heat sources, perform thermo-mechanical coupling simulation analysis to obtain the thermal stress distribution of the inertial microsystem. S4. Based on the temperature distribution and thermal stress distribution obtained in steps S2 and S3, establish a physical information neural network with position and time as inputs and temperature field at various moments of the inertial microsystem as output. Use the physical information neural network to predict the temperature field of the inertial microsystem at different moments. Specific steps include: S41. Experimentally measure the temperature at the point to be measured on the inertial microsystem; S42. Using position x and time t as inputs, the complete polynomial coefficients β i As an extended parameter of the physical information neural network, it is related to the weights and biases of the physical information neural network parameters (w). i ,b i The physical information neural network is constructed by combining the physical information, including the temperature values ​​at the measurement points, the governing equations, and the boundary conditions, into its loss function. The Adam adaptive motion estimation algorithm and the inverse rank 2-quasi-Newton method (LBFGS) are used for training and optimization to minimize the loss function, resulting in the complete polynomial coefficients β. i and weights and biases (w) i ,b i ); S43. Obtain the complete polynomial coefficients βi, weights, and biases (w). i ,b i Substituting this into a physical information neural network, we can accurately predict the temperature field of an inertial microsystem at different times. S5. Using the temperature field of the inertial microsystem at different times obtained in step S4 as the boundary condition for the mechanical simulation of the inertial microsystem structure, perform mechanical analysis to obtain the mechanical properties of the inertial microsystem structure. S6. Feed the mechanical properties obtained in step S5 into the electromagnetic simulation, perform electrical performance simulation based on mechanical properties, analyze the influence of mechanical properties on electrical performance, and obtain the electrical performance of the inertial microsystem.

2. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 1, characterized in that: The loss function for a physical information neural network is as follows: In the formula: W F The heat conduction weighting coefficient, loss F W is the mean square error of the residuals of the governing equation. N The weighting coefficients for the heat flux term, loss BCq W represents the mean square error of the residuals of the boundary heat flux. U N is the weighting coefficient for the temperature term. BCT N RC N represents the number of coordinates of the corresponding nodes. t N represents the number of time points. m The number of measurement points, loss BCT loss RC The loss is the sum of squared residuals at the boundary temperature and the initial temperature, respectively. m The mean square error of the temperature residual at the measuring point. For the predicted temperature value of the temperature field in the measurement point neural network, T m Γ represents the temperature corresponding to the measuring point. m For the boundary of the measuring point, t end This is the termination time of the transient calculation.

3. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 2, characterized in that: For the temperature weighting coefficient W U and the weighting coefficient W of the heat flow term N First, the Adam solver is used for iterative calculation, updating the weight coefficients with each calculation. The weight coefficients obtained after multiple updates are used as the optimal weight coefficients for the inertial microsystem. Then, the LBFGS algorithm is used to optimize the parameters of the physical information neural network to minimize the loss function.

4. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 3, characterized in that: Temperature weighting coefficient W U and the weighting coefficient W of the heat flow term N The update method is as follows: In the formula: l is the number of iterations, and α is the weight coefficient. and These are respectively the temperature weighting coefficients after the l-th iteration. This represents the average value of the temperature loss term during the l-th iteration. and These represent the weighting coefficients of the heat flux term after the l-th iteration. This represents the average value of the heat flow loss term during the l-th iteration.

5. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 1, characterized in that: The obtained complete polynomial coefficients β i Substituting this into a physical information neural network, specifically: using the complete polynomial coefficients β i The parameters of the temperature field heat source g(x,t) in the physical information neural network are updated using the following formula: In the formula: λ is the scaling factor, φ i (x,t) represents the polynomial basis functions, s represents the number of basis functions, and i = 1, 2, ..., s.

6. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 1, characterized in that: The obtained weights and biases (w) i ,b i Substituting into the physical information neural network, specifically: Substituting into the following formula In the formula: x1, x2, and x3 represent the x-axis, y-axis, and z-axis coordinates of the measuring point, respectively, w i b i The unknown parameters that need to be optimized in the neural network model are the weights and biases of the neural network, respectively, and k is the number of layers in the physical information neural network. The following formula can be used to predict the temperature field of an inertial microsystem at different times: T=L k (z k )oσoL k-1 (z k-1 )o…oσoL1(z1) In the formula: o is a combination operator that varies according to the number of hidden layers and neurons; the above formula represents a physical information neural network with a depth of k layers; σ is the Softplus activation function; L k For layer k, z k Let be the parameters of the k-th hidden layer of the neural network.

7. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 1, characterized in that: An electrothermal coupling simulation analysis was performed on the thermo-mechanical coupling analysis model of the inertial microsystem. The temperature distribution of the inertial microsystem was solved using the following heat conduction equation. In the formula: ρ and c are the density and specific heat capacity of the device material, respectively; k(T1) is the conductivity of the device material as a function of temperature; P is the heating power of the device; T1 is the transient spatial temperature field distribution; and h is the convective heat transfer. The coefficients are: T is the temperature of the inertial microsystem, T0 is the initial temperature, t is the time at the measurement point, n is the spatial coordinate, and Γa is the convective heat transfer boundary.

8. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 1, characterized in that: The thermal stress distribution of the inertial microsystem is: σ YL =Eε-β(T-T0) In the formula, σ YL Let E be the thermal stress on the inertial microsystem, ε be the elastic coefficient, β be the strain of the inertial microsystem, T be the temperature of the inertial microsystem, and T0 be the initial temperature.

9. The thermo-mechanical coupling analysis method for inertial microsystems based on physical information neural networks according to claim 1, characterized in that: The mechanical properties of inertial microsystem structures include thermal stress, elastoplastic strain, fatigue life, creep, deformation, fracture, and warpage.

10. A computer program product, characterized in that: When the computer program product is executed by a processor, it implements the steps of the method as described in any one of claims 1-9.

11. A thermo-mechanical coupling analysis system for inertial microsystems based on a physical information neural network, characterized in that, include: The model building module is used to set the material parameters and boundary conditions of the inertial microsystem according to the space service conditions, and to establish a thermo-mechanical coupling analysis model of the inertial microsystem. The electrothermal coupling analysis module is used to perform electrothermal coupling simulation analysis on the thermo-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each device in the inertial microsystem under working conditions. The thermo-coupling analysis module uses the temperature distribution and power loss of each device as heat sources to perform thermo-coupling simulation analysis and obtain the thermal stress distribution of the inertial microsystem. The temperature field prediction module is used to establish a physical information neural network based on temperature and thermal stress distribution, taking position and time as inputs and outputting the temperature field of the inertial microsystem at various moments. It takes position x and time t as inputs and the complete polynomial coefficients β... i As an extended parameter of the physical information neural network, it is related to the weights and biases of the physical information neural network parameters (w). i ,b i Together, they form the output of a loss function for a physical information neural network, incorporating physical information, including temperature values ​​at measurement points of the inertial microsystem obtained through experimental measurements, as well as governing equations and boundary conditions; through adaptive... The Adam motion estimation algorithm and the inverse rank 2-quasi-Newton method (LBFGS) are used for training and optimization to minimize the loss function, thereby obtaining the complete polynomial coefficients βi and the weights and biases (w). i ,b i The obtained complete polynomial coefficients βi, weights, and biases (w) i ,b i Substituting the data into a physical information neural network, we can accurately predict the temperature field of an inertial microsystem at different times using the physical information neural network. The mechanical performance analysis module is used to take the temperature field of the inertial microsystem at different times as the boundary condition for the mechanical simulation of the inertial microsystem structure, perform mechanical analysis, and obtain the mechanical performance of the inertial microsystem structure. The electrical performance analysis module is used to feed back the mechanical properties of the inertial microsystem structure to the electromagnetic simulation, perform electrical performance simulation based on mechanical properties, analyze the influence of mechanical properties on electrical performance, and obtain the electrical performance of the inertial microsystem.

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