A prediction decision method and system based on outer layer physical residual compensation correction

Abstract

The application relates to the technical field of prediction decision of physical field coupling characteristics, and discloses a prediction decision method and system based on outer layer physical residual compensation correction. The method comprises the following steps: constructing a PINN-DRL coupling model and collecting real-time observation data through an outer layer physical residual compensation network; the outer layer physical residual compensation network compensates for a calculation state compensation amount, an action compensation amount and a constraint reward weight compensation amount and injects the PINN-DRL coupling model; the PINN model, the DRL model and the outer layer physical residual compensation network are separately pre-trained through historical data; joint alternating training is carried out; and prediction decision is carried out based on the trained PINN-DRL coupling model and the outer layer physical residual compensation network. The application can simultaneously process physical prediction residual and action execution residual, and improves the accuracy, stability and robustness of physical field prediction decision.

Description

Technical Field

[0001] This invention relates to the field of prediction and decision-making technology based on multiphysics coupling characteristics, specifically a prediction and decision-making method and system based on outer physical residual compensation correction. Background Technology

[0002] Physics-Informed Neural Networks (PINNs) solve complex partial differential equations by embedding physical laws into the neural network loss function, enabling a fusion of data-driven and physics-driven approaches. In complex physical field applications such as laser-guided lightning, PINNs can be used to build environmental simulators, outputting predictions of electric fields, cloud charges, and potential energy release pathways.

[0003] Deep Reinforcement Learning (DRL) is an important method for handling complex decision-making problems. Combining PINN with DRL can form an integrated "predictive decision-making" framework: PINN provides the predicted physics field, and DRL outputs control actions based on the predicted physics field.

[0004] However, directly combining PINN with DRL presents a fundamental problem: the instability of the two-way coupling between prediction and decision-making. DRL decisions rely on the PINN physical field prediction results, and prediction errors can cause decision actions to deviate from the optimal state. At the same time, the actual execution of decision actions changes the physical field state, and the deviation in action execution, in turn, affects subsequent predictions. This causes prediction errors and decision errors to amplify each other in the interaction, ultimately resulting in inaccurate predictions, decision failures, and closed-loop control instability.

[0005] Existing technologies mainly employ two types of methods: one is to improve the PINN structure to enhance the accuracy of physical prediction; the other is to perform posterior correction on the prediction results through an error correction model. However, most of these methods are only optimized within a single prediction task or a single decision task, and fail to address both physical prediction residuals and action execution residuals simultaneously from a mechanistic perspective. Summary of the Invention

[0006] To address the technical problems existing in the prior art, this invention provides a prediction and decision-making method and system based on outer physical residual compensation and correction, which can simultaneously process physical prediction residuals and action execution residuals, thereby improving the accuracy, stability and robustness of physical field prediction and decision-making.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention discloses a prediction and decision-making method based on outer physical residual compensation correction, which constructs a PINN-DRL coupled model and an outer physical residual compensation network, and further includes the following steps: S1, PINN obtains the multi-source state at the current time t. The corrected motion after outer motion compensation at the previous time t-1 Output the predicted physics field at the current moment. and potential pathway probability ; S2, DRL are based on multi-source states Predicting physical fields and potential pathway probability Output expected action ; S3. Collect the execution feedback from the previous moment and the observation data from the current moment, including the current physical field state. The actual action performed at the previous moment Current real physical field response and target effect response ; S4, Outer Physical Residual Compensation Network based on predicted physical field Potential pathway probability Expected Action Using the observation data at the current moment, calculate the state compensation, action compensation, and constraint reward weight compensation and inject them into the PINN-DRL coupled model; S5. First, pre-train the PINN model, DRL model, and outer physical residual compensation network separately using historical data; then perform joint alternating training, first fixing the parameters of the PINN-DRL coupled model to train the outer physical residual compensation network, then fixing the parameters of the outer physical residual compensation network to update the parameters of the PINN-DRL coupled model; repeat the joint alternating training until training is complete. S6. Make prediction decisions based on the trained PINN-DRL coupled model and the outer physical residual compensation network.

[0008] Preferably, in S1: PINN environment simulator is Its output includes predicted physical fields. and potential pathway probability : The training loss function of the PINN model includes data fitting loss, physical constraint loss, boundary condition loss, and initial condition loss. The total training loss is obtained by weighted fusion of these losses.

[0009] Preferably, the DRL model in S2 adopts an Actor-Critic structure, and the Actor network strategy is as follows: The Critic network value function is ; in, Indicates the parameters of the Actor network; This indicates the fusion state of the DRL; 'a' represents the policy action generated by the Actor policy in this fusion state. Indicates the parameters of the Critic network; DRL based on the current fusion status Expected output action: ; Where Enc(·) represents the conditional coding function; Objective function using SAC strategy: ; ; In the formula, This represents the fusion state of the DRL at time t. This represents the strategy action generated by the Actor in this fusion state; make The actual control command is denoted as ; Indicates an immediate reward for environmental feedback; This represents the experience replay pool; For temperature parameters; Discount factor; This represents the action value estimated by the current Critic network; Let Actor be the policy loss function; For the Critic value loss function; Represents the mathematical expectation; This is the fusion state for the next moment; In order to be in The action obtained from downsampling.

[0010] Preferably, S4 specifically includes: S401. Construct a unified residual vector : ; in This represents the residual of environmental prediction. Indicates the action execution residual. Represents the physical constraint consistency residual. Indicates the residual of the target effect; S402, unify the residual vector Input the residual decomposition encoder and perform source, scale, and mode decomposition respectively to obtain compressed features. ,Will Input the physical confidence gating network and the three-way compensation head. The physical confidence gating network calculates the gating coefficients for state compensation, action compensation, and constraint reward weight compensation; the three-way compensation head calculates the basic compensation. S403. Calculate the state compensation amount, action compensation amount, and constraint reward weight compensation amount based on the gating coefficients and basic compensation of state compensation, action compensation, constraint reward weight compensation, and basic compensation. S404. Inject the state compensation amount into the PINN model, and inject the action compensation amount and constraint reward weight compensation amount into the DRL model to complete the decoupling correction of the PINN-DRL coupled model.

[0011] Preferably, in S401: ; ; ; ; in, For physical constraint operators; b(t) represents boundary conditions or safety thresholds; The desired control target preset by the system; This indicates the response to the target effect.

[0012] Preferably, the gating coefficients for calculating state compensation, action compensation, and constraint reward weight compensation include: ; ; in, The calculated overall physical confidence score; Indicated by Let be the residual square norm for the weights; For observing quality factors; This represents scalar multiplication. This indicates the concatenation of eigenvectors; The learnable weight matrix for the gated network layer. This is the bias vector of the gated network layer; The Sigmoid activation function is used to map the gating coefficients to the range [0,1]. Indicates model uncertainty. For residual scaling parameters, This is the residual weighting matrix; The state compensation gating coefficient. The motion compensation gating coefficient, To constrain the reward weight compensation gating coefficient.

[0013] Preferably, the will The calculation of basic compensation by inputting three compensation heads includes: Set basic compensation for: ; in, This represents the vector transpose operation, which converts a row vector into a column vector. For state compensation, The basic compensation for motion compensation, The basic compensation for constraining reward weights; After injecting compensation into the PINN-DRL coupled model, the residual vector is unified. The first-order linearization near the current point is: ; In the formula, This represents the expected first-order approximate new residual vector after the injection of compensation. for The partial derivatives; ; in, It is a partial differential operator; This refers to the system status; To perform the action; Weighting coefficients for rewards or physical constraints; The search for the optimal compensation amount is transformed into a weighted least squares problem with regularization: ; In the formula, This indicates the solution that minimizes the loss function. ; For a given positive definite or positive semi-definite diagonal weighted matrix; It is a weighted L2 norm; Let be the regularization penalty coefficient, and satisfy . ; The standard L2 norm squared; Represents vector product; Differentiate the above equation and set the derivative to zero: Obtain the outer optimal compensation operator Closed expression: ; in, An identity matrix that matches the dimensions of the variables; Let be the weighted Jacobian Gram matrix, and be the Gauss-Newton approximation Hessian term of the weighted least squares objective with respect to the compensation variables; when When the matrix is ​​a positive semi-definite matrix, add and back, It is a positive definite matrix, thus guaranteeing that the closed-form solution is unique and the matrix is ​​invertible.

[0014] By neural network right Perform approximate learning: ; in, The model uncertainty is calculated in real time using the variance of the outputs of multiple base networks in ensemble learning or the Monte Carlo random inactivation method. (Subscript) This represents the learnable parameters of a neural network.

[0015] Preferably, it also includes a composite loss function for constructing the outer physical residual compensation network: ; in, and These represent the predicted output values ​​of the outer physical residual compensation network for environmental residuals and motion residuals, respectively. , , , These are the corresponding loss weight coefficients, used to balance the magnitudes of various losses; MSE(·) is the mean squared error loss function; This is a coupling suppression term used to characterize the interaction between the prediction residual and the action residual, calculated as follows: ; in, Denotes the Frobenius norm of a matrix. Describes the L2 norm of a vector. The covariance matrix representing the environmental prediction residuals and the action execution residuals; This represents the local Jacobian matrix of the physics prediction for the action.

[0016] This invention also proposes a predictive decision system based on outer layer physical residual compensation correction, comprising: The building blocks are used to construct the PINN-DRL coupled model and the outer physical residual compensation network; The PINN model is used to obtain the multi-source state at the current time t. The correction action actually issued at the previous time t-1 after outer layer motion compensation and output predicted physics field and potential pathway probability ; DRL models are used to determine multi-source states. Predicting physical fields and potential pathway probability Output expected action ; The acquisition module is used to collect the execution feedback from the previous moment and the current real-time observation data, including the current physical field state. The actual action performed at the previous moment Real physical field response and target effect response ; The outer physical residual compensation network is used to calculate the predicted physical field. Potential pathway probability Expected Action Using the observation data at the current moment, calculate the state compensation, action compensation, and constraint reward weight compensation and inject them into the PINN-DRL coupled model; The training module is used to pre-train the PINN model, DRL model, and outer physical residual compensation network separately using historical data; then, joint alternating training is performed, first fixing the parameters of the PINN-DRL coupled model to train the outer physical residual compensation network, then fixing the parameters of the outer physical residual compensation network to update the parameters of the PINN-DRL coupled model; the joint alternating training is repeated until training is complete. The execution module makes prediction decisions based on the trained PINN-DRL coupled model and the outer physical residual compensation network.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) The present invention can reduce the mutual amplification of prediction error and decision error in closed-loop interaction, improve the accuracy, stability and robustness of prediction and decision collaborative control in complex physical environment, and is applicable to strong nonlinear multi-physics field scenarios such as laser lightning potential energy release path regulation.

[0018] (2) The present invention can dynamically adjust the compensation intensity according to the residual amplitude, model uncertainty and observation quality.

[0019] (3) The present invention adopts an alternating optimization strategy to synchronously update the parameters of the PINN model, DRL model and outer physical residual compensation network. During the execution phase, at each decision time step, PINN outputs the predicted state, DRL outputs the expected action, and the outer network estimates the residual and generates the compensation amount based on real-time observation and execution feedback, so that the system can adaptively correct itself in the dynamic environment. Attached Figure Description

[0020] Figure 1 This is a flowchart of the prediction and decision-making method based on outer layer physical residual compensation correction proposed in this embodiment of the invention.

[0021] Figure 2 This is a block diagram of the predictive decision system structure based on the outer physical residual compensation and correction mechanism proposed in this embodiment of the invention.

[0022] Figure 3 This is a schematic diagram illustrating the application deployment of laser-guided lightning in an embodiment of the present invention. Figure 4 This is a comparison chart of the overall performance of different methods proposed in the embodiments of the present invention; Figure 4 The horizontal axis represents the comparison method, and the vertical axis represents the corresponding performance index value. The six sub-graphs correspond to the success rate, average reward, average potential path formation probability, physical field prediction mean square error, action execution mean square error, and physical constraint violation degree, respectively. Figure 5 This is a graph showing the probability change of potential pathway formation during a typical regulation process proposed in an embodiment of the present invention. Figure 5 The horizontal axis represents the time step, and the vertical axis represents the probability of potential pathway formation. Different curves correspond to different comparison methods. Figure 6 The figure shows the convergence curves of the training loss of the prediction model, decision model, and outer physical residual compensation network proposed in this embodiment of the invention. Figure 6 The horizontal axis represents the number of training epochs, and the vertical axis represents the loss value. Each curve corresponds to the training loss of the PINN environment simulator, the Actor / Critic network in different comparison methods, and the outer physical residual compensation network. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Example 1 Please see Figure 1 This embodiment provides a predictive decision-making method based on outer physical residual compensation correction, including constructing a PINN-DRL coupled model and an outer physical residual compensation network, and also includes the following steps: S1, PINN obtains the multi-source state at the current time t. The correction action actually issued after outer action compensation at the previous decision time t-1. Output the predicted physics field at the current moment. and potential pathway probability Where t represents the current decision time, and t-1 represents the previous decision time; In this embodiment, the PINN environment simulator is Its output includes predicted physical fields. and potential pathway probability The predicted physical field and path probability will subsequently serve as the state input for the deep reinforcement learning controller of the DRL model.

[0025] ; The training loss function of the PINN model includes data fitting loss, physical constraint loss, boundary condition loss, and initial condition loss, denoted as: ; in, This represents the fitting loss of the observed data. Represents the residual loss of the physical equations. Indicates boundary condition loss. Represents the initial condition loss. , , For the corresponding weights.

[0026] When this application is used in laser-guided stun, the physical constraint layer may at least include the charge conservation equation, Poisson's equation, fluid / turbulent transport equation, plasma transport equation, and boundary condition constraints: ; ; ; ; Where ρ is the charge density and J is the current density. Let D be the charge source term, D be the electric displacement vector, and E be the electric field intensity. Let u be the electric potential, u be the flow velocity, and p be the pressure. Let ν be the air density and ν be the kinematic viscosity. For electron density, For electron mobility, Where is the diffusion coefficient. and These represent the ionization source term and the composite loss term, respectively.

[0027] S2, DRL are based on multi-source states Predicting physical fields and potential pathway probability Output expected action .

[0028] In detail, the DRL model can adopt an Actor-Critic structure, and the Actor network strategy is as follows: The Critic network value function is ; DRL based on the current fusion status Expected output action:

[0029] Where Enc(·) represents the conditional coding function; for continuous control tasks, the SAC policy objective function is adopted: ; ; In the formula, and They represent Multi-source states and expected actions at any given moment; Indicates an immediate reward for environmental feedback; This represents the experience replay pool; Temperature parameter, used to determine the extent of exploration of dynamic adjustment strategies; Discount factor; This represents the action value estimated by the current Critic network, while The action value estimated by the target Critic network can improve training stability.

[0030] S3. Collect the execution feedback from the previous moment and the observation data from the current moment, including the current physical field state. Actual actions taken in the previous decision-making cycle Current real physical field response and target effect response ; In this embodiment, the current physical field state can be collected in real time by using multi-source sensors deployed in the physical system. Actual actions taken in the previous decision-making cycle Real physical field response and target effect response .

[0031] The state evolution of a real physical system can be written as: ; in, A function representing the evolution of the unknown real state of a real physical system; This represents the inherent state evolution noise of the physical system and the noise from the observation sensors.

[0032] There is an execution error between the actual action and the expected action: ; in, This refers to the physical hardware execution error generated when the actuator (such as a laser-controlled gimbal) actually performs the desired action.

[0033] S4, Outer Physical Residual Compensation Network based on predicted physical field Potential pathway probability Expected Action Using the observation data at the current moment, calculate the state compensation, action compensation, and constraint reward weight compensation and inject them into the PINN-DRL coupled model.

[0034] The outer physical residual compensation network learns two types of core error signals: first, physical prediction residuals, which characterize the deviation between the PINN-predicted physical field and the actual observed physical field; and second, action execution residuals, which characterize the deviation between the DRL's expected action and the actuator's actual action. In addition, physical constraint consistency residuals and target effect residuals are introduced to ensure the physical interpretability of the compensation direction.

[0035] An outer-layer physical residual compensation network is embedded into the PINN-DRL coupled model to form an outer-loop supervised correction structure. The outer-layer network outputs state compensation, action compensation, and constraint reward weight compensation, which are then injected into the PINN environment simulator, the DRL action output terminal, and the reward function / physical constraint module, respectively, for residual correction.

[0036] S401. Construct a unified residual vector : ; in This represents the residual of environmental prediction. Indicates the action execution residual. Represents the physical constraint consistency residual. This represents the residual of the target effect. Where: ; ; ; ; in, Represents the actual physical field response; Indicates the prediction of physical fields; This indicates the actual actions taken in the previous decision-making cycle; Indicates the previous decision moment The actual correction action issued after outer layer motion compensation; For physical constraint operators; b(t) represents boundary conditions or safety thresholds; Indicates the desired target output; Indicates the target effect response. The desired control target preset by the system.

[0037] The response of the real physical field target effect (such as whether a lightning channel or discharge current amplitude was actually successfully triggered) is collected in real time by multi-source observation equipment (such as optical / lightning location equipment, electric field meter array, etc.). The system has a preset desired control target (such as the target current amplitude or the coordinates of a specified directional discharge channel). The difference between the two is the target effect residual.

[0038] S402, unify the residual vector Input the residual decomposition encoder and perform source, scale, and mode decomposition respectively to obtain compressed features. ,Will Input the physical confidence gating network and the three-way compensation head. The physical confidence gating network calculates the gating coefficients for state compensation, action compensation, and constraint reward weight compensation; the three-way compensation head calculates the basic compensation. Unify residual vector Input the residual decomposition encoder and perform source, scale, and mode decomposition respectively to obtain compressed features. ; ; ; in, The feature vector representing the source of the error; The feature vector is the error scale. This represents the eigenvectors of the error modes; , , These are source decomposition, scale decomposition, and mode decomposition encoders, respectively, and Φ(·) is the fusion mapping; Indicates through fusion mapping The fusion residual feature representation obtained after splicing and combining.

[0039] Will Input the physical confidence gating network and calculate the gating coefficients for state compensation, action compensation, and constraint reward weight compensation; then... Input the three compensation heads and calculate the basic compensation.

[0040] The gating coefficients for calculating state compensation, action compensation, and constraint reward weight compensation include: ; ; in, The calculated overall physical confidence score; Indicated by The residual vector is a quadratic form of the weights; To observe the quality factor, This represents scalar multiplication. This indicates the concatenation of eigenvectors; The learnable weight matrix for the gated network layer. This is the bias vector of the gated network layer; The Sigmoid activation function is used to map the gating coefficients to the range [0,1]. Indicates model uncertainty. Indicates the observation quality factor. For residual scaling parameters, This is the residual weighting matrix; For state compensation gating coefficients; The motion compensation gating coefficient; To constrain the gating coefficient of reward weight compensation.

[0041] The above two formulas allow for dynamic adjustment of the compensation intensity based on residual amplitude, model uncertainty, and observation quality.

[0042] Will The calculation of basic compensation by inputting three compensation heads includes: Let the outer compensation vector be: ; After injecting compensation into the PINN-DRL coupled model, the residual vector is unified. The first-order linearization near the current point is: ; In the formula, This represents the approximate first-order new residual vector that the system is expected to reach after the injection of compensation. ; Finding the optimal compensation amount can be transformed into a weighted least squares problem with regularization: ; In the formula, A positive definite or semi-positive definite diagonal weighted matrix is ​​used to measure the importance of each residual dimension (physical, action, target, etc.); Let be the regularization penalty coefficient, and satisfy . The compensation amount used for constraint solving The norm size is used to prevent overcompensation from causing system oscillations; Let be the standard L2 norm squared; , To unify the local Jacobian matrix of the residual vector with respect to state, action, and constraint / reward weights; Represents the compensation vector The first-order residual change caused at the current operating point, i.e., the Jacobian-vector product; Differentiate the above equation and set the derivative to zero: ; ; The closed-form expression of the outer optimal compensation operator is obtained: ; in, An identity matrix that matches the dimensions of the variables; By neural network right Perform approximate learning: ; in, The current physical state obtained by multi-source sensor fusion in step S1; The model uncertainty can be calculated in real time using the variance of the outputs of multiple base networks in ensemble learning or the Monte Carlo random inactivation method. This represents the learnable parameters of the compensation approximation neural network. In the specific network execution flow, this application provides the theoretically optimal analytical form of outer layer decoupling. However, in strongly nonlinear and complex physical scenarios, directly solving for the Jacobian matrix in the formula is quite difficult. Therefore, this invention employs a neural network. To implicitly learn and approximate the optimal compensation operator end-to-end .

[0043] Neural Networks Independent output basic compensation amount Then, based on the calculated gating coefficient Perform element-wise multiplication ( This enables confidence-based adaptive intensity scaling, which is then injected into the network.

[0044] S404. Inject the state compensation amount into the PINN model, and inject the action compensation amount and constraint reward weight compensation amount into the DRL model to complete the decoupling correction of the PINN-DRL coupled model.

[0045] This invention employs a gating method for adaptive compensation: ; ; ; in, The projection operator represents the physical feasible region of the action. , , These are the gating coefficients for state compensation, action compensation, and constraint reward weight compensation, respectively. and These represent the predicted state at the next moment after the compensation is injected and the current action, respectively. The initial predicted state output by the environment simulator; and These represent the weighting coefficients of the reward or physical constraint before and after compensation, respectively. Operator Represents element-wise multiplication of vectors; The smooth activation function (its mathematical expression is) This is used to ensure that the corrected weight coefficients are always positive; operator For the action's physical feasible region projection operator, for example, by using a truncation function to restrict the action to the allowable operating range [-1,1] of the laser device.

[0046] Will Substituting the calculation method into the formula for first-order linearization of the unified residual vector near the current point, we can obtain the compensated residual: ; When Ω is a positive semi-definite matrix and κ>0 The corresponding objective function is strictly convex, therefore It is the unique optimal compensation vector, and satisfies: ; This demonstrates that when the compensation direction given by the outer physical residual compensation network is sufficiently close to the optimal compensation operator, the weighted norm of the prediction residual, action residual, and target residual does not increase. This theoretically shows that the outer residual compensation correction mechanism has the effect of suppressing error propagation.

[0047] In this embodiment, a composite loss function for constructing the outer physical residual compensation network is also included: ; in, and These represent the predicted output values ​​of the outer physical residual compensation network for environmental residuals and motion residuals, respectively. , , , These are the corresponding loss weight coefficients, used to balance the magnitudes of various losses; MSE(·) is the mean squared error loss function; This is a coupling suppression term used to characterize the mutual influence between the prediction residual and the action residual. To suppress the mutual amplification of the two, this invention proposes the following coupling suppression formula, calculated as follows: ; in, Denotes the Frobenius norm of a matrix. Describes the L2 norm of a vector. This represents the covariance matrix between the environmental prediction residuals and the action execution residuals. This represents the local Jacobian matrix of the physics prediction for the action. This term constrains the propagation of action errors along the physics-sensitive direction.

[0048] S5. First, pre-train the PINN model, DRL model, and outer physical residual compensation network separately using historical data; then perform joint alternating training, first fixing the parameters of the PINN-DRL coupled model to train the outer physical residual compensation network, then fixing the parameters of the outer physical residual compensation network to update the parameters of the PINN-DRL coupled model; repeat the joint alternating training until training is complete. An alternating optimization strategy is employed to synchronously update the parameters of the PINN model, DRL model, and outer physical residual compensation network, forming a two-layer collaborative closed loop of evolution-residual outer loop monitoring. During the online execution phase, at each decision time step, PINN outputs the predicted state, DRL outputs the desired action, and the outer network estimates the residual and generates compensation based on real-time observations and execution feedback, enabling the system to adaptively correct itself in a dynamic environment.

[0049] S6. Make prediction decisions based on the trained PINN-DRL coupled model and the outer physical residual compensation network.

[0050] The predictive decision-making method proposed in this application can be applied to complex systems such as laser-guided lightning control, probe control of complex physical fields, control of nuclear fusion devices, and smart grid dispatching.

[0051] Example 2 Please see Figure 2 The present invention also proposes a predictive decision system based on outer layer physical residual compensation correction, including: Module 1 is used to build the PINN-DRL coupled model and the outer physical residual compensation network; The PINN model is used to obtain the multi-source state at time t. and DRL at time The actual correction action issued after outer layer motion compensation and output predicted physics field and potential pathway probability ; DRL models are used to determine multi-source states. Predicting physical fields and potential pathway probability Output expected action ; Acquisition module 2 is used to collect the execution feedback from the previous moment and the current real-time observation data, including the current physical field state. Actual actions taken in the previous decision-making cycle Current real physical field response and target effect response ; Outer physical residual compensation network 3 is used to calculate the predicted physical field. Potential pathway probability Expected Action Using the observation data at the current moment, calculate the state compensation, action compensation, and constraint reward weight compensation and inject them into the PINN-DRL coupled model; Training module 4 is used to pre-train the PINN model, DRL model, and outer physical residual compensation network separately using historical data; then, joint alternating training is performed, first fixing the parameters of the PINN-DRL coupled model to train the outer physical residual compensation network, then fixing the parameters of the outer physical residual compensation network to update the parameters of the PINN-DRL coupled model; the joint alternating training is repeated until training is complete. Execution module 5 performs prediction decisions based on the trained PINN-DRL coupled model and the outer physical residual compensation network.

[0052] Example 3 Please see Figure 3 This diagram illustrates the application and deployment of the present invention in a laser-guided lightning scenario, showcasing the closed-loop process from lightning monitoring to laser execution and then to outer layer compensation feedback. This embodiment further explains the technical solution of the present invention by taking the control of potential energy dissipation pathways in laser-guided lightning as an example. The outer layer residual compensation network output in the diagram... This represents the basic compensation amount. Before the actual injection into the inner loop, this basic amount will be adaptively scaled according to the gating coefficient g to ensure the physical reliability and stability of the compensation.

[0053] A high-power laser emitting device, multi-source real-time monitoring sensors, and a control and computing system are deployed at the laser-guided lightning site. The laser emitting device has continuously adjustable azimuth, elevation, and power parameters. The multi-source real-time monitoring sensor array includes an atmospheric electric field meter array, radar detection equipment, optical / lightning location equipment, and meteorological parameter acquisition devices. The computing and control system is equipped with the outer-layer physical residual compensation prediction decision decoupling system described in this invention.

[0054] The PINN model takes atmospheric electric field distribution, cloud charge density, temperature field, and humidity field as input states S(t), and outputs predicted electric field intensity and thunderstorm cloud evolution trends. The PINN model employs a multi-layer fully connected neural network or a cross-scale feature extraction network, with the number of hidden layer neurons adjustable to 256. The loss function includes data fitting loss from historical thunderstorm data and field lightning observation data, physical constraint loss based on Maxwell's equations and charge conservation equations, and boundary condition loss from the laser-induced lightning test site.

[0055] The DRL model defines parameters such as laser azimuth, elevation, and power as a continuous action space. The reward function can be designed as follows: ; in, A positive reward is given for successfully forming a directional discharge channel. To constrain safety penalties for lighting that does not point towards sensitive areas such as flight paths and residential areas, For indicator functions, The action cost coefficient, It is the square of the L2 norm; This is the baseline action.

[0056] The DRL model can employ the SAC algorithm. The DRL model uses a stochastic policy Actor network and two independent CriticQ networks, with corresponding target Q networks. The learning rate can be set to... The discount factor γ = 0.99, and the temperature parameter α is adaptively adjusted.

[0057] During the preparation phase of the laser-induced lightning experiment, training samples were collected using historical lightning-induced data and simulation data. From the historical lightning-induced experimental data, the predicted electric field evolution results of the PINN model were extracted. Compared with actual observed values Calculate the physical field residuals; during actual laser emission debugging, record the target motion output by the DRL model. With the actual action performed by the laser Calculate the residual of action execution.

[0058] When training the physics residual compensation subnetwork, the current physics state S(t) and the current predicted physics residual are used. As input, output the predicted physical residual value for the next time step. GRU or LSTM structures can be used to capture the time-dependent characteristics of the physical field evolution. When training the action residual compensation subnetwork, the current physical field state S(t) and the current decision action are used. Input is the predicted action residual. .

[0059] A joint optimization mechanism of "evolution-residual outer loop supervision" is employed for training. In the prediction pre-training phase, the PINN model, DRL model, and outer residual compensation network are pre-trained separately for several rounds using historical data. In the joint alternating training phase, the outer physical residual compensation network is first trained with fixed parameters, then the outer physical residual compensation network is fixed again, and the PINN and DRL parameters are updated with the joint output of the model and the residual compensation network as the target. This process is repeated until the parameters of the inner and outer networks converge.

[0060] Control experiment In a simulated laser-guided lightning scenario, the methods of Direct, PI-RL, PI-MPC, and the present invention were compared and verified. The experimental results are as follows: Figure 4 , Figure 5 and Figure 6 As shown.

[0061] Figure 4 This chart compares the overall performance of different methods. The horizontal axis represents the different methods compared, including the Direct method, PI-RL method, PI-MPC method, and the method of this invention; the vertical axis represents the corresponding performance index values. The six bar sub-charts sequentially represent success rate, average reward, average probability of potential pathway formation, mean square error of physics prediction, mean square error of action execution, and physical constraint violation. Specifically, success rate represents the proportion of rounds in which the expected control objective is achieved; average reward represents the overall control benefit of the DRL decision-making process; average probability of potential pathway formation represents the likelihood of forming the expected energy release pathway during the control process; mean square error of physics prediction represents the deviation between the PINN predicted physics field and the actual physics field response; mean square error of action execution represents the deviation between the control command and the actual action of the actuator; and physical constraint violation represents the degree of deviation of the prediction-decision process from the preset physical constraints. Each bar represents the average result of the corresponding method on the corresponding index, and the error bars represent the dispersion of results from multiple experiments. Figure 4 It is evident that the method of this invention maintains a high level of positive performance indicators such as success rate, average reward, and average potential path formation probability, while maintaining a low level of error indicators such as the mean square error of physical field prediction and the mean square error of action execution. This indicates that the outer physical residual compensation can effectively correct the prediction bias of PINN and the action execution bias of DRL, and improve the comprehensive control performance of the prediction-decision closed loop.

[0062] Figure 5 This is a graph showing the change in the probability of potential pathway formation during a typical control process. The horizontal axis represents the decision time step in the control process, and the vertical axis represents the probability of potential pathway formation. In the graph, the Direct curve represents the direct PINN-DRL prediction decision method without external physical residual compensation, the PI-RL curve represents the physical information reinforcement learning baseline method, the PI-MPC curve represents the physical information model prediction control baseline method, and the curve of this invention represents the prediction decision method using an external physical residual compensation correction mechanism. The probability of potential pathway formation reflects the likelihood of forming the expected energy release pathway under the current prediction state and control action conditions. During a single control process, a higher curve level indicates a higher probability of expected pathway formation, and smaller curve fluctuations indicate better online control stability of the corresponding method. Figure 5It is evident that the method of this invention can maintain the overall probability of potential pathway formation at a high and stable level during typical control processes, indicating that outer physical residual compensation can reduce the disturbance of prediction error and execution error on subsequent decision-making processes.

[0063] Figure 6 This figure shows the convergence curves of the training loss for the prediction model, decision model, and outer physical residual compensation network. The horizontal axis represents the training epoch, and the vertical axis represents the loss value, with logarithmic scales used to represent the change in loss values ​​of different orders of magnitude during the training process. In the figure, "PINN Environment Simulator Loss" represents the total loss of the PINN environment simulator during training; "Direct Method Actor Loss" and "Direct Method Critic Loss" represent the training losses of the Actor policy network and Critic action value network under the condition of no outer residual compensation, respectively; "PI-RL Method Actor Loss" and "PI-RL Method Critic Loss" represent the training losses of the Actor policy network and Critic action value network in the PI-RL baseline method, respectively; and "Outer Residual Compensation Network Loss" represents the loss of the outer physical residual compensation network of this invention during training. Figure 6 It can be seen that as the number of training rounds increases, the overall loss of each network shows a decreasing trend and gradually tends to stabilize, indicating that the PINN environment simulator, DRL decision network and outer physical residual compensation network can be optimized for parameters through the training method and have a corresponding training convergence trend.

[0064] In summary, this invention can improve the stability, robustness, and control effectiveness of prediction-decision coupling systems in complex physical environments with model prediction errors, actuator biases, and unmodeled physical residuals.

[0065] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware, and of course, it can also be implemented by special hardware including application-specific integrated circuits, special CPUs, special memory, special components, etc. Generally, any function performed by a computer program can be easily implemented by corresponding hardware, and the specific hardware structure used to implement the same function can also be diverse, such as analog circuits, digital circuits, or special-purpose circuits. However, for this application, software program implementation is more often the preferred implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a readable storage medium, such as a computer floppy disk, USB flash drive, mobile hard disk, ROM, RAM, magnetic disk, or optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of this application.

[0066] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can store or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0067] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A predictive decision-making method based on outer layer physical residual compensation correction, characterized in that, The construction of the PINN-DRL coupled model and the outer physical residual compensation network also includes the following steps: S1, PINN obtains the multi-source state at the current time t. The corrected motion after outer motion compensation at the previous time t-1 Output the predicted physics field at the current moment. and potential pathway probability ; S2, DRL are based on multi-source states Predicting physical fields and potential pathway probability Output expected action ; S3. Collect the execution feedback from the previous moment and the observation data from the current moment, including the current physical field state. The actual action performed at the previous moment Current real physical field response and target effect response ; S4, Outer Physical Residual Compensation Network based on predicted physical field Potential pathway probability Expected Action Using the observation data at the current moment, calculate the state compensation, action compensation, and constraint reward weight compensation and inject them into the PINN-DRL coupled model; S5. First, pre-train the PINN model, DRL model, and outer physical residual compensation network separately using historical data; then perform joint alternating training, first fixing the parameters of the PINN-DRL coupled model to train the outer physical residual compensation network, then fixing the parameters of the outer physical residual compensation network to update the parameters of the PINN-DRL coupled model; repeat the joint alternating training until training is complete. S6. Make prediction decisions based on the trained PINN-DRL coupled model and the outer physical residual compensation network.

2. The prediction and decision-making method based on outer layer physical residual compensation correction according to claim 1, characterized in that, In S1: PINN environment simulator is Its output includes predicted physical fields. and potential pathway probability : The training loss function of the PINN model includes data fitting loss, physical constraint loss, boundary condition loss, and initial condition loss. The total training loss is obtained by weighted fusion of these losses.

3. The prediction and decision-making method based on outer layer physical residual compensation correction according to claim 1, characterized in that, The DRL model in S2 adopts an Actor-Critic structure, and the Actor network strategy is as follows: The Critic network value function is ; in, Indicates the parameters of the Actor network; This indicates the fusion state of the DRL; 'a' represents the policy action generated by the Actor policy in this fusion state. Indicates the parameters of the Critic network; DRL based on the current fusion status Expected output action: Where Enc(·) represents the conditional coding function; Objective function using SAC strategy: In the formula, This represents the fusion state of the DRL at time t. This represents the strategy action generated by the Actor in this fusion state; make The actual control command is denoted as ; Indicates an immediate reward for environmental feedback; This represents the experience replay pool; For temperature parameters; Discount factor; This represents the action value estimated by the current Critic network; Let Actor be the policy loss function; For the Critic value loss function; Represents the mathematical expectation; This is the fusion state for the next moment; In order to be in The action obtained from downsampling.

4. The prediction and decision-making method based on outer layer physical residual compensation and correction according to claim 1, characterized in that, S4 specifically includes: S401. Construct a unified residual vector : in This represents the residual of environmental prediction. Indicates the action execution residual. Represents the physical constraint consistency residual. Indicates the residual of the target effect; S402, unify the residual vector Input the residual decomposition encoder and perform source, scale, and mode decomposition respectively to obtain compressed features. ,Will Input the physical confidence gating network and the three-way compensation head. The physical confidence gating network calculates the gating coefficients for state compensation, action compensation, and constraint reward weight compensation; the three-way compensation head calculates the basic compensation. S403. Calculate the state compensation amount, action compensation amount, and constraint reward weight compensation amount based on the gating coefficients and basic compensation of state compensation, action compensation, constraint reward weight compensation, and basic compensation. S404. Inject the state compensation amount into the PINN model, and inject the action compensation amount and constraint reward weight compensation amount into the DRL model to complete the decoupling correction of the PINN-DRL coupled model.

5. The prediction and decision-making method based on outer layer physical residual compensation and correction as described in claim 4, characterized in that, In S401: in, For physical constraint operators; b(t) represents boundary conditions or safety thresholds; The desired control target preset by the system; This indicates the response to the target effect.

6. The prediction and decision-making method based on outer layer physical residual compensation correction as described in claim 4, characterized in that, The gating coefficients for calculating state compensation, action compensation, and constraint reward weight compensation include: in, The calculated overall physical confidence score; Indicated by Let be the residual square norm for the weights; For observing quality factors; This represents scalar multiplication. This indicates the concatenation of eigenvectors; The learnable weight matrix for the gated network layer. This is the bias vector of the gated network layer; The Sigmoid activation function is used to map the gating coefficients to the range [0,1]. Indicates model uncertainty. For residual scaling parameters, This is the residual weighting matrix; The state compensation gating coefficient. The motion compensation gating coefficient, To constrain the reward weight compensation gating coefficient.

7. The prediction and decision-making method based on outer layer physical residual compensation correction as described in claim 4, characterized in that, The The calculation of basic compensation by inputting three compensation heads includes: Set basic compensation for: in, This represents the vector transpose operation, which converts a row vector into a column vector. For state compensation, The basic compensation for motion compensation, The basic compensation for constraining reward weights; After injecting compensation into the PINN-DRL coupled model, the residual vector is unified. The first-order linearization near the current point is: In the formula, This represents the expected first-order approximate new residual vector after the injection of compensation. for The partial derivatives; in, It is a partial differential operator; This refers to the system status; To perform the action; Weighting coefficients for rewards or physical constraints; The search for the optimal compensation amount is transformed into a weighted least squares problem with regularization: In the formula, This indicates the solution that minimizes the loss function. ; For a given positive definite or positive semi-definite diagonal weighted matrix; It is a weighted L2 norm; Let be the regularization penalty coefficient, and satisfy . ; The standard L2 norm squared; Represents vector product; Differentiate the above equation and set the derivative to zero: Obtain the outer optimal compensation operator Closed expression: in, An identity matrix that matches the dimensions of the variables; For weighted Jacobian Gram matrix; By neural network right Perform approximate learning: in, The model uncertainty is calculated in real time using the variance of the outputs of multiple base networks in ensemble learning or the Monte Carlo random inactivation method. (Subscript) This represents the learnable parameters of a neural network.

8. The prediction and decision-making method based on outer layer physical residual compensation correction as described in claim 5, characterized in that, S5 also includes a composite loss function for constructing the outer physical residual compensation network: in, and These represent the predicted output values ​​of the outer physical residual compensation network for environmental residuals and motion residuals, respectively. , , , These are the corresponding loss weight coefficients, used to balance the magnitudes of various losses; MSE(·) is the mean squared error loss function; This is a coupling suppression term used to characterize the interaction between the prediction residual and the action residual, calculated as follows: in, Denotes the Frobenius norm of a matrix. Describes the L2 norm of a vector. The covariance matrix representing the environmental prediction residuals and the action execution residuals; This represents the local Jacobian matrix of the physics prediction for the action.

9. A predictive decision-making system based on outer layer physical residual compensation and correction, characterized in that, include: The building blocks are used to construct the PINN-DRL coupled model and the outer physical residual compensation network; The PINN model is used to obtain the multi-source state at the current time t. The correction action actually issued at the previous time t-1 after outer layer motion compensation and output predicted physics field and potential pathway probability ; DRL models are used to determine multi-source states. Predicting physical fields and potential pathway probability Output expected action ; The acquisition module is used to collect the execution feedback from the previous moment and the current real-time observation data, including the current physical field state. The actual action performed at the previous moment Real physical field response and target effect response ; The outer physical residual compensation network is used to calculate the predicted physical field. Potential pathway probability Expected Action Using the observation data at the current moment, calculate the state compensation, action compensation, and constraint reward weight compensation and inject them into the PINN-DRL coupled model; The training module is used to pre-train the PINN model, DRL model, and outer physical residual compensation network separately using historical data; then, joint alternating training is performed, first fixing the parameters of the PINN-DRL coupled model to train the outer physical residual compensation network, then fixing the parameters of the outer physical residual compensation network to update the parameters of the PINN-DRL coupled model; the joint alternating training is repeated until training is complete. The execution module makes prediction decisions based on the trained PINN-DRL coupled model and the outer physical residual compensation network.

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