Method for optimizing design of shallow ground heat exchanger based on PINN

Abstract

The present application belongs to the technical field of ground heat exchanger, and relates to a shallow ground heat exchanger optimization design method based on PINN, comprising: 1, high-fidelity numerical simulation and benchmark dataset generation; 2, physical information neural network construction; 3, model training and physical consistency verification; 4, multi-objective automatic optimization based on differentiable proxy model; the present application endogenously embeds physical mechanism in a data-driven model and constructs a differentiable end-to-end optimization framework, fundamentally solving the core defects of the prior art, such as untrustworthy proxy model, low optimization efficiency and fragmented process, and realizing the leap from 'fast simulation' to'reliable optimization'.

Description

Technical Field

[0001] This invention belongs to the field of buried pipe heat exchange technology, specifically relating to an optimized design method for shallow buried pipe heat exchangers based on PINN. Background Technology

[0002] As a core component of ground source heat pump systems, the design quality of shallow buried pipe heat exchangers directly affects the system's energy efficiency and long-term operational stability. In current engineering practice, the design process heavily relies on traditional numerical simulations and empirical formulas. Traditional numerical methods face two major bottlenecks: first, in multi-parameter, multi-condition optimization searches, the computational cost is extremely high and optimization efficiency is low because each performance evaluation requires rerunning a time-consuming high-fidelity simulation; second, they depend on accurate geotechnical thermophysical parameters and boundary conditions, while actual geological conditions are uncertain, making it difficult to guarantee the robustness of the design scheme. To address these bottlenecks, various methods have emerged, such as the method for rapidly solving the geotechnical temperature field, as disclosed in invention CN202511689471 A, entitled "A Rapid Solution Method for Geotechnical Temperature Field Applicable to Ground Source Heat Pump Systems." For the problem of predicting the thermal response of medium-deep buried pipe heat exchangers (DBHE) considering the influence of groundwater seepage, there are methods such as the "rapid prediction method for seepage thermal response of medium-deep buried pipe heat exchangers based on artificial intelligence" disclosed in invention CN202511539772 A.

[0003] However, while purely data-driven surrogate models have accelerated optimization in recent years, their "black box" nature makes them prone to producing predictions that violate physical laws when extrapolating to design regions not covered by training data, affecting the reliability and engineering applicability of optimization results. Furthermore, although existing technologies have improved computational efficiency through model reduction and data-driven surrogate models, significant limitations remain. The common flaw of these methods is that the surrogate models they construct are purely data-driven "black boxes," with their training process entirely dependent on statistical fitting of input and output data, without embedding the physical conservation laws describing underground heat transfer processes as hard constraints into the model's learning mechanism. This leads to potentially serious violations of physical principles when the model makes predictions outside the training data distribution range, fundamentally jeopardizing the reliability and generalization ability of its extrapolation. Simultaneously, these methods treat "rapid simulation" and "parameter inversion" or "design optimization" as separate, sequential steps, failing to form a unified, differentiable framework. This prevents efficient, continuous gradient-based optimization search, limiting their potential and efficiency for automatic optimization in complex, multivariate design spaces.

[0004] Therefore, how to significantly improve the efficiency and intelligence level of the optimized design of buried pipe heat exchangers while ensuring the correct physical mechanism has become a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] This invention provides the following technical solution: an optimized design method for shallow buried pipe heat exchangers based on PINN, comprising the following steps: Step 1: High-fidelity numerical simulation and benchmark dataset generation.

[0006] Step 2: Construction of the physical information neural network.

[0007] Step 3: Verify the consistency between the trained model and the physical model.

[0008] Step 4: Automatic multi-objective optimization based on the differentiable agent model.

[0009] Preferably, step 1 specifically includes: establishing a three-dimensional unsteady-state numerical model of shallow buried pipe heat transfer using numerical simulation; extracting different soil thermal properties, geometric parameters, and operating conditions within the design space using Latin hypercube sampling; and after running the simulation, extracting temperature field T data at different spatiotemporal coordinate points (x, y, z, t2) to form a high-quality initial dataset for supervised learning.

[0010] More preferably, the soil thermal properties include: thermal conductivity and specific heat capacity; geometric parameters include: burial depth and spacing; and operating conditions include: flow rate and inlet water temperature.

[0011] Preferably, step 2 specifically includes: constructing a deep neural network, wherein the input of the deep neural network is a feature vector [d, H, v, t1, λ, a, x, y, z, t2] containing design variables, spatial coordinates, time and uncertain parameters, and the output of the deep neural network is the predicted temperature field T_pred.

[0012] More preferably, the deep neural network structure adopts a multilayer perceptron or a network with residual connections, and the activation function of the deep neural network includes a smooth and differentiable tanh function or a sin function.

[0013] More preferably, the loss function of the deep neural network is:

[0014] in, To reduce data loss weights, Weights are lost for the physical equations. Weights for boundary / initial conditions loss. For data loss, For the loss of the physical equations, For boundary / initial condition loss.

[0015] Preferably, step 3 includes the following sub-steps: Step 3-1: Define the optimization problem: with the goal of maximizing the long-term performance of the system or minimizing the total cost, design variables are used as optimization variables, and engineering constraints are considered.

[0016] Step 3-2, Gradient Calculation and Optimization: The trained physical information neural network model is used as the calculation engine for the temperature field-related parts of the objective function and constraint function. Automatic differentiation technology is used to directly calculate the gradient of the performance index relative to the design variables. Based on the gradient information, a gradient optimization algorithm is used to perform a fast and targeted search in a broad design space.

[0017] Step 3-3, Closed-loop verification and update: Feed the optimized new design points back to the high-fidelity numerical model for verification; if necessary, add new data to the dataset and fine-tune the physical information neural network model to achieve a closed loop of design-verification-model update.

[0018] Preferably, step 4 specifically includes: embedding the trained physical information neural network as an alternative model into the optimization framework, using the backpropagation algorithm to calculate the precise gradient of the objective function with respect to the design variables; and combining gradient descent algorithms or improved heuristic algorithms to quickly search for the set of optimal design schemes under the constraints.

[0019] The beneficial effects of this invention are: 1. This invention fundamentally solves the core defects of existing technologies, such as unreliable physical proxy models, low optimization efficiency, and fragmented processes, by endogenizing physical mechanisms into data-driven models and constructing a differentiable end-to-end optimization framework, thus achieving a leap from "rapid simulation" to "reliable optimization".

[0020] 2. This invention significantly improves the physical consistency and extrapolation reliability of surrogate models. Existing pure data-driven surrogate models (such as those based on POD and BP neural networks) are essentially "black boxes," their training relying entirely on data fitting. When extrapolating to operating conditions or design spaces not covered by the training data, they are prone to producing predictions that violate fundamental physical laws such as energy conservation, leading to unreliable optimization results. This invention explicitly incorporates the residuals of the physical control equations (L_pde) and boundary condition constraints (L_bc / ic) into the loss function of the neural network, forcing the model to always adhere to the fundamental laws of heat transfer during learning and prediction. This mechanism enables the trained PINN model not only to fit existing data but also to possess "physical common sense," thus maintaining physical rationality in its predictions when dealing with new combinations of design parameters or uncertain boundary conditions. This greatly enhances the model's generalization ability and reliability in engineering applications, overcoming the fundamental weakness of poor extrapolation in pure data-driven models.

[0021] 3. This invention achieves a qualitative leap in optimization efficiency by utilizing the differentiable property of PINN. Existing optimization processes typically rely on surrogate models to perform a large number of gradient-free random searches (such as genetic algorithms). While each performance evaluation is fast, it requires a massive number of trials to converge, resulting in a bottleneck in overall optimization efficiency. The core advantage of this invention lies in the fact that a trained PINN is itself a continuous, smooth, and differentiable function mapping. Therefore, automatic differentiation techniques can be conveniently used to directly calculate the precise gradient of key performance indicators (such as total system heat exchange and energy efficiency ratio) with respect to any design variable (such as pipe spacing, burial depth, and flow velocity). These gradients provide a clear search direction for optimization algorithms, enabling the use of efficient optimizers such as gradient descent, conjugate gradient methods, or gradient-enhanced evolutionary algorithms. Compared to "blind search" without gradients, this "gradient-driven" optimization approach can converge to the optimal solution or Pareto front with fewer iterations and in a shorter time. It is particularly suitable for handling complex engineering optimization problems with continuous variables and multiple constraints, elevating optimization design from "possible" to "efficiently feasible."

[0022] 4. This invention achieves intelligent and integrated design processes. Existing technologies often treat "high-fidelity simulation," "surrogate model construction," "parameter inversion," and "design optimization" as multiple independent, sequentially executed modules, requiring manual coordination and data transfer, resulting in cumbersome processes and low automation. The innovative framework of this invention organically integrates the first three into the construction and training process of PINN: high-fidelity simulation provides initialization data, physical equations ensure the model kernel, and the trained PINN simultaneously possesses the capabilities for rapid prediction and parameter sensitivity analysis. Based on this, the model can be directly embedded as a differentiable objective function into the optimization loop, forming an end-to-end automated system from design variable input to optimal solution output. This not only significantly reduces manual intervention, making rapid and automated multi-solution comparison and optimization a norm, but also ensures that the entire chain from physical modeling to final decision-making is conducted under unified physical law constraints. The output design solution possesses both high performance and high physical reliability, providing a practical next-generation technical tool for the intelligent and refined design of shallow buried pipe heat exchangers. Attached Figure Description

[0023] Figure 1 This is a flowchart of the overall design method for shallow buried pipe heat exchangers based on PINN according to the present invention. Figure 2 This is a schematic diagram illustrating the fusion of the physical information neural network architecture and loss function of this invention. Detailed Implementation

[0024] The relevant technologies of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0025] like Figures 1-2 As shown, this embodiment presents an optimization design method for shallow buried pipe heat exchangers based on PINN. Its core process includes: data preparation based on high-fidelity numerical simulation, neural network construction with embedded physical control equations, model training under physical constraints, and automated optimization design based on a differentiable surrogate model. The specific steps are as follows: Step 1: High-fidelity numerical simulation and benchmark dataset generation: A three-dimensional unsteady-state numerical model of shallow buried pipe heat transfer was established using high-precision numerical simulation software (such as OpenGeoSys or COMSOL). Different soil thermophysical parameters (thermal conductivity, specific heat capacity), geometric parameters (burial depth, spacing), and operating conditions (flow rate, inlet water temperature) were extracted within the design space using Latin hypercube sampling (LHS). After simulation, temperature field T data at different spatiotemporal coordinate points (x, y, z, t2) were extracted to form a high-quality initial dataset for supervised learning.

[0026] Step 2: Construction of Physical Information Neural Network (PINN): Construct a deep neural network whose input is a feature vector [d, H, v, t1, λ, a, x, y, z, t2] containing design variables, spatial coordinates, time, and uncertain parameters. The network output is the predicted temperature field T_pred.

[0027] The network structure of deep neural networks: multilayer perceptrons (MLP) or networks with residual connections are used, and the activation function is often a smooth and differentiable tanh or sin function.

[0028] Loss function design for deep neural networks: a. Data Loss L_data: At spatiotemporal points where sample data is available, calculate the mean square error between the network prediction value T_pred and the high-fidelity simulation value Y. This part ensures that the model fits the known data.

[0029] b. Physical equation loss L_pde: At a large number of randomly sampled "residual points" within the computational domain, the network-predicted T_pred is substituted into the governing equations describing the problem (such as the unsteady-state heat conduction equation). In the context of neural networks (including their convection terms), since neural networks can automatically differentiate, the partial derivatives of T_pred with respect to spatiotemporal coordinates can be easily calculated, and then the residual f_pred of the equation can be calculated. L_pde is the mean square value of this residual. This part forces the network output to approximately satisfy the physical conservation laws under any input (including regions not covered by the training data), fundamentally solving the problems of physical inconsistency and poor extrapolation in existing pure data-driven proxy models.

[0030] c. Boundary / Initial Condition Loss L_bc / ic: Calculate the error between the network prediction and the given boundary conditions (such as isothermal, adiabatic, convective heat transfer) or initial temperature distribution at the sampling points at the boundary and initial times.

[0031] The final loss function is:

[0032] By minimizing L using a gradient descent algorithm (such as Adam), the trained network becomes a physically constrained, differentiable surrogate model.

[0033] Step 3: Verify the consistency between the trained model and the physical model. 3-1. Define the optimization problem: with the goal of maximizing the long-term performance of the system (such as the overall energy efficiency ratio COP) or minimizing the total cost, the design variables (d, H, v, etc.) are used as optimization variables, and engineering constraints (such as maximum burial depth, minimum spacing, etc.) are considered.

[0034] 3-2. Gradient Calculation and Optimization: The trained PINN model is used as the computational engine for the temperature-related parts of the objective and constraint functions. Since PINN itself is a differentiable function, we can use automatic differentiation techniques to directly calculate the gradient of performance metrics (such as T_out or Q) with respect to design variables (such as d). Based on this precise gradient information, efficient gradient optimization algorithms (such as gradient descent, conjugate gradient method, or gradient-enhanced evolutionary algorithms) can be used to perform fast, targeted searches in a broad design space. In contrast, existing POD-BP surrogate models are either non-differentiable (black box) or their gradients have no physical meaning, typically relying on gradient-free optimizers (such as genetic algorithms) for extensive random trials, which is inefficient.

[0035] 3-3. Closed-Loop Validation and Update: The new design points obtained from the optimization are fed back to the high-fidelity numerical model for validation. If necessary, new data can be added to the dataset to fine-tune the PINN model, thereby achieving a closed loop of design-validation-model update and making the optimization results more robust and reliable.

[0036] Step 4: Automatic multi-objective optimization based on a differentiable agent model: The trained PINN is embedded as an alternative model into the optimization framework. Since PINN itself is end-to-end differentiable, this scheme can directly use the backpropagation algorithm to calculate the precise gradient of the objective function (such as maximizing heat transfer efficiency or minimizing cost) with respect to design variables (such as pipe depth and spacing). Combined with gradient descent algorithms or improved heuristic algorithms, the optimal set of design schemes (Pareto front) is quickly searched under constraints (such as soil thermal balance limitations).

[0037] The method based on physical information neural networks proposed in this invention directly encodes the partial differential equations controlling the heat transfer process and their boundary conditions into the loss function of the neural network, forcing the model to simultaneously consider data matching and the satisfaction of physical laws during training. This mechanism ensures that even when training samples are sparse or when predicting entirely new operating conditions, the model's output strictly adheres to basic physical conservation laws, thereby greatly improving the model's reliability, interpretability, and extrapolation ability. Furthermore, PINN, as an end-to-end differentiable physical constraint surrogate model, itself constitutes a continuous and differentiable "simulator." This allows us to use the design variables of the buried pipe as input to the model and the performance index as output, then directly use the backpropagation algorithm to calculate the gradient of the performance index with respect to the design variables. Based on this, various gradient optimization or gradient enhancement algorithms can be seamlessly integrated to achieve efficient, automated, and physically consistent design parameter optimization, thus completing the leap from "fast forward prediction" to "physically guided reverse design," solving the core shortcomings of existing technologies such as fragmented optimization processes and lack of physical consistency.

[0038] This invention introduces a composite loss function construction technique with embedded physical constraints. This "physical constraint" mechanism ensures that the prediction results still conform to the law of energy conservation in sparse data regions, solving the "black box" unreliability problem of pure data-driven models in engineering applications.

[0039] This invention presents a real-time physical residual calculation method based on automatic differentiation (AD). This method allows the model to perform physical consistency evaluation in a continuous spatiotemporal domain, which greatly improves the flexibility of the model in handling complex boundary conditions and unsteady heat transfer.

[0040] This invention, based on a gradient-driven automatic optimization process using a differentiable surrogate model, overcomes the drawbacks of separating "simulation" and "optimization" in existing technologies, improving optimization efficiency from traditional random trial and error to targeted, efficient search, and achieving end-to-end automation of the design process.

[0041] In summary, this invention provides an innovative and efficient optimization design scheme for shallow buried pipe heat exchangers. Through a series of closely linked and innovative steps, from data generation, model construction, training and verification to final multi-objective automatic optimization, a complete and intelligent design system is formed. In the data generation stage, high-precision numerical simulation software and scientific sampling methods are used to obtain a high-quality initial dataset, providing a solid data foundation for subsequent model training. The ingenious construction of the physical information neural network integrates physical control equations and boundary conditions into the loss function, enabling the model to fully consider physical laws during the learning process. This solves many problems of traditional pure data-driven models and significantly improves the model's physical consistency, interpretability, and extrapolation ability.

[0042] It should be emphasized that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for optimizing the design of shallow buried pipe heat exchangers based on PINN, characterized in that, Includes the following steps: Step 1: High-fidelity numerical simulation and benchmark dataset generation; Step 2: Construction of the physical information neural network; Step 3: Verify the consistency between the trained model and the physical model; Step 4: Automatic multi-objective optimization based on a differentiable agent model; Step 1 specifically includes: establishing a three-dimensional unsteady-state numerical model of shallow buried pipe heat transfer using numerical simulation; extracting different soil thermal properties, geometric parameters, and operating conditions within the design space using Latin hypercube sampling; and after running the simulation, extracting temperature field T data at different spatiotemporal coordinate points (x, y, z, t2) to form a high-quality initial dataset for supervised learning. Step 2 specifically includes: constructing a deep neural network, wherein the input of the deep neural network is a feature vector [d, H, v, t1, λ, a, x, y, z, t2] containing design variables, spatial coordinates, time and uncertain parameters, and the output of the deep neural network is the predicted temperature field T_pred; Step 3 includes the following sub-steps: Step 3-1: Define the optimization problem: with the goal of maximizing the long-term performance of the system or minimizing the total cost, using design variables as optimization variables, and considering engineering constraints; Step 3-2, Gradient Calculation and Optimization: The trained physical information neural network model is used as the calculation engine for the temperature field-related parts of the objective function and constraint function. Automatic differentiation technology is used to directly calculate the gradient of the performance index relative to the design variables. Based on the gradient information, a gradient optimization algorithm is used to perform a fast and targeted search in a wide design space. Step 3-3, Closed-loop verification and update: Feed the optimized new design points back to the high-fidelity numerical model for verification; if necessary, add new data to the dataset and fine-tune the physical information neural network model to achieve a closed loop of design-verification-model update; Step 4 specifically includes: The trained physical information neural network is embedded as an alternative model into the optimization framework, and the backpropagation algorithm is used to calculate the accurate gradient of the objective function with respect to the design variables. Combined with gradient descent algorithms or improved heuristic algorithms, the optimal set of design schemes is quickly searched under the constraints.

2. The PINN-based shallow buried pipe heat exchanger optimization design method according to claim 1, characterized in that, The soil thermal properties include thermal conductivity and specific heat capacity; the geometric parameters include burial depth and spacing; and the operating conditions include flow rate and influent temperature.

3. The PINN-based shallow buried pipe heat exchanger optimization design method according to claim 1, characterized in that, The deep neural network uses a multilayer perceptron or a network with residual connections, and the activation function of the deep neural network includes a smooth and differentiable tanh function or a sin function.

4. The PINN-based shallow buried pipe heat exchanger optimization design method according to claim 1, characterized in that, The loss function of the deep neural network is: in, To reduce data loss weights, Weights are lost for the physical equations. Weights for boundary / initial conditions loss. For data loss, For the loss of the physical equations, For boundary / initial condition loss.

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