A pinn-based optimization design method for water-heat type ground heat exchanger

Abstract

The present application belongs to the technical field of geothermal energy development and utilization, and relates to a hydrothermal type buried pipe heat exchanger optimization design method based on PINN, comprising: 1, numerical simulation and benchmark data set generation; 2, PINN construction and training: constructing a PINN neural network, converting the mass conservation equation and the energy conservation equation in the pore medium into a partial differential equation residual, and together with the discrete data error generated by the numerical simulation software to form a composite loss function; using the nonlinear fitting capability of the PINN neural network, and embedding the physical partial differential equation of fluid flow and heat transfer in the pore medium into the loss function as a soft constraint; 3, data-driven optimization based on the proxy model; the present application not only fundamentally solves the problems of poor generalization ability and easy non-physical interpretation of traditional pure data-driven models, but also breaks through the bottleneck of convergence difficulty and high training cost when solving complex engineering problems by pure PINN.

Description

Technical Field

[0001] This invention belongs to the field of geothermal energy development and utilization technology, specifically relating to an optimized design method for a hydrothermal buried pipe heat exchanger based on PINN. Background Technology

[0002] With the deepening development of geothermal energy and the utilization of underground space, the optimized design and thermal response prediction of medium-deep and hydrothermal buried pipe heat exchangers (DBHE) have become research hotspots. Currently, to overcome the time-consuming nature of traditional numerical simulation calculations, the industry has gradually introduced artificial intelligence and surrogate model technologies. The relevant existing technologies mainly include the following two types of solutions: One type of prediction method is based on pure data-driven approaches and model dimensionality reduction. This type of approach primarily utilizes dimensionality reduction techniques such as intrinsic orthogonal decomposition (POD) combined with traditional artificial neural networks to construct a surrogate model. For example, in invention CN 121365596 A, "A Rapid Prediction Method for Seepage Thermal Response of Medium-Deep Buried Pipe Heat Exchangers Based on Artificial Intelligence," the method first acquires snapshot data of the temperature field of the medium-deep buried pipe heat exchanger system under different operating conditions. Then, orthogonal decomposition processing is performed on the snapshot data to extract the main modal features and corresponding amplitudes, constructing a dimensionality-reduced temperature field. Finally, system parameters are used as input, and modal feature amplitudes are used as outputs to train and construct a three-layer BP neural network surrogate model.

[0003] Another type is scenario-specific modeling based on Physical Information Neural Networks (PINNs). To address the lack of physical constraints in purely data-driven models, PINNs have been introduced into the fields of geotechnical and geothermal engineering. For example, in invention CN 121525499 A, a permafrost hydrothermal coupling model based on PINNs, partial differential equations (PDEs) containing energy and mass conservation are derived. During the training of the neural network, these governing equations, initial conditions, and boundary conditions are collectively constructed into a multi-objective loss function. While fitting the data, the neural network calculates the derivative terms in the PDEs using automatic differentiation techniques, forcing the solution to satisfy specific physical laws.

[0004] However, existing optimization design methods for hydrothermal buried pipe heat exchangers have the following drawbacks: For prediction methods based on pure data-driven approaches and model dimensionality reduction, although dimensionality reduction and surrogate modeling significantly improve computational speed, they are essentially still pure data-driven "black box" models. The training of BP neural networks relies entirely on pre-generated snapshot data, and the network lacks awareness and constraints on the physical governing equations of fluid flow and heat transfer in porous media. Therefore, when faced with complex engineering boundary conditions or multivariate coupled optimization outside the training set distribution, the model's generalization ability and physical consistency are poor, easily leading to non-physical interpretations that violate thermodynamic laws.

[0005] The PINN-based scenario-specific modeling method primarily focuses on simulating the water-ice phase change process in permafrost environments, without addressing the complex 3D engineering design of hydrothermal geothermal systems and buried pipe heat exchangers. Furthermore, it represents an attempt to directly replace partial differential equation solvers. When facing large-scale, high-fidelity hydrothermal geothermal energy projects, relying solely on PINN to directly solve PDEs often encounters severe convergence difficulties and extremely high training costs, making it unsuitable for rapid optimization in later stages of engineering projects.

[0006] Therefore, there is a need for an optimization design method for hydrothermal buried pipe heat exchangers that can eliminate non-physical predictions and achieve multi-parameter, multi-objective global optimization in a short time to solve the above-mentioned technical problems. Summary of the Invention

[0007] This invention provides the following technical solution: an optimized design method for a PINN-based hydrothermal buried pipe heat exchanger, comprising the following steps: Step 1: Numerical simulation and benchmark dataset generation: A three-dimensional unsteady-state numerical model of shallow buried pipe heat transfer is established using numerical simulation software; different soil thermal properties, geometric parameters and operating conditions are extracted in the design space through Latin hypercube sampling; after running the simulation, temperature field data at different spatiotemporal coordinate points are extracted to form a high-quality initial dataset for supervised learning.

[0008] Step 2: Construction and Training of PINN: Construct a PINN neural network to transform the mass conservation equation and energy conservation equation in porous media into partial differential equation residuals, which together with the discrete data errors generated by numerical simulation software form a composite loss function; utilize the nonlinear fitting capability of the PINN neural network, and simultaneously embed the physical partial differential equations of fluid flow and heat transfer in porous media as soft constraints into the loss function.

[0009] Step 3: Data-driven optimization based on surrogate model: The trained PINN neural network is embedded into the optimization framework as a substitute model. The backpropagation algorithm is used to calculate the precise 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 searched under the condition of satisfying the soil thermal balance constraint.

[0010] Preferably, in step 1, the numerical simulation software includes OpenGeoSys and COMSOL.

[0011] Preferably, in step 1, 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 velocity and influent temperature.

[0012] Preferably, step 2 includes the following sub-steps: Step 2-1: Construct the PINN neural network; the input layer of the PINN neural network includes: spatiotemporal coordinates x=(x,y,z), time t, and design variables. The output layer of the PINN neural network includes: the predicted temperature field. Pressure field .

[0013] Step 2-2, Embedding the Physical Control Equations: Transform the control equations of the hydrothermal coupled system into PDE residual form, where: The residual of the mass conservation equation is:

[0014] In the formula, Indicates the water storage coefficient. Indicates fluid dynamic viscosity, Indicates fluid density, For source and sink items, Indicates flow rate, This represents the gradient operator.

[0015] The residual of the energy conservation equation is:

[0016] In the formula, Indicates porosity. , These represent the specific heat capacities of the fluid and the solid skeleton, respectively. Indicates the effective thermal conductivity. For heat source items, This indicates the density of the solid skeleton.

[0017] Steps 2-3: Definition of Composite Loss Function: The training objective of the PINN neural network is to minimize the total loss function. Minimize the total loss function for:

[0018] In the formula, , , , These represent data error, PDE residual, boundary condition residual, and initial condition residual, respectively. , , , These represent the adaptive weights for data error, PDE residual, boundary condition residual, and initial condition residual, respectively.

[0019] Steps 2-4: Model Training: Calculate the partial derivatives of the network output with respect to spatiotemporal variables using automatic differentiation techniques. Update the network weights using a strategy combining Adam and L-BFGS optimizers until the loss function converges, thus obtaining a PINN surrogate model that combines high accuracy and physical consistency.

[0020] Preferably, in step 3, the objective function includes: maximizing heat exchange efficiency and minimizing cost.

[0021] The beneficial effects of this invention are: 1. This invention deeply embeds the partial differential residuals of the mass conservation equation (Darcy flow) and the energy conservation equation into the loss function of the neural network. This "soft constraint" forces the neural network to strictly adhere to physical laws while fitting OpenGeoSys benchmark data. Even in parameter ranges where training data is sparse, the network can perform reasonable nonlinear extrapolations based on physical equations, fundamentally eliminating non-physical predictions and ensuring the absolute reliability of the model in the global optimization process.

[0022] 2. This invention employs a dual-drive model of "OpenGeoSys high-fidelity data + PINN physical equations." First, it utilizes limited high-fidelity numerical simulation results as data anchors to indicate the macroscopic gradient direction for PINN training. Then, it uses physical residuals to refine the local features of the flow and temperature fields. This collaborative mechanism significantly reduces the training difficulty of PINN and accelerates convergence. Once training is complete, the PINN surrogate model can achieve millisecond-level thermal response prediction, making multi-parameter, multi-objective global optimization of buried pipe heat exchangers a reality within an extremely short timeframe.

[0023] 3. In the numerical model establishment and subsequent training boundary setting of the surrogate model, this invention strictly abandons the coarse total flow rate index. Since the surrogate model is based entirely on the strongly constrained operating condition of a single well with a constant flow rate for physical field evolution learning, its output thermal response characteristics perfectly match the hydraulic distribution characteristics of the actual geothermal network. Therefore, the optimal well spacing, well topology, and operating parameters obtained through this system optimization can directly guide the closed-loop design and actual exploitation of hydrothermal geothermal systems without the need for complex secondary hydraulic conversion, greatly shortening the transformation chain from theory to engineering practice. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating the overall design method of a PINN-based hydrothermal buried pipe heat exchanger according to the present invention. Figure 2 This is a schematic diagram of the design architecture of the present invention. Detailed Implementation

[0025] 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.

[0026] like Figures 1-2 As shown in this embodiment, the optimization design method for a hydrothermal buried pipe heat exchanger based on a physical information neural network is described. The specific steps are as follows: First, a high-precision 3D OpenGeoSys numerical model fully coupled with hydrothermal energy was established. A sample set covering design variables such as multi-well layout, well spacing, and injection temperature was generated using Latin hypercube sampling. Temperature and pressure response data at key spatiotemporal nodes were extracted through batch computation using OpenGeoSys. Next, a deep neural network was constructed to transform the mass and energy conservation equations in the porous medium into partial differential equation residuals, which, together with the discrete data errors generated by OpenGeoSys, formed a composite loss function. Finally, using a converged PINN model as the computational engine with a second-level response, and combined with a heuristic optimization algorithm, tens of thousands of global optimizations and parameter sensitivity analyses were performed on the design variables under engineering constraints such as geothermal anti-freezing and thermal breakthrough prevention. The optimal solution was then substituted back into OpenGeoSys for a single positive validation.

[0027] Step 1: 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, influent temperature) were extracted within the design space using Latin hypercube sampling. After simulation, temperature field T data at different spatiotemporal coordinate points (x, y, z, t) were extracted to form a high-quality initial dataset for supervised learning.

[0028] Step 2, Construction and Training of PINN: By leveraging the powerful nonlinear fitting capabilities of neural networks, the physical partial differential equations (PDEs) of fluid flow and heat transfer in porous media are embedded as soft constraints into the loss function.

[0029] Step 2-1, Network Structure Design: Constructing a Fully Connected Deep Neural Network Input layer: spatiotemporal coordinates x=(x,y,z), time t, and design variables. .

[0030] Output layer: Predicted temperature field and pressure field .

[0031] Step 2-2, Embedding the physical control equations: Transform the control equations of the hydrothermal coupled system into PDE residual form.

[0032] Mass conservation equation residuals:

[0033] According to Darcy's law, the flow velocity ; The water storage coefficient, For fluid dynamic viscosity, For fluid density, For source and sink items.

[0034] Energy conservation equation residuals:

[0035] in, and These are the specific heat capacities of the fluid and the solid skeleton, respectively. For effective thermal conductivity, This is a heat source term.

[0036] Steps 2-3: Definition of the composite loss function: The training objective of PINN is to minimize the total loss function. It is composed of a weighted average of data error, PDE residual, boundary condition (BC) residual, and initial condition (IC) residual:

[0037] Where w is the adaptive weight of each loss term.

[0038] Steps 2-4: Model Training Automatic Differentiation (AD) technology is used to calculate the partial derivatives of the network output with respect to spatiotemporal variables. A strategy combining Adam and L-BFGS optimizers is used to update the network weights until the loss function converges, thus obtaining a PINN surrogate model that combines high accuracy and physical consistency.

[0039] Step 3: Data-driven optimization based on the agent model: The trained PINN model is embedded into the optimization framework as an alternative model. Since PINN is end-to-end differentiable, this approach can directly utilize the backpropagation algorithm to calculate the precise gradient of the objective function (such as maximizing heat transfer efficiency or minimizing cost) with respect to the design variables. Combined with gradient descent algorithms or improved heuristic algorithms, the optimal set of design schemes is quickly searched while satisfying soil thermal balance constraints.

[0040] Compared with existing technologies, this implementation method differs significantly in its technical approach. First, it overcomes the black-box limitation of purely data-driven surrogate models. Existing dimensionality-reduction surrogate models often rely solely on intrinsic orthogonal decomposition and BP neural network fitting of snapshot data, lacking awareness and constraints on the physical governing equations of fluid flow and heat transfer in porous media. This implementation method, however, embeds the residuals of partial differential equations based on Darcy's law and the law of conservation of energy into the loss function, either rigidly or softly, achieving effective constraints of physical priors. Second, this implementation method overcomes the convergence bottleneck of pure PINN solutions. Some existing technologies attempt to completely replace the finite element solver with PINN to directly solve partial differential equations from scratch. However, under complex 3D geological models, multi-well interactions, and complex boundary conditions, pure PINN is extremely difficult to converge and computationally very time-consuming. This implementation method does not require PINN to solve partial differential equations independently; instead, it uses high-fidelity data generated by OpenGeoSys as the data anchor for network training, and simultaneously utilizes the residuals of partial differential equations to regulate the network's predictions in non-sampling regions, achieving dual-driven development by physical priors and data. Finally, this implementation method precisely aligns with the actual boundary control mechanism of the project, making the proxy model not only conform to physical laws but also perfectly match the hydraulic distribution of the actual geothermal pipe network.

[0041] The objective improvements of this invention are as follows: On the one hand, the generalization ability and prediction accuracy of the surrogate model are significantly improved. Due to the strict constraints of physical laws, even in the sparse parameter space region of OpenGeoSys training samples, the model can still ensure that the predicted temperature and pressure fields conform to thermodynamic common sense, eliminating non-physical prediction biases. On the other hand, this invention successfully breaks through the dilemma of balancing high accuracy and high efficiency. By condensing the high accuracy of numerical simulation software into the weights of PINN, the time for a single thermal response evaluation is reduced from several hours to milliseconds when performing tens of thousands of parameter sensitivity analyses and global optimization iterations, truly making the complex optimization design of multi-variable, multi-objective buried pipes possible within the engineering timeframe. In addition, since the model is built on a strict single-well baseline flow rate, the optimized parameters such as multi-well layout and well placement strategies do not need to undergo complex secondary hydraulic conversion, and can directly guide the exploitation design of closed-loop systems or hydrothermal geothermal systems, greatly shortening the conversion chain from theoretical optimization to engineering drawings.

[0042] Example This embodiment uses a hydrothermal shallow geothermal energy development project in Lanzhou as an engineering background to demonstrate the optimized design and application of a hydrothermal buried pipe heat exchanger. The core objective of this project is to find the optimal multi-well layout parameters and operating conditions within a limited site area to maximize long-term total heat extraction and control system heat loss.

[0043] (1) A three-dimensional hydrothermal coupling numerical model of the site was established using OpenGeoSys software. When setting boundary conditions and operating conditions, hydraulic distribution was strictly based on a single well flow rate of 80 kg / s. 300 sets of samples were generated in the design space using Latin hypercube sampling, with variables including well spacing, burial depth, and influent temperature. Batch operation was used to extract temperature and pressure field data of key spatiotemporal nodes during the 3-year operation period.

[0044] (2) A fully connected PINN network with 8 hidden layers and 60 neurons in each layer was constructed. The extracted data was used as data points, and PDE residuals were calculated by uniformly scattering the data points in the input spatiotemporal domain. In the composite loss function, the residual weights of the Darcy flow equation and the energy conservation equation were initially set to 1.0 and dynamically updated using an adaptive weight adjustment algorithm. After pre-training with the Adam optimizer and fine-tuning with the L-BFGS optimizer, the loss function decreased to the order of 1e-5 after about 2 hours of training, and the model converged, successfully capturing the nonlinear physical evolution of the flow field and temperature field under constant flow pumping in a single well.

[0045] (3) The trained PINN is used as a high-fidelity surrogate model and embedded in the genetic algorithm for bi-objective global optimization. The total scale is set to 100 and the iteration is 200.

[0046] (4) Comparison of computational efficiency: If the traditional OpenGeoSys is directly called to perform these 20,000 iterations of evaluation, each calculation will take about 15 minutes, and the total time will be several months, which is completely infeasible in engineering. However, by calling the PINN proxy model of this invention, each evaluation only takes about 5 milliseconds, and 20,000 global optimizations can be completed within 2 minutes, which improves the computational efficiency by hundreds of thousands of times.

[0047] (5) Physical Reliability Verification: The optimization algorithm ultimately output a set of Pareto optimal solutions. Substituting these optimal parameters back into the original OpenGeoSys for forward numerical simulation verification, it was found that the relative errors between the temperature field distribution, thermal breakthrough time, and bottom hole flowing pressure predicted by PINN and the high-fidelity numerical solutions were all less than 2.5%. Especially in the data-sparse flow field abrupt change regions such as the center of the pumping well group, due to the strong constraint of the PDE physical residuals, PINN did not exhibit any phenomena that violated the second law of thermodynamics or the law of conservation of mass. This fully demonstrates that the method of this invention achieves significant cost reduction and efficiency improvement in the optimized design of the buried pipe heat exchange system while ensuring extremely high physical consistency and prediction accuracy.

[0048] In summary, this invention constructs an optimization design framework for hydrothermal buried pipe heat exchangers that combines physical consistency with computational efficiency by deeply integrating Physical Information Neural Network (PINN) with high-fidelity numerical simulation data. This method not only fundamentally solves the problems of poor generalization ability and susceptibility to non-physical solutions in traditional pure data-driven models, but also overcomes the bottlenecks of convergence difficulties and high training costs when using pure PINN to solve complex engineering problems. By embedding the partial differential residuals of mass and energy conservation equations into the loss function, the physical reliability of the model during the global optimization process is ensured. With the dual-drive mode of "OpenGeoSys high-fidelity data + PINN physical equations," millisecond-level thermal response prediction is achieved, making multi-parameter, multi-objective global optimization a reality within the engineering timeframe. Simultaneously, the design strictly based on a single-well constant flow condition allows the optimization results to directly guide practical engineering applications, significantly shortening the transformation chain from theory to engineering entity, and providing a new technical path for the efficient and accurate design of hydrothermal buried pipe heat exchangers.

[0049] 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. An optimized design method for a PINN-based hydrothermal buried pipe heat exchanger, characterized in that, Includes the following steps: Step 1: Numerical simulation and benchmark dataset generation: A three-dimensional unsteady-state numerical model of shallow buried pipe heat transfer is established using numerical simulation software; different soil thermal properties, geometric parameters and operating conditions are extracted in the design space through Latin hypercube sampling; after running the simulation, temperature field data at different spatiotemporal coordinate points are extracted to form a high-quality initial dataset for supervised learning. Step 2: Construction and training of PINN: Construct a PINN neural network to transform the mass conservation equation and energy conservation equation in porous media into partial differential equation residuals, which together with the discrete data errors generated by numerical simulation software form a composite loss function; utilize the nonlinear fitting capability of the PINN neural network, and embed the physical partial differential equations of fluid flow and heat transfer in porous media as soft constraints into the loss function. Step 3: Data-driven optimization based on surrogate model: The trained PINN neural network is embedded into the optimization framework as a substitute model. The backpropagation algorithm is used to calculate the precise 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 searched under the condition of satisfying the soil thermal balance constraint.

2. The optimized design method for a PINN-based hydrothermal buried pipe heat exchanger according to claim 1, characterized in that, In step 1, the numerical simulation software includes OpenGeoSys and COMSOL.

3. The optimized design method for a PINN-based hydrothermal buried pipe heat exchanger according to claim 1, characterized in that, In step 1, 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 inlet water temperature.

4. The optimized design method for a PINN-based hydrothermal buried pipe heat exchanger according to claim 1, characterized in that, Step 2 includes the following sub-steps: Step 2-1: Construct the PINN neural network; the input layer of the PINN neural network includes: spatiotemporal coordinates x=(x,y,z), time t, and design variables. The output layer of the PINN neural network includes: a predicted temperature field. Pressure field ; Step 2-2, Embedding the Physical Control Equations: Transform the control equations of the hydrothermal coupled system into PDE residual form, where: The residual of the mass conservation equation is: In the formula, Indicates the water storage coefficient. Indicates fluid dynamic viscosity, Indicates fluid density, For source and sink items, Indicates flow rate, Represents the gradient operator; The residual of the energy conservation equation is: In the formula, Indicates porosity. , These represent the specific heat capacities of the fluid and the solid skeleton, respectively. Indicates the effective thermal conductivity. For heat source items, Indicates the density of the solid skeleton; Steps 2-3: Definition of Composite Loss Function: The training objective of the PINN neural network is to minimize the total loss function. The minimization of the total loss function for: In the formula, , , , These represent data error, PDE residual, boundary condition residual, and initial condition residual, respectively. , , , These represent the adaptive weights for data error, PDE residual, boundary condition residual, and initial condition residual, respectively. Steps 2-4: Model Training: Calculate the partial derivatives of the network output with respect to spatiotemporal variables using automatic differentiation techniques. Update the network weights using a strategy combining Adam and L-BFGS optimizers until the loss function converges, thus obtaining a PINN surrogate model that combines high accuracy and physical consistency.

5. The optimized design method for a PINN-based hydrothermal buried pipe heat exchanger according to claim 1, characterized in that, In step 3, the objective function includes: maximizing heat exchange efficiency and minimizing cost.

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