Adaptive heat conduction technology based on physics–data collaborative modeling and its engineering simulation

Abstract

In engineering domains such as thermal management of high-power electronic devices, efficient and high-fidelity simulation of complex transient heat conduction processes is hindered by the high computational cost and poor adaptability of conventional numerical methods. To enhance prediction accuracy and stability, this paper proposes a novel adaptive heat conduction technology that synergistically integrates physical laws with data-driven approaches. By establishing a collaborative mechanism between physical constraints and adversarial optimization, the method achieves full-field thermal reconstruction under mesh-free and small-sample conditions. Specifically, a dual-network collaborative optimization framework is constructed by combining the physical constraints of Physics-Informed Neural Networks (PINNs) with the adversarial training of Generative Adversarial Networks (GANs) to enable high-precision solutions for heat conduction. First, a fully connected neural network embeds the physical residual derived from the governing equation via automatic differentiation. Second, a generator constructs the temperature field, which is then refined by a discriminator to enhance the physical plausibility of the generated samples. Furthermore, an adaptive sampling strategy dynamically enriches the training dataset in regions of high prediction error, thereby improving the fidelity of the reconstructed thermal field. The practical efficacy of the proposed approach is demonstrated through canonical engineering simulations, such as transient chip cooling. Results show that the physics–data collaborative modeling framework effectively captures the underlying heat conduction dynamics, yielding temperature distributions that closely approximate the ground truth. The spatiotemporal evolution of the generated thermal field adheres to the energy diffusion law governed by the heat equation, with prediction errors concentrated in the range of 0.04–0.10, confirming its high-fidelity modeling capability for complex scenarios. The adversarial training mechanism significantly enhances numerical stability: the generator and discriminator losses converge from initial values of 1.41 and 0.72 to 1.35 and 0.64, respectively, while the mean squared error (MSE) of generated samples improves from 0.037 to 0.004—indicating progressive convergence toward the true solution through dynamic competition. Moreover, the adaptive sampling strategy effectively focuses computational resources on high-error regions (e.g., near heat source boundaries or discontinuous interfaces), leading to temporal convergence of the error distribution and validating its effectiveness in local feature refinement. This work provides an efficient and robust solution for heat conduction problems that harmonizes physical consistency with data-driven flexibility.