Solution and applications of parameterized convective heat transfer equations using physics-informed neural networks

Solving parameterized governing equations is of significant importance for rapidly obtaining solutions of a series of design parameter combinations. This study introduces physics-driven parameterized Physics-Informed Neural Networks (p-PINNs) for solving parameterized convective heat transfer equations. By incorporating design parameters into the network inputs, p-PINNs eliminate the need to solve individual cases as in traditional computational fluid dynamics (CFD). The p-PINNs include two sub-networks to simulate flow and heat transfer separately, integrating specialized strategies such as a novel extended flow rate constraint to enhance training efficiency and accuracy. Taking flow and heat transfer in a wavy channel as a representative example, parameterized solutions are obtained over a Reynolds number (Re) range of [50, 400] and Prandtl number range of [0.5, 10]. Benchmarked against CFD results, extensive tests demonstrate that p-PINNs achieve accurate predictions, with the average accuracy of flow fields exceeding 99.6 %, and that of temperature surpassing 99.6 % when Peclet number (Pe) ≤ 2000, while exhibiting a drop as Pe > 3000. For computational efficiency, the trained models realize acceleration greater than 100 times compared to CFD. Finally, the trained models’ versatility is further illustrated in three distinct application scenarios. Notably, the model is capable of accurately inverting unknown boundary conditions with minimal data and can be easily and efficiently fine-tuned for improved prediction accuracy within sub-design ranges. Overall, this work presents an improved PINN method and showcase its potential for solving parameterized equations accurately and efficiently, with exceptional versatility of the trained models across diverse scenarios.