Parameterized physics-informed neural networks for a transient thermal problem: A pure physics-driven approach

Parameterization in computational fluid dynamics is crucial for exploring design ranges and optimizing systems. Traditional methods struggle with efficient parameter variation, requiring multiple simulations and significant computational resources. This study evaluates physics-informed neural networks (PINNs) to address this challenge, highlighting its ability to handle multiple parameter variations, including geometric configurations, Rayleigh, and Prandtl numbers, within different intervals in a single training process. The study focuses on a highly challenging problem in PINNs: transient natural convection, characterized by transient coupled equations with source terms. Although some issues have been previously addressed, applying pure physics-driven PINNs to transient natural convection and parameterization challenges represents a novel approach. The model, benchmarked against finite difference, finite element, and finite volume methods, shows excellent predictive accuracy but surpasses them in versatility and robustness when handling several parameter variations simultaneously. The results show that the computational cost increases by 15 % for parameterizing a single parameter and by 46 % for parameterizing all three parameters simultaneously. Moreover, special normalization techniques for large-scale parameters, such as Rayleigh number, are crucial for parameterized models; without them, the training process may diverge. This paper provides insights and techniques to overcome the challenges in parameterization for coupled problems with source terms.