Interpretable Solutions for Multi-Physics PDEs Using T-NNGP

• DOI: 10.1609/aaai.v39i13.33556
• Publication Date: 2025-04-11T12:16:09Z
• Authors: Lulu Cao; Zexin Lin; Kay Chen Tan; Min Jiang

Multiphysics simulation aims to predict and understand interactions between multiple physical phenomena, aiding in comprehending natural processes guiding engineering design. The system of Partial Differential Equations (PDEs) is crucial for representing these fields, solving PDEs fundamental such simulations. However, current methods primarily yield numerical outputs, limiting interpretability generalizability. We introduce T-NNGP, a hybrid genetic programming algorithm that integrates traditional with deep learning derive approximate symbolic expressions unknown functions within PDEs. T-NNGP initially obtains solutions using methods, then generates candidate via reinforcement learning, finally optimizes programming. Furthermore, universal decoupling strategy guides the search direction addresses coupling problems, thereby accelerating process. Experimental results on three types demonstrate our method can reliably obtain human-understandable fit both from methods. This work advances multiphysics by enhancing ability PDEs, improving understanding complex phenomena.