GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs

TL;DR

GPT-PINN introduces a meta-learning framework for parametric PDEs that significantly reduces training time and complexity by leveraging pre-trained PINNs and a hyper-reduced meta-network for efficient, accurate surrogate modeling.

Contribution

It proposes GPT-PINN, a novel meta-learning approach that uses pre-trained PINNs within a hyper-reduced network to efficiently learn parametric PDE solutions across diverse configurations.

Findings

Reduces training time for parametric PDEs.

Achieves accurate surrogate solutions with fewer trained networks.

Enables efficient multi-query and real-time PDE simulations.

Abstract

Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of modern heterogeneous hardware. However, its training is still time-consuming, especially in the multi-query and real-time simulation settings, and its parameterization often overly excessive. In this paper, we propose the Generative Pre-Trained PINN (GPT-PINN) to mitigate both challenges in the setting of parametric PDEs. GPT-PINN represents a brand-new meta-learning paradigm for parametric systems. As a network of networks, its outer-/meta-network is hyper-reduced with only one hidden layer having significantly reduced number of neurons. Moreover, its activation function at each hidden neuron is a (full) PINN pre-trained at a judiciously selected system configuration. The meta-network adaptively ``learns'' the parametric dependence of the system and ``grows'' this hidden layer one neuron at a time. In the end, by encompassing a very small number of networks trained at this set of adaptively-selected parameter values, the meta-network is capable of generating surrogate solutions for the parametric system across the entire parameter domain accurately and efficiently.