Multi-Fidelity Physics-Informed Generative Adversarial Network for Solving Partial Differential Equations

Abstract

We propose a novel method for solving partial differential equations using multi-fidelity physics-informed generative adversarial networks. Our approach incorporates physics supervision into the adversarial optimization process to guide the learning of the generator and discriminator models. The generator has two components: one that approximates the low-fidelity response of the input and another that combines the input and low-fidelity response to generate an approximation of high-fidelity responses. The discriminator identifies whether the input–output pairs accord not only with the actual high-fidelity response distribution, but also with physics. The effectiveness of the proposed method is demonstrated through numerical examples and compared to existing methods.