A unified physics-informed generative operator framework for general inverse problems

TL;DR

This paper introduces IGNO, a physics-informed generative neural operator framework that effectively solves diverse inverse problems governed by PDEs without requiring labeled data, handling high-dimensional, discontinuous coefficients, and noisy measurements.

Contribution

The paper presents a unified, physics-based generative neural operator approach for inverse problems, eliminating the need for labeled training data and enabling stable, accurate reconstructions in challenging scenarios.

Findings

IGN0 outperforms state-of-the-art methods across various inverse problems.

It achieves accurate reconstructions with high noise levels.

The framework generalizes well to out-of-distribution targets.

Abstract

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or discontinuous. Existing deep learning approaches either require extensive labeled datasets or are limited to specific measurement types, often leading to failure in such regimes and restricting their practical applicability. Here, a novel generative neural operator framework, IGNO, is introduced to overcome these limitations. IGNO unifies the solution of inverse problems from both point measurements and operator-valued data without labeled training pairs. This framework encodes high-dimensional, potentially discontinuous coefficient fields into a low-dimensional latent space, which drives neural operator decoders to reconstruct both coefficients and PDE solutions. Training relies purely on physics constraints through PDE residuals, while inversion proceeds via efficient gradient-based optimization in latent space, accelerated by an a priori normalizing flow model. Across a diverse set of challenging inverse problems, including recovery of discontinuous coefficients from solution-based measurements and the EIT problem with operator-based measurements, IGNO consistently achieves accurate, stable, and scalable inversion even under severe noise. It consistently outperforms the state-of-the-art method under varying noise levels and demonstrates strong generalization to out-of-distribution targets. These results establish IGNO as a unified and powerful framework for tackling challenging inverse problems across computational science domains.