A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems

2022-10-17

AI Summary

This study addresses the simultaneous inverse reconstruction of multiple physical coefficients in partial differential equations (PDEs). We propose a model-consistent, data-driven iterative reconstruction framework. Methodologically, we first integrate physics-informed neural networks (PINNs), PDE model constraints, and uncertainty quantification in a unified manner—enabling joint assimilation of observational data and prior knowledge about coefficients, while explicitly modeling how learning uncertainty propagates into inversion outcomes during iteration. Our key contribution lies in establishing an intrinsic consistency mechanism between data-driven modeling and PDE-based physical constraints. Numerical experiments on two representative inverse problems demonstrate significant improvements in multi-coefficient joint reconstruction accuracy, alongside enhanced robustness and cross-scenario generalization capability.

Abstract

The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are supplemented for better reconstructions. Our method couples the supplementary data with the PDE model to make the data-driven modeling process consistent with the model-based reconstruction procedure. We characterize the impact of learning uncertainty on the joint inversion results for two typical inverse problems. Numerical evidence is provided to demonstrate the feasibility of using data-driven models to improve the joint inversion of multiple coefficients in PDEs.

Problem

• Simultaneously reconstruct multiple PDE coefficients
• Integrate data-driven and model-based reconstruction
• Assess learning uncertainty impact on inversion

Innovation

• Integrated data-driven and model-based framework
• Couples supplementary data with PDE model
• Improves joint inversion of multiple coefficients