A DeepONet joint Neural Tangent Kernel Hybrid Framework for Physics-Informed Inverse Source Problems and Robust Image Reconstruction

TL;DR

This paper introduces a hybrid DeepONet-NTK framework that effectively solves inverse source problems and image reconstruction by integrating physics-informed constraints, demonstrating robustness and accuracy across diverse datasets.

Contribution

The novel hybrid DeepONet-NTK approach combines neural tangent kernels with physics-informed neural networks for improved inverse problem solving.

Findings

Successfully localizes sources governed by Navier-Stokes equations

Achieves robust image reconstruction with noisy and sparse data

Demonstrates scalability and high accuracy on synthetic and real datasets

Abstract

This work presents a novel hybrid approach that integrates Deep Operator Networks (DeepONet) with the Neural Tangent Kernel (NTK) to solve complex inverse problem. The method effectively addresses tasks such as source localization governed by the Navier-Stokes equations and image reconstruction, overcoming challenges related to nonlinearity, sparsity, and noisy data. By incorporating physics-informed constraints and task-specific regularization into the loss function, the framework ensures solutions that are both physically consistent and accurate. Validation on diverse synthetic and real datasets demonstrates its robustness, scalability, and precision, showcasing its broad potential applications in computational physics and imaging sciences.