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

2025-10-31

AI Summary

This work addresses two physics-informed inverse problems—inverse source localization and image reconstruction—governed by the Navier–Stokes equations, where challenges arise from nonlinear dynamics, sparse observations, and measurement noise. We propose a hybrid physics-informed operator learning framework that integrates DeepONet with the neural tangent kernel (NTK), incorporating hard PDE constraints and task-specific regularization to jointly enforce physical consistency and generalization capability. Compared to conventional physics-informed neural networks (PINNs) and purely data-driven approaches, our method achieves significantly improved inversion accuracy and robustness under limited-data regimes. Extensive evaluations on multiple synthetic and real-world flow field datasets demonstrate high-precision source localization and high-fidelity image reconstruction, while exhibiting strong scalability and practical deployability.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Solving physics-informed inverse source problems with nonlinearity and sparsity
• Addressing robust image reconstruction under noisy data conditions
• Developing hybrid framework for Navier-Stokes governed source localization

Innovation

• Hybrid DeepONet and Neural Tangent Kernel framework
• Incorporates physics-informed constraints and regularization
• Solves inverse source problems and image reconstruction