融合DeepONet与NTK，解决物理约束下的逆源问题与图像重建。
A DeepONet joint Neural Tangent Kernel Hybrid Framework for Physics-Informed Inverse Source Problems and Robust Image Reconstruction
- 用DeepONet结合神经正切核建模非线性物理系统。
- 在合成与真实数据上实现高精度逆源定位与图像重建。
- 适合需要物理一致性约束的计算物理与成像领域研究者。
本文提出一种新颖的混合框架，将深度算子网络（DeepONet）与神经正切核（NTK）相结合，用于求解复杂的逆问题。该方法有效应对由纳维-斯托克斯方程控制的源定位任务以及图像重建问题，克服了非线性、数据稀疏性和噪声干扰等挑战。通过在损失函数中引入物理信息约束和特定任务的正则化，确保解具备物理一致性与高准确性。在多种合成与真实数据集上的验证表明，该框架具有强鲁棒性、良好可扩展性与高精度，展现出在计算物理与成像科学中的广泛应用潜力。
原文摘要 · Abstract (English)
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.
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