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

arXiv: https://arxiv.org/abs/2511.00338 · HTML: https://mlsanity.com/paper/2511.00338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Soft-IntroVAE: Analyzing and Improving the Introspective Variational Autoencoder](https://mlsanity.com/paper/2012.13253/) (2020)
- [Differentiable Visual Computing for Inverse Problems and Machine Learning](https://mlsanity.com/paper/2312.04574/) (2023)

## Built on by (most cited first, 1 of 1)

- [Proximal-Based Generative Modeling for Bayesian Inverse Problems](https://mlsanity.com/paper/2605.13278/) (2026)

## Abstract (arXiv)

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.