Related papers: A DeepONet joint Neural Tangent Kernel Hybrid Fram…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Given the complexity of genetic risk prediction, there is a critical need for the development of novel methodologies that can effectively capture intricate genotype--phenotype relationships (e.g., nonlinear) while remaining statistically…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…

Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…

The Neural Tangent Kernel (NTK) has recently attracted intense study, as it describes the evolution of an over-parameterized Neural Network (NN) trained by gradient descent. However, it is now well-known that gradient descent is not always…

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture…

A rising trend in theoretical deep learning is to understand why deep learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method that is equivalent to using gradient descent to train a multi-layer infinitely-wide neural…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep neural networks with physics-informed loss, providing insights…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…

Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure -- a binary classification task that uses a deep fully-connected neural network to classify…

Blind single image super-resolution (SISR) is a challenging task in image processing due to the ill-posed nature of the inverse problem. Complex degradations present in real life images make it difficult to solve this problem using na\"ive…

We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…