Related papers: In-Context Operator Learning with Data Prompts for…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Optical neural networks (ONNs) are emerging as a promising neuromorphic computing paradigm for object recognition, offering unprecedented advantages in light-speed computation, ultra-low power consumption, and inherent parallelism. However,…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded this to include the…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…

Object recognition has become a crucial part of machine learning and computer vision recently. The current approach to object recognition involves Deep Learning and uses Convolutional Neural Networks to learn the pixel patterns of the…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

With the rise of large-scale models trained on broad data, in-context learning has become a new learning paradigm that has demonstrated significant potential in natural language processing and computer vision tasks. Meanwhile, in-context…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…

Hyperparameters searches are computationally expensive. This paper studies some general choices of hyperparameters and training methods specifically for operator learning. It considers the architectures DeepONets, Fourier neural operators…

Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…

When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning dynamics that can differ from those seen in direct function…

Attention-based neural networks such as transformers have demonstrated a remarkable ability to exhibit in-context learning (ICL): Given a short prompt sequence of tokens from an unseen task, they can formulate relevant per-token and…

Large pre-trained language models (PLMs) have made significant progress in encoding world knowledge and spawned a new set of learning paradigms including zero-shot, few-shot, and in-context learning. Many language tasks can be modeled as a…