相关论文: PDE Generalization of In-Context Operator Networks…

We investigate the generalization capabilities of In-Context Operator Networks (ICONs), a new class of operator networks that build on the principles of in-context learning, for higher-order partial differential equations. We extend…

In-context operator networks (ICON) are a class of operator learning methods based on the novel architectures of foundation models. Trained on a diverse set of datasets of initial and boundary conditions paired with corresponding solutions…

This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight…

In-context operator learning enables neural networks to infer solution operators from contextual examples without weight updates. While prior work has demonstrated the effectiveness of this paradigm in leveraging vast datasets, a systematic…

In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, existing ICONs process each spatial point as an individual…

Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data from multiple…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

We propose a novel transformer-based neural network architecture (ICON-OCnet) for solving optimal order execution problems in the presence of unknown price impact. Our architecture facilitates data-driven in-context operator learning for…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

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 paper explores in-context learning for image copy detection (ICD), i.e., prompting an ICD model to identify replicated images with new tampering patterns without the need for additional training. The prompts (or the contexts) are from…

In-context learning (ICL) enables large language models to adapt to new tasks from demonstrations without parameter updates. Despite extensive empirical studies, a principled understanding of ICL emergence at scale remains more elusive. We…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Building models that generalize across physical systems without retraining remains a central challenge in computational science. Here we introduce In-Context Modeling (ICM), a retrain-free paradigm that infers physical relationships…

In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

In-context learning (ICL) refers to the ability of a model to learn new tasks from examples in its input without any parameter updates. In contrast to previous theories of ICL relying on toy models and data settings, recently it has been…