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The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as…

In this paper, we explore and compare multiple solutions to the problem of data augmentation in image classification. Previous work has demonstrated the effectiveness of data augmentation through simple techniques, such as cropping,…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…

Data preparation, also called data wrangling, is considered one of the most expensive and time-consuming steps when performing analytics or building machine learning models. Preparing data typically involves collecting and merging data from…

The accuracy of solving partial differential equations (PDEs) on coarse grids is greatly affected by the choice of discretization schemes. In this work, we propose to learn time integration schemes based on neural networks which satisfy…

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

Image classification has been a popular task due to its feasibility in real-world applications. Training neural networks by feeding them RGB images has demonstrated success over it. Nevertheless, improving the classification accuracy and…

The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those…

Manipulating data, such as weighting data examples or augmenting with new instances, has been increasingly used to improve model training. Previous work has studied various rule- or learning-based approaches designed for specific types of…

This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…

We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…

Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively…

This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully…

This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…