相关论文: Unisolver: PDE-Conditional Transformers Towards Un…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical…

The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on a fixed benchmark distribution but generalization under…

In scientific computing, the formulation of numerical discretisations of partial differential equations (PDEs) as untrained convolutional layers within Convolutional Neural Networks (CNNs), referred to by some as Neural Physics, has…

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…

Efficient physics simulations are essential for numerous applications, ranging from realistic cloth animations or smoke effects in video games, to analyzing pollutant dispersion in environmental sciences, to calculating vehicle drag…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

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…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…

In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies…

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…