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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…
The development of efficient surrogates for partial differential equations (PDEs) is a critical step towards scalable modeling of complex, multiscale systems-of-systems. Convolutional neural networks (CNNs) have gained popularity as the…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the…
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…
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…
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 solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…
The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…
The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…
Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural…
In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring…
Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high computational costs, especially when multiple evaluations must…
Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the…
Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…
Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
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…