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Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

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…

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…

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…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

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…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework 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…

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…

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…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.

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…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…