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Machine learning and artificial neural networks (ANNs) have increasingly become integral to data analysis research in astrophysics due to the growing demand for fast calculations resulting from the abundance of observational data.…

We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the learning abilities of artificial neural networks with…

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Evolutional deep neural networks (EDNN) solve partial differential equations (PDEs) by marching the network representation of the solution fields, using the governing equations. Use of a single network to solve coupled PDEs on large domains…

Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…

Time-fractional differential equations offer a robust framework for capturing intricate phenomena characterized by memory effects, particularly in fields like biotransport and rheology. However, solving inverse problems involving fractional…

Physics-informed neural networks (PiNNs) recently emerged as a powerful solver for a large class of partial differential equations under various initial and boundary conditions. In this paper, we propose trapz-PiNNs, physics-informed neural…

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…

We propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary both in space and time. In the first inverse problem, we…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

We have designed a new method to fit the energy and atomic forces using a single artificial neural network (SANN) for any number of chemical species present in a molecular system. The traditional approach for fitting the potential energy…

There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…

This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…

This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…