相关论文: Physics-constrained neural differential equations …

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

We present a modeling study of a nanopore-based transistor computed by a mean-field continuum theory (Poisson-Nernst-Planck, PNP) and a hybrid method including particle simulation (Local Equilibrium Monte Carlo, LEMC) that is able to take…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…

Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

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…

Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS$_2$),…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Solving partial differential equations with deep learning makes it possible to reduce simulation times by multiple orders of magnitude and unlock scientific methods that typically rely on large numbers of sequential simulations, such as…

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore…

There is a significant need for precise and reliable forecasting of the far-field noise emanating from shipping vessels. Conventional full-order models based on the Navier-Stokes equations are unsuitable, and sophisticated model reduction…

Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with…

The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…

Recently deep learning and machine learning approaches have been widely employed for various applications in acoustics. Nonetheless, in the area of sound field processing and reconstruction classic methods based on the solutions of wave…

The coupling of Proper Orthogonal Decomposition (POD) and deep learning-based ROMs (DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly accurate, surrogates for the real time solution of parametric nonlinear…