相关论文: Evolving Neural Network (ENN) Method for One-Dimen…

We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined…

We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative…

We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal…

The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are…

In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in…

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…

We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…

Deep neural networks continue to show improved performance with increasing depth, an encouraging trend that implies an explosion in the possible permutations of network architectures and hyperparameters for which there is little intuitive…

This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differential equations, specifically linear advection-reaction…

We introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the method outperforms mesh-based numerical methods in terms of the number of…

We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differential equations (PDEs) are challenging to solve,…

In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph.…

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling…

Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based…

The remarkable success of Deep Neural Networks(DNN) is driven by gradient-based optimization, yet this process is often undermined by its tendency to produce disordered weight structures, which harms feature clarity and degrades learning…

A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…

We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…

This work focuses on the numerical solution of hyperbolic conservations laws (possibly endowed with a source term) using the Active Flux method. This method is an extension of the finite volume method. Instead of solving a Riemann Problem,…

We study a conservative data-driven discretization for one-dimensional hyperbolic conservation laws based on the classical fifth-order WENO finite-volume scheme and a hypernetwork architecture. In the proposed Hyper--WENO5 Conservative-Form…