Related papers: ExaHyPE: An Engine for Parallel Dynamically Adapti…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…

While exogenous variables have a major impact on performance improvement in time series analysis, inter-series correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of…

Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

In this talk I discuss the general question of the portability of Molecular Dynamics codes for diffusive systems on parallel computers of the APE family. The intrinsic single precision arithmetics of the today available APE platforms does…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…

We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…

A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the…

This document is one of the deliverable reports created for the ESCAPE project. ESCAPE stands for Energy-efficient Scalable Algorithms for Weather Prediction at Exascale. The project develops world-class, extreme-scale computing…

The limited availability of high-quality training data poses a major obstacle in data-driven PDE solving, where expensive data collection and resolution constraints severely impact the ability of neural operator networks to learn and…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Controlling systems governed by partial differential equations is an inherently hard problem. Specifically, control of wave dynamics is challenging due to additional physical constraints and intrinsic properties of wave phenomena such as…

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics…

We present the design and scalable implementation of an exascale climate emulator for addressing the escalating computational and storage requirements of high-resolution Earth System Model simulations. We utilize the spherical harmonic…