Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Publication

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray
2020
Journal Articles

Abstract

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithms are generally not tailored to respect such constraints.

Official source

Jan Sickmann Hesthaven, Deep Ray
2020
Journal Articles

Abstract

Official source

Related concepts (32)

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Euler equations (fluid dynamics)

In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible or compressible flow. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is a solenoidal field.

Computer simulation

Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.

Related publications (37)

Constraint-aware neural networks for Riemann problems

Graph Chatbot

Transfer learning-based approach for evaluating residual stiffness in carbon fiber reinforced composites and adhesives

Development of a blind control occupant behaviour model (BC-OBM) based on contextual and time-related factors through supervised machine learning approaches

A smoothed particle hydrodynamics framework for fluid simulation in robotics