The continuous partial differential equations governing a given physical phenomenon, such
as the Navier–Stokes equations describing the fluid motion, must be numerically discretized …

We present a methodology combining neural networks with physical principle constraints in
the form of partial differential equations (PDEs). The approach allows to train neural …

The heart is a fantastic machine; during a normal lifetime it beats about 2.5 billion times and
pumps 200.000 tons of blood through an enormous system of vessels extending 160.000 …

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

This work considers a general structure of the additively partitioned Runge--Kutta methods
by allowing for different stage values as arguments of different components of the right-hand …

We demonstrate a high-performance vendor-agnostic method for massively parallel solving
of ensembles of ordinary differential equations (ODEs) and stochastic differential equations …

In this paper, we develop new techniques for solving the large, coupled linear systems that
arise from fully implicit Runge–Kutta methods. This method makes use of the iterative …

Hierarchical decays of N matter species to radiation may balance against Hubble expansion
to yield stasis, a new phase of cosmological evolution with constant matter and radiation …

Abstract We present the Einstein-Boltzmann module of the Disco-Dj (DIfferentiable
Simulations for COsmology—Done with J ax) software package. This module implements a …

This paper presents details of the solver Aghora for the simulation of unsteady compressible
turbulent flows. Different modelling levels are used: Reynolds averaged Navier-Stokes …