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04/13/2023
Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms
We demonstrate a high-performance vendor-agnostic method for massively p...
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07/17/2022
Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations
Numerically solving ordinary differential equations (ODEs) is a naturall...
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01/29/2022
Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression
Most computer algebra systems (CAS) support symbolic integration as core...
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05/12/2021
Composing Modeling and Simulation with Machine Learning in Julia
In this paper we introduce JuliaSim, a high-performance programming envi...
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05/09/2021
High-performance symbolic-numerics via multiple dispatch
As mathematical computing becomes more democratized in high-level langua...
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05/09/2021
Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics
Democratization of machine learning requires architectures that automati...
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03/09/2021
ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling
Getting good performance out of numerical equation solvers requires that...
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10/07/2020
Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks
Modern design, control, and optimization often requires simulation of hi...
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01/13/2020
Universal Differential Equations for Scientific Machine Learning
In the context of science, the well-known adage "a picture is worth a th...
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02/06/2019
DiffEqFlux.jl - A Julia Library for Neural Differential Equations
DiffEqFlux.jl is a library for fusing neural networks and differential e...
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12/05/2018