92 citations · 244 across the 9 of their papers we have counts for
11 papers
Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma +8
We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations…
Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression
Shahriar Iravanian, Carl Julius Martensen, Alessandro Cheli +4
Most computer algebra systems (CAS) support symbolic integration as core functionality. The majority of the integration packages use a combination of heuristic algebraic and rule-b…
NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations
Kirill Zubov, Zoe McCarthy, Yingbo Ma +11
Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical…
Composing Modeling and Simulation with Machine Learning in Julia
Chris Rackauckas, Ranjan Anantharaman, Alan Edelman +10
In this paper we introduce JuliaSim, a high-performance programming environment designed to blend traditional modeling and simulation with machine learning. JuliaSim can build acce…
High-performance symbolic-numerics via multiple dispatch
Shashi Gowda, Yingbo Ma, Alessandro Cheli +4
As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the…
Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics
Avik Pal, Yingbo Ma, Viral Shah +1
Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framewo…
ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling
Yingbo Ma, Shashi Gowda, Ranjan Anantharaman +3
Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be…
Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks
Ranjan Anantharaman, Yingbo Ma, Shashi Gowda +4
Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs. These costs can be amortized by evaluatin…
Universal Differential Equations for Scientific Machine Learning
Christopher Rackauckas, Yingbo Ma, Julius Martensen +6
In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciM…
DiffEqFlux.jl - A Julia Library for Neural Differential Equations
Chris Rackauckas, Mike Innes, Yingbo Ma +3
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the…
A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions
Yingbo Ma, Vaibhav Dixit, Mike Innes +2
Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of cho…