Search Results for author: Christopher Rackauckas

Found 10 papers, 8 papers with code

Differentiating Metropolis-Hastings to Optimize Intractable Densities

1 code implementation13 Jun 2023 Gaurav Arya, Ruben Seyer, Frank Schäfer, Kartik Chandra, Alexander K. Lew, Mathieu Huot, Vikash K. Mansinghka, Jonathan Ragan-Kelley, Christopher Rackauckas, Moritz Schauer

We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete components within it.

Continuous Deep Equilibrium Models: Training Neural ODEs faster by integrating them to Infinity

1 code implementation28 Jan 2022 Avik Pal, Alan Edelman, Christopher Rackauckas

Additionally, we address the question: is there a way to simultaneously achieve the robustness of implicit layers while allowing the reduced computational expense of an explicit layer?

Julia for Biologists

1 code implementation21 Sep 2021 Elisabeth Roesch, Joe G. Greener, Adam L. MacLean, Huda Nassar, Christopher Rackauckas, Timothy E. Holy, Michael P. H. Stumpf

Increasing emphasis on data and quantitative methods in the biomedical sciences is making biological research more computational.

Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics

3 code implementations9 May 2021 Avik Pal, Yingbo Ma, Viral Shah, Christopher Rackauckas

While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver.

BIG-bench Machine Learning

High-performance symbolic-numerics via multiple dispatch

4 code implementations9 May 2021 Shashi Gowda, Yingbo Ma, Alessandro Cheli, Maja Gwozdz, Viral B. Shah, Alan Edelman, Christopher Rackauckas

We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations.

Vocal Bursts Intensity Prediction

Stiff Neural Ordinary Differential Equations

1 code implementation29 Mar 2021 Suyong Kim, Weiqi Ji, Sili Deng, Yingbo Ma, Christopher Rackauckas

We first show the challenges of learning neural ODE in the classical stiff ODE systems of Robertson's problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems.

Time Series Time Series Analysis

Universal Differential Equations for Scientific Machine Learning

8 code implementations13 Jan 2020 Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, Alan Edelman

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."

BIG-bench Machine Learning

A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions

1 code implementation5 Dec 2018 Christopher Rackauckas, Yingbo Ma, Vaibhav Dixit, Xingjian Guo, Mike Innes, Jarrett Revels, Joakim Nyberg, Vijay Ivaturi

In this manuscript we investigate the performance characteristics of Discrete Local Sensitivity Analysis implemented via Automatic Differentiation (DSAAD) against continuous adjoint sensitivity analysis.

Numerical Analysis

Confederated Modular Differential Equation APIs for Accelerated Algorithm Development and Benchmarking

no code implementations17 Jul 2018 Christopher Rackauckas, Qing Nie

Performant numerical solving of differential equations is required for large-scale scientific modeling.

Software Engineering Mathematical Software

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