JuliaCall Update: Automated Julia Installation for R Packages
January 18 2021 in Differential Equations, Julia, Mathematics, Programming, R | Tags: devops, differentialequations, installation, julia, juliacall, modelingtoolkit, r | Author: Christopher Rackauckas
Some sneakily cool features made it into the JuliaCall v0.17.2 CRAN release. With the latest version there is now an install_julia function for automatically installing Julia. This makes Julia a great high performance back end for R packages. For example, the following is an example from the diffeqr package that will work, even without Julia installed:
install.packages("diffeqr")
library(diffeqr)
de <- diffeqr::diffeq_setup()
lorenz <- function (u,p,t){
du1 = p[1]*(u[2]-u[1])
du2 = u[1]*(p[2]-u[3]) - u[2]
du3 = u[1]*u[2] - p[3]*u[3]
c(du1,du2,du3)
}
u0 <- c(1.0,1.0,1.0)
tspan <- c(0.0,100.0)
p <- c(10.0,28.0,8/3)
prob <- de$ODEProblem(lorenz,u0,tspan,p)
fastprob <- diffeqr::jitoptimize_ode(de,prob)
sol <- de$solve(fastprob,de$Tsit5(),saveat=0.01)
Under the hood it’s using the DifferentialEquations.jl package and the SciML stack, but it’s abstracted from users so much that Julia is essentially an alternative to Rcpp with easier interactive development. The following example really brings the seamless … READ MORE
GPU-Accelerated ODE Solving in R with Julia, the Language of Libraries
August 24 2020 in Differential Equations, Julia, Programming, R, Uncategorized | Tags: diffeqr, differentialequations, gpu, high-performance, jit, r | Author: Christopher Rackauckas
R is a widely used language for data science, but due to performance most of its underlying library are written in C, C++, or Fortran. Julia is a relative newcomer to the field which has busted out since its 1.0 to become one of the top 20 most used languages due to its high performance libraries for scientific computing and machine learning. Julia’s value proposition has been its high performance in high level language, known as solving the two language problem, which has allowed allowed the language to build a robust, mature, and expansive package ecosystem. While this has been a major strength for package developers, the fact remains that there are still large and robust communities in other high level languages like R and Python. Instead of spawning distracting language wars, we should ask the … READ MORE
COVID-19 Epidemic Mitigation via Scientific Machine Learning (SciML)
July 7 2020 in Differential Equations, Julia, Mathematics, Programming, Science, Scientific ML | Tags: covid-19, epidemic modeling, scientific machine learning, sciml | Author: Christopher Rackauckas
Chris Rackauckas
Applied Mathematics Instructor, MIT
Senior Research Analyst, University of Maryland, Baltimore School of Pharmacy
This was a seminar talk given to the COVID modeling journal club on scientific machine learning for epidemic modeling.
Resources:
https://sciml.ai/
https://diffeqflux.sciml.ai/dev/
https://datadriven.sciml.ai/dev/
https://docs.sciml.ai/latest/
https://safeblues.org/
Cheap But Effective: Instituting Effective Pandemic Policies Without Knowing Who’s Infected
July 2 2020 in Biology, Differential Equations, Julia, Mathematics, Science, Scientific ML | Tags: covid-19, scientific machine learning, sciml | Author: Christopher Rackauckas
Cheap But Effective: Instituting Effective Pandemic Policies Without Knowing Who’s Infected
Chris Rackauckas
MIT Applied Mathematics Instructor
One way to find out how many people are infected is to figure out who’s infected, but that’s working too hard! In this talk we will look into cheaper alternatives for effective real-time policy making. To this end we introduce SafeBlues, a project that simulates fake virus strands over Bluetooth and utilizes deep neural networks mixed within differential equations to accurately approximate infection statistics weeks before updated statistics are available. We then introduce COEXIST, a quarantine policy which utilizes inexpensive “useless” tests to perform accurate regional case isolation. This work is all being done as part of the Microsoft Pandemic Modeling Project, where the Julia SciML tooling has accelerated the COEXIST simulations by … READ MORE
Glue AD for Full Language Differentiable Programming
June 15 2020 in Julia, Science, Scientific ML | Tags: | Author: Christopher Rackauckas
No design choice will be the best choice for all possible users. That’s a statement that is provocative but at the same time I think everyone would easily agree with it. But that should make us all question whether it’s a good idea to ever try and make all users happy with one piece of code. Under the differentiable programming mindset we are trying to make all code in the entire programming language be differentiable, but why would we think that a single system with a single set of rules and assumptions would be the best for everyone?
Optimized Algorithms Across Scientific Computing and Machine Learning
Differentiable programming is a subset of modeling where you model with a program where each of the steps are differentiable, for the purpose of being able to find the correct program with parameter fitting using said … READ MORE
Generalized Physics-Informed Learning through Language-Wide Differentiable Programming (Video)
March 31 2020 in Differential Equations, Mathematics, Science, Scientific ML | Tags: physics-informed machine learning, pinn, scientific machine learning, scientific ml, sciml | Author: Christopher Rackauckas
Chris Rackauckas (MIT), “Generalized Physics-Informed Learning through Language-Wide Differentiable Programming”
Scientific computing is increasingly incorporating the advancements in machine learning to allow for data-driven physics-informed modeling approaches. However, re-targeting existing scientific computing workloads to machine learning frameworks is both costly and limiting, as scientific simulations tend to use the full feature set of a general purpose programming language. In this manuscript we develop an infrastructure for incorporating deep learning into existing scientific computing code through Differentiable Programming (∂P). We describe a ∂P system that is able to take gradients of full Julia programs, making Automatic Differentiation a first class language feature and compatibility with deep learning pervasive. Our system utilizes the one-language nature of Julia package development to augment the existing package ecosystem with deep learning, supporting almost all … READ MORE
Universal Differential Equations for Scientific Machine Learning (Video)
March 6 2020 in Uncategorized | Tags: neural ODEs, neural ordinary differential equations, scientific machine learning, scientific ml, sciml | Author: Christopher Rackauckas
Colloquium with Chris Rackauckas
Department of Mathematics
Massachusetts Institute of Technology
“Universal Differential Equations for Scientific Machine Learning”
Feb 19, 2020, 3:30 p.m., 499 DSL
https://arxiv.org/abs/2001.04385
Abstract:
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.” Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. … READ MORE
Scientific Machine Learning: Interpretable Neural Networks That Accurately Extrapolate From Small Data
January 14 2020 in Differential Equations, Julia, Mathematics, Science, Scientific ML | Tags: neural ode, physics-informed, sciml, small data, universal differential equations | Author: Christopher Rackauckas
The fundamental problems of classical machine learning are:
- Machine learning models require big data to train
- Machine learning models cannot extrapolate out of the their training data well
- Machine learning models are not interpretable
However, in our recent paper, we have shown that this does not have to be the case. In Universal Differential Equations for Scientific Machine Learning, we start by showing the following figure:
Indeed, it shows that by only seeing the tiny first part of the time series, we can automatically learn the equations in such a manner that it predicts the time series will be cyclic in the future, … READ MORE
How Inexact Models and Scientific Machine Learning Can Guide Decision Making in Quantitative Systems Pharmacology
December 15 2019 in Biology, Julia, Pharmacology, Science | Tags: differential equations, julia, pharmacology, pumas, qsp | Author: Christopher Rackauckas
Pre-clinical Quantitiative Systems Pharmacology (QSP) is about trying to understand how a drug target effects an outcome. If I effect this part of the biological pathways, how will it induce toxicity? Will it be effective?
Recently I have been pulling in a lot of technical collegues to help with the development of next generation QSP tooling. Without a background in biological modeling, I found it difficult to explain the "how" and "why" of pharmacological modeling. Why is it differential equations, and where do these "massively expensive global optimization" runs come from? What kinds of problems can you solve with such models when you know that they are only approximate?
To solve these questions, I took a step back and tried to explain a decision making scenario with a simple model, to showcase how playing with a model can allow one to distinguish … READ MORE
Recent advancements in differential equation solver software
October 16 2019 in Differential Equations, Julia, Mathematics, Scientific ML, Uncategorized | Tags: | Author: Christopher Rackauckas
This was a talk given at the Modelica Jubilee Symposium – Future Directions of System Modeling and Simulation.
Recent Advancements in Differential Equation Solver Software
Since the time of the ancient Fortran methods like dop853 and DASSL were created, many advancements in numerical analysis, computational methods, and hardware have accelerated computing. However, many applications of differential equations still rely on the same older software, possibly to their own detriment. In this talk we will describe the recent advancements being made in differential equation solver software, focusing on the Julia-based DifferentialEquations.jl ecosystem. We will show how high order Rosenbrock and IMEX methods have been proven advantageous over traditional BDF implementations in certain problem domains, and the types of issues that give rise to general performance characteristics between the methods. Extensions of these … READ MORE