The Use and Practice of Scientific Machine Learning
November 18 2021 in Uncategorized | Tags: | Author: Christopher Rackauckas
The Use and Practice of Scientific Machine Learning
Scientific machine learning (SciML) methods allow for the automatic discovery of mechanistic models by infusing neural network training into the simulation process. In this talk we will start by showcasing some of the ways that SciML is being used, from discovery of extrapolatory epidemic models to nonlinear mixed effects models in pharmacology. From there, we will discuss some of the increasingly advanced computational techniques behind the training process, focusing on the numerical issues involved in handling differentiation of highly stiff and chaotic systems. The viewers will leave with an understanding of how compiler techniques are being infused into the simulation stack to increasingly automate the process of developing mechanistic models.
When does the mean and variance define an SDE?
November 1 2021 in Uncategorized | Tags: | Author: Christopher Rackauckas
I recently saw a paper that made the following statement:
“Innes et al. [22] trained neural SDEs by backpropagating through the operations of the solver, however their training objective simply matched the first two moments of the training data, implying that it could not consistently estimate diffusion functions.”
However, given that the statement “could not consistently estimate diffusion functions” had no reference to it and no proof in the appendix, I was interested to figure out the mathematical foundation behind the claim. Furthermore, I know from the DiffEqFlux documentation example that there was at least one case where second order method of moments seems to estimate the diffusion function. So a question arose, when does the mean and variance define an SDE?
Of course, in 2021 a Twitter thread captures the full discussion. But I want to take a step back … READ MORE
Learning Epidemic Models That Extrapolate, AI4Pandemics
July 25 2021 in Differential Equations, Julia, Mathematics, Science, Scientific ML | Tags: epidemics, scientific machine learning, sciml | Author: Christopher Rackauckas
I think this talk was pretty good so I wanted to link it here!
Title: Learning Epidemic Models That Extrapolate
Speaker Chris Rackauckas, https://chrisrackauckas.com/
Abstract:
Modern techniques of machine learning are uncanny in their ability to automatically learn predictive models directly from data. However, they do not tend to work beyond their original training dataset. Mechanistic models utilize characteristics of the problem to ensure accurate qualitative extrapolation but can lack in predictive power. How can we build techniques which integrate the best of both approaches? In this talk we will discuss the body of work around universal differential equations, a technique which mixes traditional differential equation modeling with machine learning for accurate extrapolation from small data. We will showcase how incorporating different variations of the technique, such as … READ MORE
Useful Algorithms That Are Not Optimized By Jax, PyTorch, or Tensorflow
July 21 2021 in Julia, Programming, Science, Scientific ML | Tags: automatic differentiation, differentiable programming, julia, machine learning | Author: Christopher Rackauckas
In some previous blog posts we described in details how one can generalize automatic differentiation to give automatically stability enhancements and all sorts of other niceties by incorporating graph transformations into code generation. However, one of the things which we didn’t go into too much is the limitation of these types of algorithms. This limitation is what we have termed “quasi-static” which is the property that an algorithm can be reinterpreted as some static algorithm. It turns out that for very fundamental reasons, this is the same limitation that some major machine learning frameworks impose on the code that they can fully optimize, such as Jax or Tensorflow. This led us to the question: are there algorithms which are not optimizable within this mindset, and why? The answer is now published at ICML 2021, so lets dig into … READ MORE
ModelingToolkit, Modelica, and Modia: The Composable Modeling Future in Julia
April 19 2021 in Differential Equations, Julia, Mathematics, Programming, Science, Scientific ML | Tags: acausal, dae, language, modelica, modeling, modelingtoolkit, modia | Author: Christopher Rackauckas
Let me take a bit of time here to write out a complete canonical answer to ModelingToolkit and how it relates to Modia and Modelica. This question comes up a lot: why does ModelingToolkit exist instead of building on tooling for Modelica compilers? I’ll start out by saying I am a huge fan of Martin and Hilding’s work and we work very closely with them on the direction of Julia-based tooling for modeling and simulation. ModelingToolkit, being a new system, has some flexibility in the design space it explores, and while we are following a different foundational philosophy, we have many of the same goals.
Composable Abstractions for Model Transformations
Everything in the SciML organization is built around a principle of confederated modular development: let other packages influence the capabilities of your own. This is highlighted in a … READ MORE
Generalizing Automatic Differentiation to Automatic Sparsity, Uncertainty, Stability, and Parallelism
March 10 2021 in Differential Equations, Julia, Mathematics, Programming, Science, Scientific ML | Tags: abstract interpretation, automatic differentiation, non-standard interpretation, Pantelides algorithm | Author: Christopher Rackauckas
Automatic differentiation is a “compiler trick” whereby a code that calculates f(x) is transformed into a code that calculates f'(x). This trick and its two forms, forward and reverse mode automatic differentiation, have become the pervasive backbone behind all of the machine learning libraries. If you ask what PyTorch or Flux.jl is doing that’s special, the answer is really that it’s doing automatic differentiation over some functions.
What I want to dig into in this blog post is a simple question: what is the trick behind automatic differentiation, why is it always differentiation, and are there other mathematical problems we can be focusing this trick towards? While very technical discussions on this can be found in our recent paper titled “ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling” and descriptions of methods like intrusive uncertainty quantification, I want … READ MORE
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