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
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
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, in a … 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