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JuliaCon 2019 | Scientific AI: Domain Models with Integrated Machine Learning | Chris Rackauckas

The Julia Language · Youtube · 31 HN points · 1 HN comments
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Chris Rackauckas, Massachusetts Institute of Technology, JuliaCon 2019

Modeling practice seems to be partitioned into scientific models defined by mechanistic differential equations and machine learning models defined by parameterizations of neural networks. While the ability for interpretable mechanistic models to extrapolate from little information is seemingly at odds with the big data "model-free" approach of neural networks, the next step in scientific progress is to utilize these methodologies together in order to emphasize their strengths while mitigating weaknesses. In this talk we will describe four separate ways that we are merging differential equations and deep learning through the power of the DifferentialEquations.jl and Flux.jl libraries. The result is a high-performance state-of-the-art tool for scientific AI and scientific machine learning (scientific ML). Data-driven hypothesis generation of model structure, automated real-time control of dynamical systems, accelerated of PDE solving, and memory-efficient deep learning workflows will all shown to be derived from this common computational structure of differential equations mixed with neural networks (neural ODEs, neural SDE, neural PDEs). The audience will leave with a new appreciation of how these two disciplines can benefit from one another, and how neural networks can be used for more than just data analysis.
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Jul 31, 2019 · 31 points, 4 comments · submitted by StefanKarpinski
StefanKarpinski
This may well be the future of scientific modeling for problems that are too hard to find complete analytic solutions to. It's often the case that most of the problem is tractable but there's a core part that's hard/impossible to analyze. Traditional reinforcement learning (RL) has allowed treating the entire process as a black box which can be "machine learned" by approximating it with a neural network. This works remarkably well, but it's inefficient because it discards everything we know about the parts of the problem that are easy to model, like basic physics, chemistry, electronics, optics—whatever domain the problem is in. Differentiable programming (∂P) now allows you to write a program that models what you do know about the problem, leaving a much smaller black box function to learn for the part that you cannot model. You can run this program with a random untrained neural net for the part of the model you don't know, look at the loss function of the result, and then differentiate (aka back-propagate) through the rest of the program (aka model) to improve the black box. This lets you efficiently approximate just the hard non-analytic core part of the model with a neural network instead of having to learn to approximate the entire problem as in traditional RL. Since you already have a good analytic model of the surrounding problem and don't have to learn those parts, this gives a huge—orders of magnitude—improvement in terms of learning speed, while also improving accuracy and reducing the risk of over-fitting.
ccapo
Thanks for sharing that information about Differential Programming, I was not aware of its existence. I'm curious if this approach will help solve some problems I am investigating.

Do you have any suggestions for papers or libraries that implement Differential Programming?

StefanKarpinski
Hope it helps you solve some very hard problems :)

The Zygote package for Julia (part of the Flux ML framework) is the state of the art, see:

https://news.ycombinator.com/item?id=20477873

(This talk was given at JuliaCon last week.)

If you need any guidance or help getting started, you may want to join the Julia Slack: https://slackinvite.julialang.org/. There's a very active and helpful #machine-learning channel on there.

ccapo
Thanks, I will have a look at it.
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