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Universal Differential Equations for Scientific Machine Learning

Modeling, Computation, Nonlinearity, Randomness and Waves Seminar

Universal Differential Equations for Scientific Machine Learning
Series: Modeling, Computation, Nonlinearity, Randomness and Waves Seminar
Location: Zoom Meeting
Presenter: Christopher Rackauckas, Mathematics, Massachusetts Institute of Technology, Mathematics, Massachusetts Institute of Technology

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. A central challenge is reconciling data that is at odds with simplified models without requiring "big data". In this work we develop a new methodology, universal differential equations (UDEs), which augments scientific models with machine-learnable structures for scientifically-based learning. We show how UDEs can be utilized to discover previously unknown governing equations, accurately extrapolate beyond the original data, and accelerate model simulation, all in a time and data-efficient manner. This advance is coupled with open-source software that allows for training UDEs which incorporate physical constraints, delayed interactions, implicitly-defined events, and intrinsic stochasticity in the model. Our examples show how a diverse set of computationally-difficult modeling issues across scientific disciplines, from automatically discovering biological mechanisms to accelerating climate simulations by 15,000x, can be handled by training UDEs.   Zoom link:

Bio: Christopher Rackauckas is an Applied Mathematics Instructor at the Massachusetts Institute of Technology and a Senior Research Analyst at University of Maryland, Baltimore, School of Pharmacy in the Center for Translational Medicine. Chris's research is focused on numerical differential equations and scientific machine learning with applications from climate to biological modeling. He is the developer of many core numerical packages for the Julia programming language, including DifferentialEquations.jl for which he won the inaugural Julia community prize, and the Pumas.jl for pharmaceutical modeling and simulation.  

Zoom link: