Abstract: Scientific machine learning is a burgeoning discipline for mixing machine learning into scientific simulation. Use cases of this field include automated discovery of physical equations and accelerating physical simulators. However, making the analyses of this field automated will require building a set of tools that handle stiff and ill-conditioned models without requiring user tuning. The purpose of this talk is to demonstrate how the methods and tools of scientific machine learning can be consolidated to give a single high performance and robust software stack. We will start by describing universal differential equations, a flexible mathematical object which is able to represent methodologies for equation discovery, 100-dimensional differential equation solvers, and discretizations of physics-informed neural networks. Then we will showcase how adjoint sensitivity analysis on the universal differential equation solving process gives rise to efficient and stiffly robust training methodologies for a large variety of scientific machine learning problems. With this understanding of differentiable programming we will describe how the Julia SciML Software Organization is utilizing this foundation to provide high performance tools for deploying battery powered airplanes, neural improved climate modeling, improving the energy efficiency of buildings, allow for navigation via the Earth's magnetic field, and more.

 

Bio: Chris Rackauckas is an Applied Mathematics Instructor at MIT, a Senior Research Analyst in the University of Maryland School of Pharmacy, and the Director of Scientific Research at Pumas-AI. He is the lead developer of the SciML open source scientific machine learning organization which develops widely used software for scientific modeling and inference. One such software is DifferentialEquations.jl for which the solvers won an IEEE Outstanding Paper Award and the inaugural Julia Community Prize. Chris' work on high performance differential equation solving is the centerpiece accelerating many applications from the MIT-CalTech CLiMA climate modeling initiative to the SIAM DSWeb award winning DynamicalSystems.jl toolbox. Chris is also the lead developer of Pumas, the foundational software of Pumas-AI for nonlinear mixed effects modeling in clinical pharmacology. These efforts on Pumas led to the International Society of Pharmacology's (ISoP) Mathematical and Computational Special Interest Group Award at the American Conference of Pharmacology (ACoP) 2019 for his work on improved clinical dosing via Koopman Expectations, along with the ACoP 2020 Quality Award for his work on GPU-accelerated nonlinear mixed effects modeling via generation of SPMD programs. For this work in pharmacology, Chris received the Emerging Scientist award from ISoP, the highest early career award in pharmacometrics. His PhD research at UC Irvine focused on the control of intrinsic stochasticity in biological and pharmacological systems for which his thesis won the Kovalesvsky Outstanding Thesis Award and he was a recipient of the Mathematical and Computational Biology institutional fellowship, the Graduate Dean's Fellowship, the National Science Foundation's Graduate Research Fellowship, the NIH T32 Predoctural Training Grant, and the Data Science Initiative Summer Fellowship.