Scientific Machine Learning and Stiffness

Christopher Rackauckas, Massachusetts Institute of Technology

Scientific machine learning (SciML) is the burgeoning field combining scientific knowledge with machine learning for data-efficient predictive modeling. We will introduce SciML as the key to effective learning in many engineering applications, such as improving the fidelity of climate models to accelerating clinical trials. This will lead us to the question on the frontier of SciML: what about stiffness? Stiffness is a pervasive quality throughout engineering systems and the most common cause of numerical difficulties in simulation. We will see that handling stiffness in learning, and thus real-world models, requires new training techniques. We will showcase how learning accurate models of battery degradation and the energy efficiency of buildings fails with previous techniques like physics-informed neural networks but succeeds with new stiffly-aware architectures like continuous-time echo state networks. This deep understanding of numerical issues in learning will feedback into traditional machine learning where we showcase how regularizing stiffness in a neural ODEs can halve the training time for image classification tasks. Together the audience will leave with a firm understanding of the role stiffness will play in the next decade of SciML.

Bio: Chris Rackauckas is an Applied Mathematics Instructor at MIT 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 its innovative solvers won an IEEE Outstanding Paper Award and the inaugural Julia Community Prize. Chris' work on high performance differential equation solving is seen in many applications from the MIT-CalTech CLiMA climate modeling initiative to the SIAM DSWeb award winning DynamicalSystems.jl toolbox. Chris is also the creator 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 in 2020, the highest early career award in pharmacometrics.


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