Simulating Big Models in Julia with ModelingToolkit
07-24, 14:00–17:00 (UTC), Green

It can be hard to build and solve million equation models. Making them high performance, stable, and parallel? Introducing ModelingToolkit.jl! The modeling auto-optimizer for all of your performance needs! We will show many use cases on differential equations and beyond (optimization, nonlinear solving, etc.).

It can be hard to build and solve million equation models. Making them high performance, stable, and parallel? Introducing ModelingToolkit.jl! In this workshop we will showcase ModelingToolkit as a system for building large differential equation models in a hierarchical component-wise way. This acausal modeling system is reminiscent of widely used tools like Simulink and Modelica, but we will showcase how ModelingToolkit's deep integration with interactive symbolic programming leads to a more intuitive pure Julia modeling system. The audience will be walked through a live demonstration of using ModelingToolkit to compose models and add transformations, like index reduction of differential-algebraic equations (DAEs) and tearing of nonlinear systems, to improve stability and performance of the generated code. We will demonstrate how to use the automated parallelism easily solve millions of equations in the most performant way. We will show how ModelingToolkit extends far beyond differential equations, featuring how it can be used for similarly generating high performance code for nonlinear optimization, solving nonlinear equations, doing nonlinear optimal control, generating models from chemical reaction descriptions, and more. The user will leave with a better understanding of the growing symbolic-numeric modeling ecosystem and the future of large-scale accurate and high-performance SciML modeling.

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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