2025-07-23 – 16:00-16:30 (Africa/Abidjan), Main Room 2
The Julia SciML solvers in DifferentialEquations.jl are already pretty optimized for stiff ODEs and DAEs, so where does the next order of magnitude in performance come from? In this talk we will describe how symbolic-numeric compiler tricks are being integrated in to the solver architecture in order to achieve performance that is beyond anything possible with purely numerical systems.
A lot of ODE solver systems, from Python's scipy to MATLAB ode15s, are purely numerical algorithms. They run under the assumption that you give the solver an ODE model description in the form of f and it calls f in special ways to build a numerical approximation to the solution. The assumption for almost all researchers for the last half century of having computers has been that the numerical approximation to ODEs uses a numerical solver. But with Julia, we don't like conventions?
In this talk we will discuss what happens when we break that convention and integrate specialized computation and symbolic-numeric techniques into the ODE solver. Specifically, we will showcase how specializations on the implicit handling of stiff ODE/DAE solvers, such as BDF methods and SDIRK methods, can greatly change the robustness and performance of the solvers. We will showcase how splitting the nonlinear system into strongly connected components, using specialized tearing passes, integrating symbolic nonlinear solvers, and utilizing homotopy routines can all be done automatically via the codegen of ModelingToolkit in order to enhance the performance of the numerical solver. The results are good enough that it's almost cheating: orders of magnitude faster than other open source solvers because we're not even playing the same game anymore.
The hope is that the audience walks away from this talk with a new understanding of what kinds of algorithms are possible when symbolic techniques are integrated into numerics.
Dr. Chris Rackauckas is the VP of Modeling and Simulation at JuliaHub, the Director of Scientific Research at Pumas-AI, Co-PI of the Julia Lab at MIT, and the lead developer of the SciML Open Source Software Organization. For his work in mechanistic machine learning, his work is credited for the 15,000x acceleration of NASA Launch Services simulations and recently demonstrated a 60x-570x acceleration over Modelica tools in HVAC simulation, earning Chris the US Air Force Artificial Intelligence Accelerator Scientific Excellence Award. See more at https://chrisrackauckas.com/. He is the lead developer of the Pumas project and has received a top presentation award at every ACoP in the last 3 years for improving methods for uncertainty quantification, automated GPU acceleration of nonlinear mixed effects modeling (NLME), and machine learning assisted construction of NLME models with DeepNLME. For these achievements, Chris received the Emerging Scientist award from ISoP.