2026-08-12 –, Room 6
There are hundreds of ODE solvers in DifferentialEquations.jl. Which is the best one for your problem? In this talk we go through the many classes and types of solvers and build a map to help you understand when to use various choices. We start by highlighting the basics, the core solvers that tend to do well for all problems, and then start to showcase more specialized methods and detail when they are likely to be improvements.
For most people, you use the default solver solve(prob), and in most cases, this is pretty good. But in some cases, you may choose a solver. Some choices are generic: Tsit5(), FBDF(), etc. that tend to just do well in general. But then it can get detailed:
- You know about stiff and non-stiff equations, but what about semi-stiffness where your eigenvalues are dominated by real parts? Try to ROCK methods.
- What about stiff equations of 3-200 equations on multicore devices? Try the implicit extrapolation methods.
- What about non-stiff equations which are smooth and able to be symbolically analyzed? Try the adaptive Taylor methods
- What about highly stiff equations which are real valued and require very high precision? Try the adaptive Radau methods.
Etc. etc. This will walk through the space with benchmarks, a high level intuition behind the method, and give an idea of how much these optimizations may give over using the generic methods. By the end you should feel more comfortable going into the details of the DifferentialEquations.jl library to further optimize the choices for your specific code.
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.