Fast probabilistic inference for ODEs with ProbNumDiffEq.jl | Bosch | JuliaCon 2024

Fast probabilistic inference for ODEs with ProbNumDiffEq.jl by Nathanael Bosch

PreTalx: https://pretalx.com/juliacon2024/talk...
Slides: https://pretalx.com/media/juliacon202...
GitHub: https://github.com/nathanaelbosch/Pro...

Probabilistic numerical methods interpret numerical problems as problems of Bayesian inference, and then solve them accordingly. For ODEs, one popular class of such methods treats ODEs as Bayesian state estimation problems, and then essentially solves the ODE with a Bayesian filtering and smoothing method such as the extended Kalman filter. [ProbNumDiffEq.jl](https://github.com/nathanaelbosch/Pro...) provides an efficient implementation of these methods and makes them availabe in the the DifferentialEquations.jl ecosystem.

This talk starts with a brief introduction to probabilistic numerics and to probsbilistic ODE solvers, and then presents ProbNumDiffEq.jl. We will cover some example usages for different problem types, then dive into some implementation details that matter to make these solvers stable and fast, share some experiences on working with other Julia packages, and discuss the future prospects of probabilistic numerics within the Julia ecosystem.

Features of ProbNumDiffEq.jl
For a new user, ProbNumDiffEq.jl looks just like a standard ODE solver library and it covers many features that users often want from solvers:
Explicit and semi-implicit solvers of varying order
Specialized solvers:
for second-order ODEs
for Manifolds (using a specific callback)
Exponential integrators
Rosenbrock-type exponential integrators
Adaptive step-size selection (inherited from OrdinaryDiffEq.jl)
Dense output
Plotting
Callback support (inherited from OrdinaryDiffEq.jl)
All solvers are compatible with mass-matrix DAEs
In addition, ProbNumDiffEq.jl also has many features that relate to the probabilistic formulation of the solves, and provides a range of priors_, multiple _calibration approaches, and a likelihood model for parameter estimation.

Links
*Github repository:* https://github.com/nathanaelbosch/Pro...
*Tutorial* Getting started with ProbNumDiffEq.jl: https://nathanaelbosch.github.io/Prob...
*References:* https://nathanaelbosch.github.io/Prob...