iiinova — where your digital self keeps evolving

iiinova is part of the Atmosphere — an open, public network where you own your identity.

Nathanael Bosch

@nathanaelbosch.de

337 followers 114 following 10 posts

Postdoc at EPFL working on Bayesian optimization for inverse materials design. Interested in probabilistic numerics, Bayesian optimization, Gaussian processes, state-space models, differential equations, and Bayesian ML. nathanaelbosch.github.io

Posts Replies Media

Nathanael Bosch @nathanaelbosch.de · 30/05/2025

Two more examples: We can add linear ODEs to the prior to create a probabilistic version of "exponential integrators". onlinear information (e.g. conservation laws) can be included in the likelihood to get more plausible solutions - see gif. [2] tinyurl.com/2av3e4te [3] tinyurl.com/bddfkwcu 4/6

150 5

Nathanael Bosch @nathanaelbosch.de · 30/05/2025

It turns out that this framework is quite convenient: You can easily customize each building block - prior, likelihood, inference - to adjust the solver and its properties. For example, by using a time-parallel smoother we obtain a parallel-in-time ODE solver! [1] www.jmlr.org/papers/v25/2... 3/6

140 4

Nathanael Bosch @nathanaelbosch.de · 30/05/2025

The main trick is to reformulate "solving an ODE" as "Bayesian state estimation" by turning the ODE into a nonlinear observation model. With a suitable prior - a Gauss-Markov process - you can solve the resulting problem with Bayesian filtering to obtain a probabilistic numerical ODE solution. 2/6

160 6

Nathanael Bosch @nathanaelbosch.de · 30/05/2025

🎉 My PhD dissertation is now online! Traditional ODE solvers compute a single solution estimate - Probabilistic solvers also tell you how reliable they are! In my PhD, I established them as a Flexible and Efficient Framework for Probabilistic Simulation and Inference. 📄 tinyurl.com/mt3sffb 🧵 1/6

3281 28