@nathanaelbosch.de
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
```javascript
javascript:(function(){var url=window.location.href;if(url.match(/arxiv\.org\/pdf\//)){window.location.href=url.replace('/pdf/','/abs/');}else if(url.match(/openreview\.net\/pdf\?id=/)){window.location.href=url.replace('/pdf?id=','/forum?id=');}})();
```
Thanks to this meme I finally did something I should have done a long time ago and created a javascript bookmarklet that changes the URL, and did the same for openreview links. To try it out, just create a bookmark with the JS code below and click it to be redirected to the abstract/forum page!
Thanks! Yes they should also work for larger nonlinear systems as long as they are not too stiff. And there is also a Python implementation by @pnkraemer.bsky.social: github.com/pnkraemer/pr...
And because methods are only useful if people can actually use them: I wrote ProbNumDiffEq.jl to make all of this accessible. Give it a try!
💻 github.com/nathanaelbos...
📖 nathanaelbosch.github.io/ProbNumDiffE...
▶️ www.youtube.com/watch?v=iH_G...
6/6
There are many more things that I'd love to write about - e.g. robust parameter inference in neuroscience ODEs - but I think my thesis does a better job at explaining everything.
📄 Full thesis: tobias-lib.uni-tuebingen.de/xmlui/handle...
5/6
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
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
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
🎉 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
🙋
We are organising the First International Conference on Probabilistic Numerics (ProbNum 2025) at EURECOM in southern France in Sep 2025. Topics: AI, ML, Stat, Sim, and Numerics. Reposts very much appreciated!
probnum25.github.io
