iiinova — where your digital self keeps evolving

Nathanael Bosch @nathanaelbosch.de · 24/10/2025

```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=');}})(); ```

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Nathanael Bosch @nathanaelbosch.de · 24/10/2025

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!

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

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

github.com

GitHub - nathanaelbosch/ProbNumDiffEq.jl: Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing - nathanaelbosch/ProbNumDiffEq.jl

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

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

tobias-lib.uni-tuebingen.de

A Flexible and Efficient Framework for Probabilistic Numerical Simulation and Inference

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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

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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

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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

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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

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Reposted by Nathanael Bosch

Motonobu Kanagawa @motonobu-kanagawa.bsky.social · 17/11/2024

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

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