Nathanael Bosch
@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
nathanaelbosch.github.io
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
[2] tinyurl.com/2av3e4te
[3] tinyurl.com/bddfkwcu
4/6
May 30, 2025 at 10:02 AM
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
[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
[1] www.jmlr.org/papers/v25/2...
3/6
May 30, 2025 at 10:02 AM
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
[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
2/6
May 30, 2025 at 10:02 AM
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
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
📄 tinyurl.com/mt3sffb
🧵 1/6
May 30, 2025 at 10:02 AM
🎉 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
📄 tinyurl.com/mt3sffb
🧵 1/6