Peter Nicholas Krämer
PhD Student Machine Learning // University of Tübingen

New preprint

We have a new preprint on arXiv: "Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs". UQ for neural operators has not been studied much yet, but is so sorely needed. Have a look at the paper! As always, links are on the research page.

August 10, 2022

Paper published in the Journal of Computational Neuroscience

The paper "Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models" has been published in the Journal of Computational Neuroscience!

August 10, 2022

Paper published at JMLR

Our paper "Probabilistic ODE solutions in millions of dimensions" has been accepted to ICML 2022! We're gonna go to Baltimore and present it in person. Reach out if you wanna meet.

July 1, 2022

High-dimensional ODE solvers: Code release

We have just open-sourced the JAX code for the probabilistic ODE solvers used in the Probabilistic ODE Solvers in Millions of Dimensions paper (also check out the research page). You can find the code here. Install it with pip install tornadox. Let me know what you think!

Mar 10, 2022

ProbFinDiff

I just made ProbFinDiff public! It contains schemes for probabilistic numerical finite difference schemes, and has been designed to be minimally invasive to your remaining code. Give it a try and let me know what you think!

Feb 8, 2022

TUEplots

Hey matplotlib-users: go check out TUEplots. It is a lightweight matplotlib extension that makes your figures fit common journal formats.

Jan 26, 2022

PN method of lines

How exciting that ``Probabilistic numerical method of lines for time-dependent partial differential equations'', which explains how to solve time-dependent PDEs with probabilistic numerics, has been accepted to AISTATS 2022! Link to the paper: research page.

Jan 26, 2022

New preprint

We recently uploaded a preprint that discusses the ProbNum library. A link to the PDF is on on the research page.

Dec 10, 2021

Neurips 2021

I am excited to announce that our papers "Linear-time probabilistic solutions of boundary value problems" and "A probabilistic state space model for joint inference on differential equations and data" have been accepted at Neurips 2021. As always, links are on the research page.

Dec 2, 2021

Teaching: Data literacy

This term, I will be a TA for the data literacy lecture, taught by Philipp Hennig.

Nov 2, 2021

Dagstuhl 2021

I just came back from the Dagstuhl '21 Seminar: Probabilistic Numerical Methods - From Theory to Implementation ( link ). Thanks a lot to the organisers! It was a lot of fun, and we had some great discussions.

Nov 1, 2021

New preprints

We just uploaded two new preprints to arXiv. The first one, ``Probabilistic ODE solutions in millions of dimensions``, discusses how to construct probabilistic ODE solvers that scale to high-dimensional settings. The second one, ``Probabilistic numerical method of lines for time-dependent partial differential equations'', explains a fully probabilistic numerical approach to solving time-dependent PDEs. Links are on the research page.

Oct 24, 2021

New preprint

We just uploaded a new preprint to arXiv: ``Linear-time probabilistic solutions of boundary value problems`` (see the research page). We give probabilistic BVP solutions linear-time complexity and introduce some other practical considerations, like mesh refinement and hyperparameter calibration.

Jun 16, 2021

New preprint

We just uploaded a new preprint to bioRxiv: ``Numerical uncertainty can critically affect simulations of mechanistic models in neuroscience`` (see the research page). We use probabilistic numerical ODE solvers to detect how much numerical uncertainty affects ODE simulation of some popular neuroscience models. I am really excited to see probabilistic numerical ODE solvers in action!

April 15, 2021

Seminar about ODEs and ML

Next term, Nathanael Bosch, Philipp Hennig, and I will organise a seminar about ``Machine Learning for and with Dynamical Systems``. The plan is to cover ODE inverse problems, neural ODEs, physics-informed neural networks, and more. More information here. If you're studying in Tübingen, have a look at Ilias.

Febuary 20, 2021

New preprint

We just uploaded a new preprint to arXiv: ``A Probabilistic State Space Model for Joint Inference from Differential Equations and Data`` (see the research page). We explain how latent forces in differential equation models can be inferred by merging probabilistic ODE solvers with Gauss--Markov process regression. This came out of Jonathan Schmidt's research project, what a great result!

Febuary 15, 2021

New preprint

We just uploaded a new preprint to arXiv: ``Stable implementation of probabilistic ODE solvers`` (see the research page). We explain which steps are necessary in order to compute probabilistic ODE solutions with up to 11th order solvers on a range of non-stiff and stiff systems!

December 22, 2020

Time Series Lecture

The upcoming winter term, I will be a teaching assistant for the time series analysis lecture, taught by Filip Tronarp.

September 3, 2020

Accepted paper

I am excited that ICML accepted our paper on ``Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems``. See you all at the virtual conference!

July 10, 2020

BSc/MSc theses

I am offering supervision for BSc/MSc theses about probabilistic numerics for differential equations and related topics. If you are studying in Tübingen, please reach out (link).

June 1, 2020

New notes

Recently I came across some old notes I typed up about reproducing kernel Hilbert spaces during my MSc two years ago. I decided to share them on the media page. Hope they are useful to someone.

May 31, 2020

Unittest recipes for ML

If you are writing machine learning, statistics or numerics related code and---like I usually do--- wonder how to meaningfully unittest it, take a look at this page. Everything else is explained there.

Mar 5, 2020

Twitter & Google Scholar

From now on you can find me on Twitter and Google Scholar. Get in touch :)

Mar 5, 2020

New Preprint

Here you can find a preprint of our newest paper ``Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems``. Hans Kersting, Martien Schiegg, Christian Daniel, Michael Tiemann, Philipp Hennig and I argue that inverse problems based on ordinary differential equations should not be treated as likelihood-free inference problems, among some other things.

Mar 3, 2020

Seminar: 10 Minutes

I am happy to announce that from Nov 8 on, every Friday we will be able to bring together young ML researchers from all over Tübingen to have a joint seminar called 10 Minutes. As the name suggests, each week two of us will give a short presentation about their ongoing research. Save the date: Fridays, 2 p.m. MvL6. Hope to see you there.

Nov 7, 2019

Sequential Monte Carlo Methods 2019

This summer I will participate at the Department of Information Technology's course about sequential Monte Carlo methods which takes place August 26 - 30 at Uppsala University (link).

July 3, 2019

PhD

I am excited to announce that in September 2019 I will start a PhD in Machine Learning at the University of Tübingen under supervision of Prof. Dr. Philipp Hennig. We will be working on automated, data-driven inference for mechanical models as part of the ADIMEM project; see here. Stay tuned for more!

July 2, 2019

New slides and new abstract

This afternoon I gave the final presentation concluding my MSc thesis about Gaussian processes and Uncertainty quantification. In this thesis, I analyse Gaussian process emulators for Bayesian inverse problems. See the media page for an abstract as well as for the slides of my presentation. Some of the python scripts I used for simulations can be found on my GitHub page: see here.

May 17, 2019

New slides

Today in the post-graduate seminar at the Institute for Numerical Simulation, I gave a presentation about Gaussian process emulators for expensive simulations. I surveyed Gaussian process emulators and applications to Bayesian inverse problems. Further, I show some ideas for experimental design. Find the slides on the media page!

December 13, 2018

New slides

Yesterday I gave a presentation about Gaussian process approximations in Bayesian inverse problems. It was the first of three presentations I have to give about my MSc thesis. In this presentation I survey Gaussian processes and radial basis function interpolation, Bayesian inverse problems and Gaussian process approximations in Bayesian inverse problems. Find the slides on the media page!

December 7, 2018

Welcome back

The website is back with a new look, as of December 6, 2018! Thanks to GitHub Pages!

December 6, 2018

New slides and notes

From May to July I participated in a seminar about high-dimensional approximation and uncertainty quantification. There, I gave a talk about stochastic collocation. I also typed up a summary of what I said in the talk. Find the slides and the notes on the media page!

August 2, 2018

New slides

Last week I gave a presentation about the H2Lib at a post-graduate seminar at the University of Bonn. The H2Lib is an open source software library for hierarchical matrices, also known as H-matrices, and H2-matrices. In the presentation I explain how to get started on the H2Lib and show some experiments with scattered data approximation. Find the slides on the media page!

May 22, 2018

We are online

Welcome to my website! Here, you can find some information about me, especially who I am and how to get in touch. In the news section, I will occasionally ramble about what I think is interesting. In the media section, you can find slides of some of my presentations, among other things. Enjoy!

March 15, 2018