When randomising the timestep sizes in Euler‘s method, we need to linearly interpolate between subsequent timepoints to approximate the ODE solution at times of interest. The resulting piecewise linear path can sometimes be written as a Markov process. I have analysed this Markov process:

The random timestep Euler method and its continuous dynamics

Abstract. Ordinary differential equation (ODE) solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differentia

academic.oup.com

Andrea Bertozzi, Nadia Drenska, Matt Thorpe, and I have guest edited a theme issue on “Partial differential equations in data science” in the Philosophical Transactions of the Royal Society A. Take a look: royalsocietypublishing.org/toc/rsta/202... @royalsociety.org @royalsocietypublishing.org

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences: Vol 383, No 2298

royalsocietypublishing.org

#Oberwolfach: every mathematician’s happy place

Exciting news! 😊 Best of luck for the election, Master!

Mohamed A. El-Erian@elerianm.bsky.social · last yr.

I just wanted to let you know that, having been encouraged by many and received over four times the number of nominations required, I announced today that I am throwing my hat into the ring for the election of the next Chancellor of the University of Cambridge... 1 of 2

A few years ago, Björn Sprungk and I had written a contribution towards the “Snapshots of Modern Mathematics from #Oberwolfach” (publications.mfo.de/handle/mfo/3...). Once in a while a collection of snapshots is published in a volume. I have received my copy today. 😊

Why do people call it _adaptive MCMC_ instead of - CMC - “M”CMC - \hat{M}CMC - M😉CMC

#sciencememe

Please find below the announcement for the 2nd RSS/Turing Workshop on Gradient Flows for Sampling, Inference, and Learning (I am a speaker ☺️)

Earlier today I gave my first talk for 2025 — in the Applied Mathematics Seminar at the University of Glasgow! Great audience and nice discussions afterwards. 😊

Did you know that Schengen is a small village in Luxembourg? It is right at the French-German-Luxembourgish trijunction. I grew up nearby and I can assure you that it is my favourite border to cross. See you in 2025! ☺️

Stationary Gaussian processes are often inappropriate as priors in Bayesian image reconstruction. When using non-stationary priors, the non-stationarity needs to be carefully estimated. New preprint (with Aretha L. Teckentrup and Simon Urbainczyk) arxiv.org/abs/2412.10248

Deep Gaussian Process Priors for Bayesian Image Reconstruction

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is repres...

arxiv.org

Overleaf is down. What was the last thing you were writing about on there? I‘ll start: the K-Means method

At last year‘s Edinburgh Science Festival, we organised a ‚Mathematics Showdown‘: five PhD students give engaging research talks for a general audience, the audience votes for a winner. Here are the talks:

Mathematics Showdown 2023 - YouTube

Contributions to the Mathematics Showdown 2023 at the Edinburgh Science Festival.

youtube.com

Markovian #Meme.

Open PhD position Anna Scaife and I are looking for a PhD student interested in analysing astronomical images using modern physics-on-graphs-based machine learning methods. The position is within the UKRI-CDT AI in Decision Making for Complex Systems. Please share with potential candidates! 😊

Image segmentation in radioastronomy with physical models on graphs at The University of Manchester on FindAPhD.com

PhD Project - Image segmentation in radioastronomy with physical models on graphs at The University of Manchester, listed on FindAPhD.com

findaphd.com

Me talking to my algorithm… #meme

Discretisation memes! 😊

I need to slowly move all my #mathematics #memes to the #mathsky. Let’s start with _Tolkien and convergence to stationarity_.

A few weeks ago, my student Alix Leroy and I were visiting Siemens Energy in Berlin for #knowledgeexchange and a guided tour around their production facilities. 😊

Say, you discretise an ODE with forward Euler choosing iid exponentially distributed stepsizes and linearly interpolate between discretisation points. Then, your interpolated path can be written as a continuous-time Markov process. An analysis of this Markov process: arxiv.org/abs/2408.01409

The random timestep Euler method and its continuous dynamics

ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this wo...

arxiv.org

Finding the Lyapunov function you are looking for = finding happiness. 😊

Ever felt insecure about your own work? You are not alone. Gauss in a letter to Bessel: “When I am new to a subject, I distrust my own notions - especially if they contradict Laplace.” (from W. Ahrens: “Scherz und Ernst in der Mathematik”, Teubner, Leipzig 1904.)

Hi #mathsky and everyone! My name is Jonas, I do applied maths for living — usually solving problems that concern data, uncertainties, or both. I am based at the University of Manchester, UK.