Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields
Fast probabilistic counterparts to numerical PDE solvers, powered by SPDEs & sparse linear algebra.
tim@timwei.land
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Name
▌
Status
PhD student ☕️
Affiliations
Methods of Machine Learning @ Uni Tübingen
Research
Scalable Probabilistic PDE solvers
Education
M.Sc. Machine Learning, University of Tübingen (2023)
Interests
Physics-informed ML, Bayesian Inference, ML Algorithms, Deep Learning
Stack
Julia, Python, PyTorch, JAX
Focus
Fundamental ML research & scalable algorithms
Theme
Gruvbox [Terminal Scholar]
tim@timwei.land:~$ news
[May 04 2025]
Attending AISTATS in Mai Khao to talk about our work on GMRFs for PDEs.
[Mar 01 2025]
I started my six month visit to Simo Särkkä's lab at Aalto University.
[Feb 21 2025]
Tobias Weber and I organized a seminar on Physics-Informed ML. Check out the results here: https://github.com/ClimatePDE/physics-informed-machine-learning
[Jan 31 2025]
I gave a talk at Oberwolfach on probabilistic PDE solvers.
[Jan 23 2025]
Our AISTATS submission on GMRFs for PDEs got accepted!
Featured Publications
Scaling up Probabilistic PDE Simulators with Structured Volumetric Information
Introduces GP-FVM, a probabilistic counterpart to the finite volume method, enabling large-scale probabilistic PDE simulations.
Recent Posts
Finding Important Words: tf-idf
10 min readLearn how tf-idf combines term frequency and inverse document frequency to identify the most important words in a document by balancing local relevance with global rarity.
Why Maximum Likelihood works
6 min readAn intuitive explanation of why maximum likelihood estimation works, using the Kullback-Leibler divergence to provide theoretical grounding for this fundamental statistical method.
Featured Projects
GaussianMarkovRandomFields.jl
Fast, flexible and user-centered Julia package for Bayesian inference with sparse Gaussians
Scaling GP-based PDE Solvers
MSc Research Project. A case study on the shallow-water equations.
AI Exhibition Object on Decision Trees
Teaching people about machine learning by predicting apartment rents with decision trees.