Jonathan Schmidt Jonathan Schmidt
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Postdoctoral researcher · University of Tübingen

Jonathan Schmidt

I develop probabilistic methods for simulation and inference in dynamical systems, from Kalman filters in millions of dimensions to generative models of the climate. Lately, I am drawn to a new question: what these tools can tell us about social dynamics.

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  • Tübingen, Germany
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Portrait of Jonathan Schmidt
Research

What I work on

Together with Philipp Hennig and the Methods of Machine Learning group in Tübingen.

01

Inference in dynamical systems

Bayesian filtering and smoothing for high-dimensional systems, and probabilistic numerical solvers for ODEs and PDEs. Exploiting structure (low rank, Kronecker, sparsity) allows scaling principled uncertainty quantification to real-world problems.

02

Generative models for physical simulation

Diffusion models for simulation generates output that comes with uncertainty instead of yielding a point estimate. Practical example: turn coarse climate simulations into spatiotemporally coherent, probabilistic weather-scale fields.

03

Social dynamics and simulation

A new direction, currently in the process of sharpening the focus. Currently investigating heterogeneous-agent models of wealth and income, and the (stochastic-process) machinery behind them. I am interested both in the application and in the methodology; and happy to chat about both, anytime!

Blog

Latest writing

All posts
Sample paths of a stochastic process
September 17, 2026 ·22 min

On the Distribution of Wealth, Income, and Functions—Part 1

The Generator of a Stochastic Process

How do functions of a noisy state evolve over time? A tour of the generator of an Itô process, guided by a simple macroeconomic model of wealth and income.

stochastic processesmacroeconomicssocial dynamics
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News

Recent updates

  1. Sep 2026
    New blog post: On the Distribution of Wealth, Income, and Functions — Part 1, on the generator of a stochastic process. Read the post
  2. Apr 2026
    Started a new position as a postdoc in Tübingen.
  3. Jan 2026
    Successfully defended my PhD 🥳
  4. Jul 2025
    Paper published in npj Climate and Atmospheric Science: A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation. Read the paper
  5. Dec 2023
    Paper accepted at NeurIPS 2023: The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering in High Dimensions. Read the paper
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Papers

Selected publications

All publications
  • npj Climate and Atmospheric Science · 2025 A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation
  • NeurIPS · 2023 The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering in High Dimensions
  • ICML · 2022 Probabilistic ODE Solutions in Millions of Dimensions
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© 2026 Jonathan Schmidt · Tübingen, Germany

 

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