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. The recurring theme: exploit structure (low rank, Kronecker, sparsity) so that principled uncertainty quantification scales to problems that matter.

02

Generative models for physical simulation

Diffusion models that turn coarse climate simulations into spatiotemporally coherent, probabilistic weather-scale fields. Simulation output that comes with calibrated uncertainty instead of a single guess.

03

Social dynamics and simulation

A new direction, currently in the process of sharpening the focus. Current direction: heterogeneous-agent models of wealth and income, and the (stochastic-process) machinery behind them. Interested both in the application and in the methodology. 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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