Tobias Blickhan

📄 TPF paper 📄 Stochastic paper 📄 NGIF paper 📄 DICE preprint 📄 HOAM preprint

Instead of learning the dynamics of a single stochastic system $t \mapsto X_t$, we learn the evolution of a population of them: the distribution $\rho_t$ of states over many realizations. It follows the continuity equation $\partial_t \rho_t + \text{div}(\rho_t u_t) = 0$, and the task is to infer the velocity field $u_t$ from unlabeled samples at a few time points.

Barotropic turbulence
Barotropic turbulence with more than $10^4$ state dimensions. Top: ground truth. Middle: samples from a two-parameter flow. Bottom: pointwise trajectory fitting.

Many velocity fields are compatible with the same population data. This gauge freedom lets us pick fields by a criterion of our choice, such as minimal kinetic energy. Population dynamics offer the potential for a massive complecity reduction in the learned field, if one is willing to give up the goal of following sample trajectories.

TPF marginals
Snapshots of a curve $t \mapsto \rho_t$. Samples keep their color over time; the learned flow is similar to piecewise optimal transport, but more regular.

Papers

Two-Parameter Flows for Learning Population Dynamics of Physical Systems

Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer
ICML 2026

📄 OpenReview 📄 arXiv 📊 Poster 💻 Code

Stochastic Lifting for Generating Trajectories of Stochastic Physical Systems

Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
ICML 2026

📄 OpenReview 📄 arXiv 📊 Poster 💻 Code

Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems

Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
arXiv preprint, 2026

📄 arXiv 💻 Code

DICE: Discrete Inverse Continuity Equation for Learning Population Dynamics

Tobias Blickhan, Jules Berman, Andrew Stuart, Benjamin Peherstorfer
Submitted to Journal of Machine Learning Research

📄 arXiv

Parametric Model Reduction of Mean-Field and Stochastic Systems via Higher-Order Action Matching

Tobias Blickhan, Jules Berman, Benjamin Peherstorfer
NeurIPS 2024

📄 Paper 📄 arXiv 📊 Poster 💻 Code

Acknowledgements

This work was supported by the National Science Foundation and the Air Force Office of Scientific Research.