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

Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:7641-7656, 2026.

Abstract

In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize with general vector fields as well as choose other selection criteria beyond minimal energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-berman26a, title = {Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems}, author = {Berman, Jules and Blickhan, Tobias and Peherstorfer, Benjamin}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {7641--7656}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/berman26a/berman26a.pdf}, url = {https://proceedings.mlr.press/v306/berman26a.html}, abstract = {In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize with general vector fields as well as choose other selection criteria beyond minimal energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.} }
Endnote
%0 Conference Paper %T Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems %A Jules Berman %A Tobias Blickhan %A Benjamin Peherstorfer %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-berman26a %I PMLR %P 7641--7656 %U https://proceedings.mlr.press/v306/berman26a.html %V 306 %X In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize with general vector fields as well as choose other selection criteria beyond minimal energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.
APA
Berman, J., Blickhan, T. & Peherstorfer, B.. (2026). Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:7641-7656 Available from https://proceedings.mlr.press/v306/berman26a.html.

Related Material