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Project B8: Stochastic PDE with conservative noise


Principal Investigator(s)
Benjamin Gess
Sebastian Herr
Investigator(s)
Sarah Geiß
Visitor(s)
Currently no visitors.

Summary:

In this project we analyze diffusive, stochastic PDE with conservative noise. This class of stochastic PDE arises in various fields of applications, for example, in nonequilibrium statistical physics, and in interacting particle systems with common noise. Moreover, stochastic PDE of related structure appear in fluctuating hydrodynamics, and as stochastic kinetic equations, such as the stochastic Boltzmann and the stochastic Vlasov-Poisson equation. Several of these applications lead to space time white noise, and thus to typically ill-posed and supercritical stochastic PDE. We aim to investigate questions of well-posedness, regularity, qualitative behavior, equilibrium and non-equilibrium large deviations and their numerical simulation.


Recent Preprints:

25025 Benjamin Gess, Sebastian Herr, Anne Dorothea Niesdroy PDF

Existence of martingale solutions to a stochastic kinetic model of chemotaxis

Project: A1, B8

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Existence of martingale solutions to a stochastic kinetic model of chemotaxis


Authors: Benjamin Gess, Sebastian Herr, Anne Dorothea Niesdroy Projects: A1, B8
Submission Date: 02.04.2025 Submitter: Matthias Erbar
Download: PDF Link: 25025

24099 Sebastian Kassing, Simon Weissmann PDF

Polyak's heavy ball method achieves accelerated local rate of convergence under Polyak-Lojasiewicz inequality

Project: B8

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Polyak's heavy ball method achieves accelerated local rate of convergence under Polyak-Lojasiewicz inequality


Authors: Sebastian Kassing, Simon Weissmann Projects: B8
Submission Date: 17.12.2024 Submitter: Matthias Erbar
Download: PDF Link: 24099

24060 Benjamin Gess, Vitalii Konarovskyi PDF

A quantitative central limit theorem for the simple symmetric exclusion process

Project: B8

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A quantitative central limit theorem for the simple symmetric exclusion process


Authors: Benjamin Gess, Vitalii Konarovskyi Projects: B8
Submission Date: 29.08.2024 Submitter: Michael Röckner
Download: PDF Link: 24060

24059 Benjamin Gess, Rishabh S. Gvalani, Vitalii Konarovskyi PDF

Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent

Project: B8

Published: Probab. Theory Relat. Fields (2025)

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Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent


Authors: Benjamin Gess, Rishabh S. Gvalani, Vitalii Konarovskyi Projects: B8
Submission Date: 29.08.2024 Submitter: Michael Röckner
Download: PDF Link: 24059
Published: Probab. Theory Relat. Fields (2025)

24056 Andrey Dorogovtsev, Vitalii Konarovskyi, Max von Renesse PDF

A central limit theorem for modified massive Arratia flow

Project: B8

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A central limit theorem for modified massive Arratia flow


Authors: Andrey Dorogovtsev, Vitalii Konarovskyi, Max von Renesse Projects: B8
Submission Date: 29.08.2024 Submitter: Benjamin Gess
Download: PDF Link: 24056

24013 Benjamin Gess, Michael Röckner, Weina Wu PDF

SVI solutions to stochastic nonlinear diffusion equations on general measure spaces

Project: B1, B8

To appear: Journal of Evolution Equations (2024)

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SVI solutions to stochastic nonlinear diffusion equations on general measure spaces


Authors: Benjamin Gess, Michael Röckner, Weina Wu Projects: B1, B8
Submission Date: 07.02.2024 Submitter: Martina Hofmanová
Download: PDF Link: 24013
To appear: Journal of Evolution Equations (2024)

23113 Vitalii Konarovskyi, Fenna Müller PDF

Dean-Kawasaki equation with initial condition in the space of positive distributions

Project: B8

Published: Journal of Evolution Equations 24 (2024), Article number 92

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Dean-Kawasaki equation with initial condition in the space of positive distributions


Authors: Vitalii Konarovskyi, Fenna Müller Projects: B8
Submission Date: 29.08.2024 Submitter: Benjamin Gess
Download: PDF Link: 23113
Published: Journal of Evolution Equations 24 (2024), Article number 92

23112 Benjamin Gess, Sebastian Kassing, Vitalii Konarovskyi PDF

Stochastic modified flows, mean-field limits and dynamics of stochastic gradient descent

Project: B8

Published: Journal of Machine Learning Research 25, no. 30 (2024), 1−27

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Stochastic modified flows, mean-field limits and dynamics of stochastic gradient descent


Authors: Benjamin Gess, Sebastian Kassing, Vitalii Konarovskyi Projects: B8
Submission Date: 29.08.2024 Submitter: Michael Röckner
Download: PDF Link: 23112
Published: Journal of Machine Learning Research 25, no. 30 (2024), 1−27

23111 Steffen Dereich, Sebastian Kassing PDF

On the existence of optimal shallow feedforward networks with ReLU activation

Project: B8

Published: Journal of Machine Learning 3, no. 1 (2024), 1−22

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On the existence of optimal shallow feedforward networks with ReLU activation


Authors: Steffen Dereich, Sebastian Kassing Projects: B8
Submission Date: 29.08.2024 Submitter: Michael Röckner
Download: PDF Link: 23111
Published: Journal of Machine Learning 3, no. 1 (2024), 1−22

23110 Steffen Dereich, Arnulf Jentzen, Sebastian Kassing PDF

On the existence of minimizers in shallow residual ReLU neural network optimization landscapes

Project: B8

Published: SIAM Journal on Numerical Analysis 62, no. 6 (2024), 2640−2666

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On the existence of minimizers in shallow residual ReLU neural network optimization landscapes


Authors: Steffen Dereich, Arnulf Jentzen, Sebastian Kassing Projects: B8
Submission Date: 29.08.2024 Submitter: Michael Röckner
Download: PDF Link: 23110
Published: SIAM Journal on Numerical Analysis 62, no. 6 (2024), 2640−2666


All Publications of this Project


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