Fluctuations in Continuum: conference at TU Berlin, 19–23 April 2027
Our group organizes Fluctuations in Continuum at TU Berlin, 19–23 April 2027. Poster title and abstract deadline: 15 January 2027.
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Weak synchronisation for McKean–Vlasov SDEs
Synchronisation by noise for McKean–Vlasov stochastic differential equations is investigated. A transfer principle is introduced by which synchronisation by noise and diagonal mixing can be transferred from an associated limiting frozen-diffusion SDE to a genuinely law-dependent McKean–Vlasov SDE. The usefulness…
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NumGM project approved
The DFG has approved the 36-month project “Numerically Efficient Learning of Generative Models and Beyond (NumGM).”
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New paper: The Advective Fisher–Rao Geometry of Deterministic Measure Transport
Benjamin Gess and Johannes Müller introduce an advective Fisher–Rao metric for optimization on paths of probability measures.
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The Advective Fisher-Rao Geometry of Deterministic Measure Transport
A novel advective Fisher-Rao metric is introduced for optimization tasks on paths of probability measures governed by the continuity equation. This metric is shown to lead to optimal descent directions. It is then shown that this metric arises naturally from three different…
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Effective fluctuating continuum models for stochastic gradient descent
Workshop report · Oberwolfach Reports 23(1), 821–822 (2026). Fluctuating continuum descriptions of stochastic gradient descent.
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Introduce thermal noise before discretizing, not afterwards!
Workshop report · Oberwolfach Reports 23(1), 803–806 (2026). Incorporating thermal noise before discretising a continuum model.
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Large spikes in SGD: a large-deviations view of catapults
Workshop report · Oberwolfach Reports 23(1), 698–700 (2026). A large-deviations perspective on spikes and catapult behaviour in stochastic gradient descent.
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The Incompressible Navier–Stokes–Fourier System with Thermal Noise
We establish a solution theory for the incompressible Navier–Stokes–Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity can be solved independently of the temperature, the inclusion of the effects of…
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Large Spikes in Stochastic Gradient Descent: A Large-Deviations View
Large loss spikes in stochastic gradient descent are studied through a rigorous large-deviations analysis for a shallow, fully connected network in the NTK scaling. In contrast to full-batch gradient descent, the catapult phase is shown to split into inflationary and deflationary regimes,…
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The Porous Medium Equation: Multiscale Integrability in Large Deviations
We consider a zero-range process $η^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12Δu^α, α>1$. As a main result we obtain a large deviation principle in any scaling regime of vanishing…
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Probabilistically Strong Solutions to Stochastic Euler Equations
In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier–Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically strong solutions for the stochastic incompressible Euler equations. In particular, this solves the…