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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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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Asymptotics of Multi-Scale McKean–Vlasov Diffusions with Super-Linear Kernels: a Lifted Semigroup Approach
In this work, we establish the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large deviation principle) for multi-scale McKean–Vlasov diffusions with super-linear kernels. In this setting, the interaction depends on the laws of both the slow component…
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An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Small-Noise Results
Published · Electronic Journal of Probability 31 (2026), 1–55. We study an additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics, which is proposed as an approximate model to the fluctuating hydrodynamics of chemotactically interacting particles around their mean-field limit. As such, the interaction potential…
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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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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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THINNs: Thermodynamically Informed Neural Networks
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that…
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Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential
For a system of mean field interacting diffusion on $\mathbb{T}^d$, the empirical measure $μ^N$ converges to the solution $μ$ of the Fokker-Planck equation. Refining this mean field limit as a Central Limit Theorem, the fluctuation process $ρ^N_t= \sqrt{N}( μ^N_t -μ_t)$ convergences to…
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Matching Large Deviation Bounds of the Zero-Range Process in the whole space
We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $\mathbb{Z}^d$ in any dimension $d\ge 1$. Under mild and canonical hypotheses on the local jump rate, we obtain matching upper and lower bounds, thus resolving the problem opened…
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A Dynamical Systems Perspective on the Analysis of Neural Networks
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic) gradient descent, and related topics into dynamical statements.…