Welcome Johanna Weinberger
We welcome Johanna Weinberger as a joint postdoctoral researcher with Benjamin Gess, Felix Otto, and Nicolas Perkowski at MPI MiS.
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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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Compact Support Property of Super-Brownian Motion with Irregular Drift
We prove the compact support property for a one-dimensional super-Brownian motion with irregular drift and establish support-radius estimates and positive extinction probability.
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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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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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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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Ergodicity for SPDEs driven by divergence-free transport noise
We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the uniqueness of invariant probability measures, even…
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Mixing at the Batchelor Scale for White-In-Time Flows
We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffusivity parameter goes to zero, we show that the almost-sure exponential dissipation rate stays bounded from…
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Weak Existence and Uniqueness for Super-Brownian Motion with Irregular Drift
We establish weak existence and uniqueness for one-dimensional super-Brownian motion with a broad class of bounded irregular drifts.
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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.…
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Random dynamical systems for McKean–Vlasov SDEs via rough path theory
The existence of random dynamical systems for McKean–Vlasov SDEs is established. This is approached by considering the joint dynamics of the corresponding nonlinear Fokker-Planck equation governing the law of the system and the underlying stochastic differential equation (SDE) as a dynamical system…
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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks
Published · Scientific Machine Learning: Emerging Topics, SEMA SIMAI Springer Series (2026). In this work, we provide a non-asymptotic convergence analysis of projected gradient descent for physics-informed neural networks for the Poisson equation. Under suitable assumptions, we show that the optimization error can be…