NumGM project approved
The DFG has approved the 36-month project “Numerically Efficient Learning of Generative Models and Beyond (NumGM).”
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NumGM postdoctoral position — application deadline passed
The stated application deadline for this NumGM postdoctoral position was 11 September 2026.
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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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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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Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems…
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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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Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
Published · Computer Methods in Applied Mechanics and Engineering 462, 119289 (2026). Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy — faithfully capturing complex physical behavior governed by differential equations. In…
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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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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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Functional Neural Wavefunction Optimization
We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional optimization dynamics into tractable parameter-space algorithms through a Galerkin projection onto the…
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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.…