Published · Communications on pure and applied mathematics, 78 (2025) 9, pp. 1609-1655. The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied…
Published · Journal of Nonlinear Science 34, 54 (2024). We prove that a version of Smagorinsky Large Eddy model for a 2D fluid in vorticity form is the scaling limit of suitable stochastic models for large scales, where the influence of…
Published · Proceedings of the International Conference on Machine Learning (ICML 2023). We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method. As…
Published · Journal of machine learning research, 25 (2024) 30, pp. 1-27. We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called…
Published · Mathematical programming, (2026). We prove explicit bounds on the exponential rate of convergence for the momentum stochastic gradient descent scheme (MSGD) for arbitrary, fixed hyperparameters (learning rate, friction parameter) and its continuous-in-time counterpart in the…
Published · Transactions of the American Mathematical Society 378(1) (2025). We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle…
Published · Nonlinearity 36(12), 7149–7190 (2023). We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2d Navier-Stokes equations in vorticity…
Published · Vietnam Journal of Mathematics 52, 775–806 (2024). We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderón’s mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth…
Published · Communications in Mathematical Physics 402, 1807–1843 (2023). We prove the positivity of Lyapunov exponents for the normal form of a Hopf bifurcation, perturbed by additive white noise, under sufficiently strong shear strength. This completes a series of related results…
Published · Journal of functional analysis, 286 (2024) 4, p. 110269. The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them…
Published · Journal of Symbolic Computation 121, 102241 (2024). We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as…
Published · Information Geometry (2024). We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that…
