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 · 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 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…
Published · Journal of Mathematical Fluid Mechanics 25, 28 (2023). A stochastic version of the two-layer quasi-geostrophic model (2LQG) with multiplicative transport noise is analysed. This popular intermediate complexity model describes large scale atmosphere and ocean dynamics at the mid-latitudes. The transport…
Published · Stochastic Transport in Upper Ocean Dynamics, Mathematics of Planet Earth 10, pp. 69–85 (2023).
Published · Stochastics and Partial Differential Equations: Analysis and Computations 12(2), 1046–1099 (2024). We consider in a smooth and bounded two dimensional domain the convergence in the $L^2$ norm, uniformly in time, of the solution of the stochastic second-grade fluid equations with transport noise and no-slip boundary conditions to the solution of the…
Published · Information Geometry (2023). The natural gradient field is a vector field that lives on a model equipped with a distinguished Riemannian metric, e.g. the Fisher-Rao metric, and represents the direction of steepest ascent of an…
