11 citations · 16 across the 3 of their papers we have counts for
5 papers
Directed mean curvature flow in noisy environment
Andris Gerasimovics, Martin Hairer, Konstantin Matetski
We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled…
Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics
Cristopher Salvi, Maud Lemercier, Andris Gerasimovics
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the noti…
Feature Engineering with Regularity Structures
Ilya Chevyrev, Andris Gerasimovics, Hendrik Weber
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to…
Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
Andris Gerasimovics, Antoine Hocquet, Torstein Nilssen
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_…
Hörmander's theorem for semilinear SPDEs
Andris Gerasimovics, Martin Hairer
We consider a broad class of semilinear SPDEs with multiplicative noise driven by a finite-dimensional Wiener process. We show that, provided that an infinite-dimensional analogue…