9 citations · 15 across the 12 of their papers we have counts for
12 papers
ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
Roberto Nuca, Giovanni Testa, Luca Galimberti +1
Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate. We in…
Structure-informed operator learning for parabolic Partial Differential Equations
Fred Espen Benth, Nils Detering, Luca Galimberti
In this paper, we present a framework for learning the solution map of a backward parabolic Cauchy problem. The solution depends continuously but nonlinearly on the final data, sou…
Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
Luca Galimberti, Helge Holden, Kenneth H. Karlsen +1
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term.…
Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis
Luca Galimberti, Anastasis Kratsios, Giulia Livieri
Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contempora…
Pricing options on flow forwards by neural networks in Hilbert space
Fred Espen Benth, Nils Detering, Luca Galimberti
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hi…
Neural Networks in Fréchet spaces
Fred Espen Benth, Nils Detering, Luca Galimberti
We define a neural network in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functio…
Stochastic Integrals and Gelfand Integration in Fréchet Spaces
Fred Espen Benth, Luca Galimberti
We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the G…
Well-posedness of stochastic continuity equations on Riemannian manifolds
Luca Galimberti, Kenneth H. Karlsen
We analyze continuity equations with Stratonovich stochasticity, , defined on a smoot…
Renormalization of stochastic continuity equations on Riemannian manifolds
Luca Galimberti, Kenneth H. Karlsen
We consider the initial-value problem for stochastic continuity equations of the form $$ \partial_t ρ+ \text{div}_h \left[ρ\left(u(t,x) + \sum_{i=1}^N a_i(x)\circ \frac{dW^i}{dt}\r…
Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds
Luca Galimberti, Kenneth H. Karlsen
We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Ito) noise. The Cauchy problem defined on a Riemannian manifold is shown to be we…
"Large" conformal metrics of prescribed Q-curvature in the negative case
Luca Galimberti
Given a compact and connected four dimensional smooth Riemannian manifold with and a smooth non-constant function with $\max_{p\…
Compactness issues and bubbling phenomena for the prescribed Gaussian curvature equation on the Torus
Luca Galimberti
In the spirit of the paper "Large conformal metrics of prescribed Gauss curvature on surfaces of higher genus" by Borer-Galimberti-Struwe, where we dealt with the case of a closed…