3 papers
math.NA2026
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…
math.DS2025
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…
math.AP2024
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…