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math.NA2026
A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials
Enrico Ballini, Allan Peter Engsig-Karup, Tito Andriollo
We present a neural-network-based framework for the solution of three-dimensional boundary value problems where the solution is expressible in terms of harmonic potentials. The app…
math.NA2026
Model reduction of parametric ordinary differential equations via autoencoders: representation properties and convergence analysis
Enrico Ballini, Marco Gambarini, Alessio Fumagalli +3
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps rep…