3 papers
math.NA2026
RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation
Dimitrios G. Patsatzis, Alessandro Della Pia, Lucia Russo +1
We introduce RANDSMAPs (Random-feature/multi-scale neural decoders with Mass Preservation), numerical analysis-informed, explainable neural decoders designed to explicitly respect…
math.NA2024
GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
Dimitrios G. Patsatzis, Mario di Bernardo, Lucia Russo +1
We present GoRINNs: numerical analysis-informed (shallow) neural networks for the solution of inverse problems of non-linear systems of conservation laws. GoRINNs is a hybrid/blend…
math.DS2019
A Numerical Method for the Parametrization of Stable and Unstable Manifolds of Microscopic Simulators
Constantinos Siettos, Lucia Russo
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for w…