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20192026
most citedConstructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach

49 citations · 271 across the 22 of their papers we have counts for

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Showing 2024 · math.NAShow all

2 papers · 2 filters

math.NA2024★ 2 cited

Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs

Gianluca Fabiani, Erik Bollt, Constantinos Siettos +1

We present a linear stability analysis of physics-informed random projection neural networks (PI-RPNNs), for the numerical solution of {the initial value problem (IVP)} of (stiff)…

math.NA2024★ 17 cited

Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks

Hector Vargas Alvarez, Gianluca Fabiani, Ioannis G. Kevrekidis +2

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization…