20 citations · 42 across the 14 of their papers we have counts for
16 papers
Autoencoders vs. Numerical Analysis--Informed Manifold Learning for Navier--Stokes Flows
Alessandro Della Pia, Lucia Russo, Ioannis Kevrekidis +1
Autoencoders (AEs) have become a dominant approach to nonlinear latent-space construction in data-driven reduced-order modelling (ROM), with their decoders lifting latent represent…
Learning Contractive Integral Operators with Fredholm Integral Neural Operators
Kyriakos C. Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
We generalize the framework of Fredholm Neural Networks, to learn non-expansive integral operators arising in Fredholm Integral Equations (FIEs) of the second kind in arbitrary dim…
Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach
Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos +1
We present a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the solutions are sought in the function spa…
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…
HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs
Kyriakos Georgiou, Gianluca Fabiani, Constantinos Siettos +1
We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a si…
PDE-Free Mass-Constrained Learning of Complex Systems with Hidden States
Gianmaria Viola, Alessandro Della Pia, Lucia Russo +2
We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex system…