49 citations · 271 across the 22 of their papers we have counts for
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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…
Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators
Gianluca Fabiani, Constantinos Siettos, Ioannis G. Kevrekidis
The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approac…
Enabling Local Neural Operators to perform Equation-Free System-Level Analysis
Gianluca Fabiani, Hannes Vandecasteele, Somdatta Goswami +2
Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly lear…