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cs.LG2025
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…
cs.LG2024
RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators
Gianluca Fabiani, Ioannis G. Kevrekidis, Constantinos Siettos +1
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their imple…
cs.LG2024
Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications
Gianluca Fabiani
We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs…