Neural-Network Approximation

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Period ending 2026-09-21

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May 22, 2026 · cs.LGJ/K move · Enter open · S save

Optimization of randomized neural networks for transfer operator approximation

Mohammad Tabish, Stefan Klus

Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot–Watt University, Edinburgh, UK · School of Mathematical & Computer Sciences, Heriot–Watt University, Edinburgh, UK

RaNNDy is a randomized neural network architecture for the data-driven approximation of transfer operators associated with complex dynamical systems. The weights and biases of the hidden layers of the network are randomly initialized and kept fixed, only the output layer is trained. This has several advantages over fully optimized neural networks, notably a closed-form solution for the output layer and significantly lower training costs. Despite these advantages, RaNNDy is restricted to the initial selection of weights and biases that parametrize the basis functions required for the operator approximation. Since the basis functions are determined by the activation function, choosing an appropriate activation function for the hidden layers is crucial. In this work, we propose an algorithm that optimizes the activation function itself, while keeping the weights and biases in the randomized neural network fixed, providing a more suitable dictionary. We illustrate the efficacy of the approach using various benchmark problems, including stochastic differential equations and random walks on graphons.

Neural-Network Approximation Neural Network Optimization Activation Functions Neural Network Dynamical Systems

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