# Optimization of randomized neural networks for transfer operator approximation

arXiv: https://arxiv.org/abs/2605.23689 · HTML: https://mlsanity.com/paper/2605.23689/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 9 of 9)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Random vector functional link network: recent developments, applications, and future directions](https://mlsanity.com/paper/2203.11316/) (2022)
- [Dynamical systems and complex networks: A Koopman operator perspective](https://mlsanity.com/paper/2405.08940/) (2024)
- [Learning graphons from data: Random walks, transfer operators, and spectral clustering](https://mlsanity.com/paper/2507.18147/) (2025)
- [How deep is your network? Deep vs. shallow learning of transfer operators](https://mlsanity.com/paper/2509.19930/) (2025)

## Abstract (arXiv)

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.