A Novel Reservoir Computing Framework for Chaotic Time Series Prediction Using Time Delay Embedding and Random Fourier Features S. K. Laha Advanced Design and Analysis Group CSIR - Central Mechanical Engineering Research Institute MG Avenue, Durgapur, West Bengal, PIN - 713209, India Abstract: Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that integrates time - delay embedding with Random Fourier Feature (RFF) mappings to construct a dynamical reservoir without the need for traditional recurrent architectures. Unlike standard RC, which relies on high - dimensional recurrent connectivity, the proposed RFF - RC explicitly approximates non linear kernel transformations that uncover latent dynamical relations in the reconstructed phase space. This hybrid formulation offers two key advantages: (i) it provides a principled way to approximate complex nonlinear interactions among delayed coordina tes, thereby enriching the effective dynamical representation of the reservoir, and (ii) it reduces reliance on manual reservoir hyperparameters such as spectral radius and leaking rate. We evaluate the framework on canonical chaotic systems - the Mackey - Gla ss equation, the Lorenz system, and the Kuramoto - Sivashinsky equation. This novel formulation demonstrates that RFF - RC not only achieves superior prediction accuracy but also yields robust attractor reconstructions and long - horizon forecasts.

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear behavior has been a key challenge in predicting whether all oscillators in such a system will eventually synchronize. In this paper, we demonstrate that, surprisingly, such nonlinear behavior of coupled oscillators can be effectively linearized in certain latent dynamic spaces. The key insight is that there is a small number of `latent dynamics filters', each with a specific association with synchronizing and non-synchronizing dynamics on subgraphs so that any observed dynamics on subgraphs can be approximated by a suitable linear combination of such elementary dynamic patterns. Taking an ensemble of subgraph-level predictions provides an interpretable predictor for whether the system on the whole graph reaches global synchronization. We propose algorithms based on supervised matrix factorization to learn such latent dynamics filters. We demonstrate that our method performs competitively in synchronization prediction tasks against baselines and black-box classification algorithms, despite its simple and interpretable architecture.

This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We verify that this method can recover the spatial operators in the fractional heat equation and the Kuramoto-Sivashinsky equation from numerical solutions of the equations.

In the advertising industry, we've been using'robots' to deliver personalization better than humans can for the past few decades. So if our digital intelligence grows and artificial intelligence takes over marketing activities, does it mean we'll all be replaced by robots? There aren't many industries left where robots don't coexist with humans. We like to believe that we're still somehow always ahead of robots. While they may be smarter and faster, human traits like creativity and empathy are features that machines have only had in sci-fi.

On weekdays, Daisuke Kuramoto, 36, is just another computer engineer who develops education materials for an e-learning content provider. But once a month, he becomes Qramo, organizer of a computer programming workshop for children. "If you say I am'teaching' programming, that's incorrect," said Kuramoto, who heads the Tokyo-based volunteer group Otomo. "At the workshop, I'm just a participant who loves to play around with programming." Kuramoto started the workshop in 2008 and launched Otomo the following year, recruiting professional programmers, computer science students, parents and others with a knack for the activity.