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We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…

We study the theoretical capacity to statistically learn local landscape information by Evolution Strategies (ESs). Specifically, we investigate the covariance matrix when constructed by ESs operating with the selection operator alone. We…

The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian…

We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal…

We present neural machine translation (NMT) models inspired by echo state network (ESN), named Echo State NMT (ESNMT), in which the encoder and decoder layer weights are randomly generated then fixed throughout training. We show that even…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of…

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…

El Ni\~no-Southern Oscillation (ENSO) exerts global climate and societal impacts, but real-time prediction with lead times beyond one year remains challenging. Dynamical models suffer from large biases and uncertainties, while deep learning…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian…

This article introduces a robust hybrid method for solving supervised learning tasks, which uses the Echo State Network (ESN) model and the Particle Swarm Optimization (PSO) algorithm. An ESN is a Recurrent Neural Network with the…

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model…

Echo State Networks (ESNs) are a special type of the temporally deep network model, the Recurrent Neural Network (RNN), where the recurrent matrix is carefully designed and both the recurrent and input matrices are fixed. An ESN uses the…

We present a deep neural network which predicts the stability of isotropic steady states of the asymptotically flat, spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates. The network takes as input the energy profile…

In recent years, studying and predicting alternative mobility (e.g., sharing services) patterns in urban environments has become increasingly important as accurate and timely information on current and future vehicle flows can successfully…

Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…

Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…