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We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic orbits, these SSMs are low-dimensional inertial manifolds…

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…

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that…

We introduce a new approach to prediction in graphical models with latent-shift adaptation, i.e., where source and target environments differ in the distribution of an unobserved confounding latent variable. Previous work has shown that as…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

Most forecasting methods use recent past observations (lags) to model the future values of univariate time series. Selecting an adequate number of lags is important for training accurate forecasting models. Several approaches and heuristics…

Being able to predict what may happen in the future requires an in-depth understanding of the physical and causal rules that govern the world. A model that is able to do so has a number of appealing applications, from robotic planning to…

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…

Due to simplicity and strong stability guarantees, predictor feedback methods have stood as a popular approach for time delay systems since the 1950s. For time-varying delays, however, implementation requires computing a prediction horizon…

Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a…

We consider the problem of forecasting multiple values of the future of a vector time series, using some past values. This problem, and related ones such as one-step-ahead prediction, have a very long history, and there are a number of…

This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…

This study suggests a new prediction model for chaotic time series inspired by the brain emotional learning of mammals. We describe the structure and function of this model, which is referred to as BELPM (Brain Emotional Learning-Based…

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…

Parametric analysis is a powerful tool for designing modern embedded systems, because it permits to explore the space of design parameters, and to check the robustness of the system with respect to variations of some uncontrollable…

Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically…

This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…

Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…