Prediction of chaotic dynamics from data: An introduction

2026/04/13 by Luca Magri, Andrea Nóvoa, Elise Özalp · 1 voice · 3 citations
Physics and Astronomy · #nlin.CD

paper · pdf

Abstract

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for time-forecasting chaotic dynamics, such as echo state networks and long-short-term memory networks, whilst keeping a dynamical systems' perspective. Third, the lecture contains informal interpretations and pedagogical examples with prototypical chaotic systems (e.g., the Lorenz system), which elucidate the theory. The chapter is complemented by coding tutorials (online) at https://github.com/MagriLab/Tutorials.

Citations

• Data-driven prediction and control of extreme events in a chaotic flow
• Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics
• Physics-Informed Echo State Networks
• Array Programming with NumPy
• Learning ergodic averages in chaotic systems
• Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius
• Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics
• Stability, sensitivity and optimisation of chaotic acoustic oscillations
• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Ensemble-LES Analysis of Perturbation Response of Turbulent Partially-Premixed Flames
• Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model
• Reservoir observers: Model-free inference of unmeasured variables in chaotic systems
• Toward a chaotic adjoint for LES
• Lyapunov spectrum of separated flows and its dependence on numerical discretization
• Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)
• Scaling of Lyapunov Exponents in Homogeneous Isotropic Turbulence
• Predictability: a way to characterize complexity
• Long Short-Term Memory
• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application
• Atmospheric Predictability as Revealed by Naturally Occurring Analogues
• Deterministic Nonperiodic Flow

Cited by

• Attractor reconstruction in attracting subspaces: Slow-spectrum preshaping for reservoir computing under partial observation

Discussions

• Luca Magri, Andrea N\'ovoa, Elise \"Ozalp: Prediction of chaotic dynamics from data: An introduction https://arxiv.org/abs/2604.11624 https://arxiv.org/pdf/2604.11624 https://arxiv.org/html/2604.11624 [bsky, 0 points, 0 comments]

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