Effective models and predictability of chaotic multiscale systems via machine learning

Reservoir Computing as a Tool for Climate Predictability Studies

Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate-models. In this context, the Linear-Inverse-Modeling (LIM) approach, by capturing a few essential interactions between dynamical components of the full system, has proven valuable in providing insights into predictability of the full system. We demonstrate that Reservoir Computing (RC), a form of learning suitable for systems with chaotic dynamics, provides an alternative nonlinear approach tha…

Physics-Informed Echo State Networks for Chaotic Systems Forecasting

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapun…

Physics-Informed Echo State Networks

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training, which is based on the system's governing equations. The additional loss function penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system and a truncation of the …

Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics

An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the predictability time. Existing studies, however, also showed that small changes in the hyperparameters may markedly affect the network's performance. The aim of this paper is to assess and improve the robustness of Echo State Networks for the time-accurate prediction of chaotic solutions. The goal is three-fold. First, we investigate the robustness of routinel…

可预测性使非线性状态空间模型并行化

Predictability Enables Parallelization of Nonlinear State Space Models

本研究揭示了可预测性对非线性状态空间模型并行化效率的影响，通过分析系统动态与优化问题条件的关系，证明可预测系统可显著提升并行计算效率。

Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics

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 multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where inpu…