Delay-Embedding-based Forecast Machine for Accurate Multistep-Ahead Prediction of High-Dimensional Chaotic Systems

핵심 개념
The DEFM framework leverages deep neural networks to effectively extract both the spatially and temporally associated information from high-dimensional observed time series, enabling accurate multistep-ahead prediction of the future values of a target variable.
The article presents a novel neural network-based framework called the Delay-Embedding-based Forecast Machine (DEFM) for accurately predicting the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. Key highlights: The DEFM combines delay embedding theory and deep learning techniques to transform the spatial information of a high-dimensional time series into the temporal information of a target variable. The DEFM utilizes a spatiotemporal architecture with temporal, spatial, and merging modules to effectively extract both the spatial interactions and temporally associated information from the high-dimensional data. The DEFM is trained in a self-supervised manner using a "consistently self-constrained scheme" to maintain the integrity and temporal consistency of the nonlinear mapping from the high-dimensional variables to the delay embeddings of the target variable. The DEFM demonstrates superior performance and robustness in multistep-ahead prediction tasks on various benchmark systems, including a 90-dimensional coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky equation with inhomogeneity. The DEFM also shows promising results on real-world datasets spanning different fields, outperforming several existing prediction methods.
The DEFM accurately predicts the future values of the target variables with Pearson correlation coefficients above 0.999 and root mean square errors below 0.06 on the 90-dimensional coupled Lorenz system. The DEFM achieves a mean Pearson correlation coefficient of approximately 0.92 and low root mean square errors even with short-term information from only 40 time points on the 90-dimensional coupled Lorenz system.
"Through a delay embedding scheme21,22, a delay attractor 𝒟 is reconstructed for a target variable 𝑧𝑘 with appropriately reconstructed dimensions, and this attractor is topologically conjugated with the original attractor 𝒪." "The DEFM fully extracts rich spatial and temporal information from high-dimensional data with temporal and spatial modules and integrates this spatiotemporal information via a merging module." "The cooperation between the future-consistency loss ℒ𝐹𝐶 and the determined-state loss ℒ𝐷𝑆 helps to solve the DEFM-based STI equation (Eq. (4))."

핵심 통찰 요약

by Hao Peng,Wei... 게시일 04-09-2024

더 깊은 질문

How can the DEFM framework be extended to handle missing data or irregularly sampled time series in high-dimensional systems

To handle missing data or irregularly sampled time series in high-dimensional systems, the DEFM framework can be extended by incorporating techniques such as data imputation and interpolation. For missing data, methods like mean imputation, interpolation, or using predictive models can be employed to fill in the gaps in the time series data. Additionally, techniques like time series resampling or alignment can be used to regularize irregularly sampled data, ensuring a consistent time interval between data points. By integrating these approaches into the DEFM architecture, the model can adapt to varying data availability and maintain its predictive capabilities even in the presence of missing or irregularly sampled data.

What are the potential limitations of the DEFM approach, and how can it be further improved to handle more complex real-world scenarios

While the DEFM framework shows promising results in forecasting high-dimensional systems, there are potential limitations that can be addressed for further improvement. One limitation is the scalability of the model to extremely large datasets, as processing high-dimensional data can be computationally intensive. Implementing parallel processing or distributed computing techniques can help enhance the scalability of the DEFM. Additionally, the model's performance may be affected by the choice of hyperparameters, such as the number of layers in the neural network modules. Fine-tuning these hyperparameters through techniques like grid search or Bayesian optimization can optimize the model's performance. Furthermore, incorporating mechanisms for handling nonlinear interactions and dependencies among variables can enhance the model's ability to capture complex dynamics in real-world scenarios.

Given the DEFM's ability to extract spatiotemporal information, how could it be applied to problems in fields like climate modeling, epidemiology, or neuroscience to gain new insights into the underlying dynamics

The DEFM's capability to extract spatiotemporal information can be leveraged in various fields like climate modeling, epidemiology, and neuroscience to gain new insights into underlying dynamics. In climate modeling, the DEFM can be applied to analyze and predict complex climate patterns, such as temperature variations, precipitation levels, and atmospheric dynamics. In epidemiology, the model can be used to forecast disease outbreaks, analyze the spread of infectious diseases, and evaluate the effectiveness of intervention strategies. In neuroscience, the DEFM can help in understanding brain activity patterns, predicting neural responses, and studying the dynamics of neural networks. By applying the DEFM to these domains, researchers can uncover hidden patterns, make accurate predictions, and enhance decision-making processes based on spatiotemporal information extracted from high-dimensional data.