Model-free forecasting of partially observable spatiotemporally chaotic systems

Delayed self-feedback echo state network for long-term dynamics of hyperchaotic systems

Analyzing the long-term behavior of hyperchaotic systems poses formidable challenges in the field of nonlinear science. This paper proposes a data-driven model called the delayed self-feedback echo state network (self-ESN) specifically designed for the evolution behavior of hyperchaotic systems. Self-ESN incorporates a delayed self-feedback term into the dynamic equation of a reservoir to reflect the finite transmission speed of neuron signals. Delayed self-feedback establishes a connection between the current and previous m time steps of the reservoir state and provides an effective means to capture the dynamic characteristics of the system, thereby significantly improving memory performance. In addition, the concept of local echo state property (ESP) is introduced to relax the conventional ESP condition, and theoretical analysis is conducted on guiding the selection of feedback delay and gain to ensure the local ESP. The judicious selection of feedback gain and delay in self-ESN improves prediction accuracy and overcomes the challenges associated with obtaining optimal parameters of the reservoir in conventional ESN models. Numerical experiments are conducted to assess the long-term prediction capabilities of the self-ESN across various scenarios, including a 4D hyperchaotic system, a hyperchaotic network, and an infinite-dimensional delayed chaotic system. The experiments involve reconstructing bifurcation diagrams, predicting the chaotic synchronization, examining spatiotemporal evolution patterns, and uncovering the hidden attractors. The results underscore the capability of the proposed self-ESN as a strategy for long-term prediction and analysis of the complex systems.

Neural Causal Information Extractor for Unobserved Causes

Causal inference aims to faithfully depict the causal relationships between given variables. However, in many practical systems, variables are often partially observed, and some unobserved variables could carry significant information and induce causal effects on a target. Identifying these unobserved causes remains a challenge, and existing works have not considered extracting the unobserved causes while retaining the causes that have already been observed and included. In this work, we aim to construct the implicit variables with a generator-discriminator framework named the Neural Causal Information Extractor (NCIE), which can complement the information of unobserved causes and thus provide a complete set of causes with both observed causes and the representations of unobserved causes. By maximizing the mutual information between the targets and the union of observed causes and implicit variables, the implicit variables we generate could complement the information that the unobserved causes should have provided. The synthetic experiments show that the implicit variables preserve the information and dynamics of the unobserved causes. In addition, extensive real-world time series prediction tasks show improved precision after introducing implicit variables, thus indicating their causality to the targets.