Spatiotemporal information conversion machine for time-series forecasting

Reconstructing and predicting stochastic dynamical systems using probabilistic deep learning

Stochastic effects introduce significant uncertainty into dynamical systems, making the data-driven reconstruction and prediction of these systems highly complex. This study incorporates uncertainty learning into a deep learning model for time-series prediction, proposing a deep stochastic time-delay embedding model to improve prediction accuracy and robustness. First, this model constructs a deep probabilistic catcher to capture uncertainty information in the reconstructed mappings. These uncertainty representations are then integrated as meta-information into the reconstruction process of time-delay embedding, enabling it to fully capture system stochasticity and predict target variables over multiple time steps. Finally, the model is validated on both the Lorenz system and real-world datasets, demonstrating superior performance compared to existing methods, with robust results under noisy conditions.

Ultralow-Dimensionality Reduction for Identifying Critical Transitions by Spatial-Temporal PCA

Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand interpretable data representations to facilitate comprehension of both spatial and temporal information within the original data space. This study proposes a general and analytical ultralow-dimensionality reduction method for dynamical systems named spatial-temporal principal component analysis (stPCA) to fully represent the dynamics of a high-dimensional time-series by only a single latent variable without distortion, which transforms high-dimensional spatial information into one-dimensional temporal information based on nonlinear delay-embedding theory. The dynamics of this single variable is analytically solved and theoretically preserves the temporal property of original high-dimensional time-series, thereby accurately and reliably identifying the tipping point before an upcoming critical transition. Its applications to real-world datasets such as individual-specific heterogeneous ICU records demonstrate the effectiveness of stPCA, which quantitatively and robustly provides the early-warning signals of the critical/tipping state on each patient.

One-core neuron deep learning for time series prediction

The enormous computational requirements and unsustainable resource consumption associated with massive parameters of large language models and large vision models have given rise to challenging issues. Here, we propose an interpretable 'small model' framework characterized by only a single core-neuron, i.e. the one-core-neuron system (OCNS), to significantly reduce the number of parameters while maintaining performance comparable to the existing 'large models' in time-series forecasting. With multiple delay feedback designed in this single neuron, our OCNS is able to convert one input feature vector/state into one-dimensional time-series/sequence, which is theoretically ensured to fully represent the states of the observed dynamical system. Leveraging the spatiotemporal information transformation, the OCNS shows excellent and robust performance in forecasting tasks, in particular for short-term high-dimensional systems. The results collectively demonstrate that the proposed OCNS with a single core neuron offers insights into constructing deep learning frameworks with a small model, presenting substantial potential as a new way for achieving efficient deep learning.

DEFM: Delay-embedding-based forecast machine for time series forecasting by spatiotemporal information transformation

Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, delay-embedding-based forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting.

SGAE: single-cell gene association entropy for revealing critical states of cell transitions during embryonic development

The critical point or pivotal threshold of cell transition occurs in early embryonic development when cell differentiation culminates in its transition to specific cell fates, at which the cell population undergoes an abrupt and qualitative shift. Revealing such critical points of cell transitions can track cellular heterogeneity and shed light on the molecular mechanisms of cell differentiation. However, precise detection of critical state transitions proves challenging when relying on single-cell RNA sequencing data due to their inherent sparsity, noise, and heterogeneity. In this study, diverging from conventional methods like differential gene analysis or static techniques that emphasize classification of cell types, an innovative computational approach, single-cell gene association entropy (SGAE), is designed for the analysis of single-cell RNA-seq data and utilizes gene association information to reveal critical states of cell transitions. More specifically, through the translation of gene expression data into local SGAE scores, the proposed SGAE can serve as an index to quantitatively assess the resilience and critical properties of genetic regulatory networks, consequently detecting the signal of cell transitions. Analyses of five single-cell datasets for embryonic development demonstrate that the SGAE method achieves better performance in facilitating the characterization of a critical phase transition compared with other existing methods. Moreover, the SGAE value can effectively discriminate cellular heterogeneity over time and performs well in the temporal clustering of cells. Besides, biological functional analysis also indicates the effectiveness of the proposed approach.