Next Article in Journal
Sustainable Mixed-Model Assembly Line Balancing with an Analytical Lower Bound and Adaptive Large Neighborhood Search
Previous Article in Journal
Exponentially Fitted Midpoint Scheme for a Stochastic Oscillator
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Review

An Overview of Spatiotemporal Network Forecasting: Current Research Status and Methodological Evolution

1
School of Environmental Science and Engineering, Yangzhou University, Yangzhou 225127, China
2
School of Mathematics, Yangzhou University, Yangzhou 225127, China
3
School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(1), 18; https://doi.org/10.3390/math14010018 (registering DOI)
Submission received: 9 November 2025 / Revised: 8 December 2025 / Accepted: 19 December 2025 / Published: 21 December 2025
(This article belongs to the Special Issue Advanced Machine Learning Research in Complex System)

Abstract

Time series and spatio-temporal forecasting are fundamental tasks for complex system modeling and intelligent decision-making, with broad applications in transportation, meteorology, finance, healthcare, and public safety. Compared with simple univariate time series, real-world spatio-temporal data exhibit rich temporal dynamics and intricate spatial interactions, leading to heterogeneity, non-stationarity, and evolving topologies. Addressing these challenges requires modeling frameworks that can simultaneously capture temporal evolution, spatial correlations, and cross-domain regularities. This survey provides a comprehensive synthesis of forecasting methods, spanning statistical algorithms, traditional machine learning approaches, neural architectures, and recent generative and causal paradigms. We review the methodological evolution from classical linear models to deep learning–based temporal modules and emphasize the role of attention-based Transformers as general-purpose sequence architectures. In parallel, we distinguish these architectural advances from pre-trained foundation models for time series and spatio-temporal data (e.g., large models trained across diverse domains), which leverage self-supervised objectives and exhibit strong zero-/few-shot transfer capabilities. We organize the review along both data-type and architectural dimensions—single long-term time series, Euclidean-structured spatio-temporal data, and graph-structured spatio-temporal data—while also examining advanced paradigms such as diffusion models, causal modeling, multimodal-driven frameworks, and pre-trained foundation models. Through this taxonomy, we highlight common strengths and limitations across approaches, including issues of scalability, robustness, real-time efficiency, and interpretability. Finally, we summarize open challenges and future directions, with a particular focus on the joint evolution of graph-based, causal, diffusion, and foundation-model paradigms for next-generation spatio-temporal forecasting.
Keywords: time series forecasting; spatio-temporal modeling; deep learning; transformer architecture time series forecasting; spatio-temporal modeling; deep learning; transformer architecture

Share and Cite

MDPI and ACS Style

Yang, C.; Zhang, W.; Zhou, Y. An Overview of Spatiotemporal Network Forecasting: Current Research Status and Methodological Evolution. Mathematics 2026, 14, 18. https://doi.org/10.3390/math14010018

AMA Style

Yang C, Zhang W, Zhou Y. An Overview of Spatiotemporal Network Forecasting: Current Research Status and Methodological Evolution. Mathematics. 2026; 14(1):18. https://doi.org/10.3390/math14010018

Chicago/Turabian Style

Yang, Chenchen, Wenbing Zhang, and Yingjiang Zhou. 2026. "An Overview of Spatiotemporal Network Forecasting: Current Research Status and Methodological Evolution" Mathematics 14, no. 1: 18. https://doi.org/10.3390/math14010018

APA Style

Yang, C., Zhang, W., & Zhou, Y. (2026). An Overview of Spatiotemporal Network Forecasting: Current Research Status and Methodological Evolution. Mathematics, 14(1), 18. https://doi.org/10.3390/math14010018

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Article metric data becomes available approximately 24 hours after publication online.
Back to TopTop