SegTSim: A Big Data Driven Segmented Temporal Simulation Framework for Heterogeneous Multivariate Systems

We introduce Equilibrium State Estimation (ESE), a novel paradigm for simultaneous prediction, where multiple interacting systems require separate yet coordinated forecasts. Such scenarios often arise in real-world settings such as economics and healthcare modeling. Unlike existing approaches that predict one system at a time, ESE forecasts all systems in a single pass. It first estimates the equilibrium state across systems, then generates holistic forecasts based on the difference between the current state and the estimated equilibrium. Extensive experiments on synthetic and real-world datasets, including currency exchange and COVID-19 spread modeling, demonstrate that ESE is at least as accurate as state-of-the-art (SOTA) methods while being significantly faster. In addition, ESE integrates seamlessly with conventional predictors, combining their accuracy with its exceptional efficiency and delivering a 10-70x speedup. With linear-time complexity, ESE scales far better than SOTA methods as the number of systems increases. Moreover, it remains accurate under diverse perturbations, establishing ESE as a fast, generalizable, robust, and scalable multi-prediction method.

Time series forecasting models often benefit from historical patterns. Inspired by Retrieval-Augmented Generation (RAG), recent research explored retrieving relevant historical time series segments to enhance forecasting. However, relying solely on time series similarity is often insufficient for retrieval under non-stationarity. To address this, we propose a multimodal approach: a \textbf{S}emantics-\textbf{E}nhanced \textbf{R}etrieval-\textbf{A}ugmented Time Series \textbf{F}orecasting framework, SERAF. Unlike mainstream approaches that depend only on time series similarity, SERAF conducts dual retrieval over the time series and their self-generated textual descriptions. It retrieves two complementary sets of historical patterns and corresponding futures, which are selectively and jointly used to guide future predictions. Experiments across seven real-world datasets demonstrate the effectiveness of SERAF in bridging numerical and semantic views of time series compared with state-of-the-art baselines.

Multivariate time series forecasting (MTSF) is a fundamental task in many real world applications. Existing patch based forecasting methods generally fall into three categories: fixed partitioning, multi-scale partitioning, and extendable partitioning. Fixed partitioning often breaks meaningful temporal boundaries, multi-scale partitioning may introduce redundant representations across scales, and extendable partitioning improves flexibility but still lacks an explicit mechanism for organizing semantic structure and modeling interactions among heterogeneous temporal patterns. To address these limitations, we propose SCPaT, a Transformer based framework built on semantic structured partitioning. SCPaT first decomposes input sequences into semantically consistent units through adaptive semantic unit generation, then constructs a dynamic semantic graph to model directed dependencies among these units and organize them into higher order semantic blocks. Based on these structured representations, an importance aware routing mechanism adaptively dispatches different semantic blocks to different experts for customized modeling. Extensive experiments on 12 real world datasets demonstrate the effectiveness of SCPaT.