Multi-Knowledge Fusion Network for Time Series Representation Learning

TL;DR

The paper tackles multi-horizon forecasting of high-dimensional MTS with complex spatio-temporal dependencies, where explicit graphs may be incomplete and higher-order relations matter. It introduces EIKF-Net, an end-to-end framework that jointly learns explicit graph and implicit hypergraph structures (HgI/HgRL) and combines them with a graph-based representation (GRL) through a mixture-of-experts temporal predictor, with optional uncertainty modeling via a Gaussian likelihood $\ ext{N}(\mu_\phi,\sigma_\phi^2)$. Key contributions include integrating explicit priors with learned higher-order hypergraphs, time-conditioned spatio-temporal inductive biases, differentiable hypergraph structure learning via Gumbel-softmax, and comprehensive ablations demonstrating gains across real traffic datasets. The approach yields improved forecast accuracy and calibrated uncertainty, supporting more reliable decision-making in sensor networks and smart-city applications, while remaining scalable to large MTSF tasks and robust to missing data.

Abstract

Forecasting the behaviour of complex dynamical systems such as interconnected sensor networks characterized by high-dimensional multivariate time series(MTS) is of paramount importance for making informed decisions and planning for the future in a broad spectrum of applications. Graph forecasting networks(GFNs) are well-suited for forecasting MTS data that exhibit spatio-temporal dependencies. However, most prior works of GFN-based methods on MTS forecasting rely on domain-expertise to model the nonlinear dynamics of the system, but neglect the potential to leverage the inherent relational-structural dependencies among time series variables underlying MTS data. On the other hand, contemporary works attempt to infer the relational structure of the complex dependencies between the variables and simultaneously learn the nonlinear dynamics of the interconnected system but neglect the possibility of incorporating domain-specific prior knowledge to improve forecast accuracy. To this end, we propose a hybrid architecture that combines explicit prior knowledge with implicit knowledge of the relational structure within the MTS data. It jointly learns intra-series temporal dependencies and inter-series spatial dependencies by encoding time-conditioned structural spatio-temporal inductive biases to provide more accurate and reliable forecasts. It also models the time-varying uncertainty of the multi-horizon forecasts to support decision-making by providing estimates of prediction uncertainty. The proposed architecture has shown promising results on multiple benchmark datasets and outperforms state-of-the-art forecasting methods by a significant margin. We report and discuss the ablation studies to validate our forecasting architecture.

Figures (7)

• Figure 1: Overview of EIKF-Net framework
• Figure 2: Overview of spatial inference component.
• Figure 3: Pointwise prediction error for multi-horizon forecasting tasks on benchmark datasets.
• Figure 4: Sensitivity to embedding dimension and number of hyperedges
• Figure 5: Traffic forecasting visualization on PeMSD3, PeMSD4 and PeMSD8.