Title: Rethinking Nonlinear Dynamics in Deep Time Series Models
Primary area: learning on time series and dynamical systems
Keywords: Nonlinear Dynamics system, Discrete Volterra series, Time series

Abstract: Deep learning models have achieved remarkable success in modeling complex time series data, yet their black-box nature limits interpretability and explicit representation of intrinsic dynamic structures such as nonlinear interactions and memory effects. Observing the inherent compatibility of Volterra series' polynomial integral kernels with GPU-accelerated deep learning frameworks, we propose the Discrete Volterra Network (DiVo), a novel deep learning model family integrating Volterra series to explicitly learn dynamic characteristics from time series data. Specifically, DiVo computes discrete Volterra coefficient matrices via polynomial expansions, converting nonlinear time series modeling into linear polynomial coefficient learning. To address practical challenges, we introduce adaptive channel selection to remove strict dependence on time-invariant sequences, and propose a redundancy-aware sparsification strategy that combines fixed masking of Volterra features with sparsified low-rank decomposition to eliminate redundancy in both the feature and parameter spaces, yielding a compact model representation.Extensive experiments on diverse real-world datasets show DiVo significantly outperforms traditional deep models in prediction accuracy, interpretability, and parameter efficiency.

TL;DR: DiVo is a compact, interpretable deep learning model that integrates Volterra series to capture nonlinear dynamics and memory in time series, outperforming traditional models in accuracy and efficiency.