Technology Category
Machine Learning: Time-Series/Data StreamsCognitive Modeling & Cognitive Systems: Neural Spike CodingSearch and Optimization: Mixed Discrete/Continuous Search
Modeling Time Series Dynamics with Fourier Ordinary Differential Equations
🤖 AI Summary
Neural ordinary differential equations (NODEs) face two key bottlenecks in time-series modeling: (i) time-domain representations struggle to capture long-range dependencies and intrinsic periodic structures, and (ii) continuous-time dynamics suffer from granularity mismatch with discrete-time observations. To address these, we propose Fourier Ordinary Differential Equations (FODE), the first neural ODE framework operating directly in the frequency domain. FODE leverages the Fast Fourier Transform (FFT) to extract global periodic patterns, employs learnable element-wise frequency filters to model dynamic evolution in the spectral domain, and explicitly aligns continuous-time dynamics with discrete sampling via a differentiable reconstruction layer. This design unifies short- and long-term dependency modeling while mitigating discretization error. Extensive experiments across multiple benchmark time-series datasets demonstrate that FODE consistently outperforms state-of-the-art NODE-based and deep sequential models—achieving new SOTA in both predictive accuracy and computational efficiency.
Technology Category
Application Category
📝 Abstract
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on time-domain representations often limits their ability to capture long-term dependencies and periodic structures; second, the inherent mismatch between their continuous-time formulation and the discrete nature of real-world data can lead to loss of granularity and predictive accuracy. To address these limitations, we propose Fourier Ordinary Differential Equations (FODEs), an approach that embeds the dynamics in the Fourier domain. By transforming time-series data into the frequency domain using the Fast Fourier Transform (FFT), FODEs uncover global patterns and periodic behaviors that remain elusive in the time domain. Additionally, we introduce a learnable element-wise filtering mechanism that aligns continuous model outputs with discrete observations, preserving granularity and enhancing accuracy. Experiments on various time series datasets demonstrate that FODEs outperform existing methods in terms of both accuracy and efficiency. By effectively capturing both long- and short-term patterns, FODEs provide a robust framework for modeling time series dynamics.
Problem
Research questions and friction points this paper is trying to address.
Modeling long-term dependencies in time series data
Capturing periodic structures through frequency domain transformation
Aligning continuous models with discrete observations for accuracy
Innovation
Methods, ideas, or system contributions that make the work stand out.
Embedding dynamics in the Fourier domain
Using Fast Fourier Transform for frequency analysis
Applying learnable filtering to align outputs
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