Neural ODEs

ODE: Ordinary Differential Equation

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Overview

Neural ODEs represent hidden states or physical systems as evolving continuously according to a learned vector field, with numerical solvers used to compute their trajectories. Researchers use them for irregular time-series forecasting, scientific simulation, control, and generative modeling, often combining them with controlled or stochastic dynamics, graph networks, or known physical laws. Common approaches include hybrid mechanistic-neural models, physics-informed constraints, and structure-preserving methods such as Hamiltonian or symplectic models; evaluations span dynamical-system benchmarks, irregular clinical data, and engineering simulations. A central tension is balancing flexible learned dynamics with physical consistency and long-horizon reliability, while managing solver cost, stiffness, noisy observations, and sensitivity to numerical error.

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91 papers7 papers in the last four weeks, up 40% on the four weeks before. 0.0% of all new papers.

Jan 10, 2024

DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysis

Real-world time series analysis faces significant challenges when dealing with irregular and incomplete data. While Neural Differential Equation (NDE) based methods have shown promise, they struggle with limited expressiveness, scalability issues, and stability concerns. Conversely, Neural Flows offer stability but falter with irregular data. We introduce 'DualDynamics', a novel framework that synergistically combines NDE-based method and Neural Flow-based method. This approach enhances expressive power while balancing computational demands, addressing critical limitations of existing techniques. We demonstrate DualDynamics' effectiveness across diverse tasks: classification of robustness to dataset shift, irregularly-sampled series analysis, interpolation of missing data, and forecasting with partial observations. Our results show consistent outperformance over state-of-the-art methods, indicating DualDynamics' potential to advance irregular time series analysis significantly.

YongKyung Oh, Dong-Young Lim, Sungil Kim

Medical & Imaging Informatics (MII) Group, University of California, Los Angeles (UCLA), CA, USA · Department of Industrial Engineering, Ulsan National Institute of Science and Technology (UNIST), Republic of Korea · Artificial Intelligence Graduate School, Ulsan National Institute of Science and Technology (UNIST), Republic of Korea

Irregular Time-Series ModelingTime Series ImputationTime Series ForecastingNeural ODEs
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