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DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysis
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Proposes DualDynamics, which couples a Neural CDE (implicit) encoder with a invertible neural flow (explicit) latent stage to model irregular and incomplete time series, evaluated on classification, interpolation, sepsis classification and forecasting.
Problem
Irregular and incomplete time series modeling: NDE-based methods (Neural ODE/CDE/SDE) have limited expressiveness, scalability and stability issues, while Neural Flows are stable but struggle with irregularly sampled data.
Approach
Combine an implicit NDE (primarily Neural CDE) latent trajectory with a secondary explicit neural flow that maps an initial state derived from the CDE trajectory to a regularized latent state, trained jointly via adjoint backpropagation, with Hutchinson trace estimation for density-change analysis.
Key results
- On 18 UEA/UCR datasets averaged over regular and missing settings, the proposed method reaches 0.708 mean accuracy with average rank 4.9, versus 0.674 for Transformer and 0.667 for Neural CDE.
- On PhysioNet Sepsis, the proposed method achieves 0.918 AUROC with observation intensity and 0.873 without, above EXIT (0.913 / 0.836).
- On Google stock forecasting, test MSE is 0.0010 in the regular setting versus 0.0016 for the next-best EXIT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Combine an implicit Neural CDE with an explicit flow component | Neural CDE time-series classifier · UEA/UCR classification, Average across missingness conditions | Accuracy: 0.667 (0.075) -> 0.708 (0.092) | Helped |
| Combine an implicit encoder with an explicit flow component | PhysioNet Mortality interpolation model · PhysioNet Mortality, 50% observed | Test MSE × 10^-3: 4.139 ± 0.029 -> 3.631 ± 0.049 | Helped |
| Combine an implicit component with an explicit flow component | Irregular time-series classifier · PhysioNet Sepsis, OI | Test AUROC: 0.913 ± 0.002 -> 0.918 ± 0.003 | Helped |
| Combine an implicit component with an explicit flow component | Partial-observation forecaster · MuJoCo, Regular | Test MSE: 0.022 ± 0.002 -> 0.006 ± 0.001 | Helped |
| Combine an implicit component with an explicit flow component | Partial-observation forecaster · Google, Regular | Test MSE: 0.0016 ± 0.002 -> 0.0010 ± 0.0001 | Helped |
| Use the flow output ẑ(t) instead of z(t) (ablation) | DualDynamics Neural CDE classifier · BasicMotions, 70% Missing | Accuracy: 0.883 (0.095) -> 0.983 (0.037) | Helped |
| Add the flow component to the Neural CDE classifier (ablation) | BasicMotions classifier · BasicMotions, 70% Missing | Accuracy: 0.900 (0.037) -> 0.983 (0.037) | Helped |
| Replace a conventional MLP with the flow component (ablation) | DualDynamics Neural CDE classifier · UEA/UCR classification, Regular | Accuracy: 0.592 (0.084) -> 0.724 (0.090) | Helped |
| Replace a conventional MLP with the flow component (ablation) | DualDynamics Neural CDE classifier · BasicMotions, 50% Missing | Accuracy: 0.950 (0.046) -> 0.983 (0.037) | Helped |
| Use Neural CDE instead of Neural ODE as the implicit component (ablation) | DualDynamics classifier · BasicMotions classification, Average | Accuracy: 0.540 (0.059) -> 0.724 (0.090) | Helped |
| Use Neural CDE instead of Neural SDE as the implicit component (ablation) | DualDynamics classifier · BasicMotions classification, Average | Accuracy: 0.538 (0.066) -> 0.724 (0.090) | Helped |
| Replace the flow component with ResNet Flow (ablation) | DualDynamics Neural CDE classifier · BasicMotions, 70% Missing | Accuracy: 0.983 (0.037) -> 1.000 (0.000) | Mixed |
Surprising findings
- Neural Flow alone performs worse than a conventional RNN on the BasicMotions irregular settings, and Neural ODE-based variants of the proposed method show accuracy near chance on BasicMotions (about 0.53).
Limitations
- Results on the BasicMotions Neural ODE variant show near-chance accuracy, indicating sensitivity to the implicit component choice.
- Flow configuration (ResNet, GRU, or coupling) must be selected by hyperparameter tuning, with no single best choice.
- Theoretical density-preservation argument relies on the assumption that the flow is perfectly estimated.
Experimental setup
Datasets: UEA/UCR time series classification repository (18 datasets) PhysioNet 2012 Mortality PhysioNet Sepsis MuJoCo (Hopper) Google stock 2011-2021
Benchmarks: UEA/UCR 18 datasets with 30/50/70% missingness PhysioNet 2012 Mortality interpolation PhysioNet Sepsis AUROC MuJoCo forecasting Google stock forecasting
Metrics: accuracy average rank MSE AUROC cross-entropy loss memory (MB) computation time
Baselines: RNN LSTM GRU GRU-D GRU-Δt Transformer MTAN MIAM GRU-ODE ODE-RNN ODE-LSTM Latent-ODE
Builds on: Neural CDE Neural Flows Neural ODE Neural SDE ANCDE EXIT
Closest papers by meaning
- Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data (ICLR 2024 · similarity 0.87)
- Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series (NeurIPS 2024 · similarity 0.86)
- Physiome-ODE: A Benchmark for Irregularly Sampled Multivariate Time-Series Forecasting Based on Biological ODEs (ICLR 2025 · similarity 0.85)
- DDN: Dual-domain Dynamic Normalization for Non-stationary Time Series Forecasting (NeurIPS 2024 · similarity 0.85)
- Irregular Multivariate Time Series Forecasting: A Transformable Patching Graph Neural Networks Approach (ICML 2024 · similarity 0.84)
- Trajectory Flow Matching with Applications to Clinical Time Series Modelling (NeurIPS 2024 · similarity 0.84)
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