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Zero-Shot Transfer of Neural ODEs
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Learns a Hilbert space of dynamics spanned by neural ODE basis functions (function encoders) so unseen system dynamics can be identified zero-shot from a short trajectory via inner products, without gradient updates.
Problem
Neural ODEs model a single dynamical system and must be retrained for each new scenario, which is too slow for real-time adaptation and zero-shot transfer in autonomous systems.
Approach
Combine function encoders with neural ODEs: learn k neural ODE basis functions spanning a space of dynamics, and compute the coefficients of a new system online via a Monte-Carlo inner product over observed state differences, requiring no gradients at runtime; optionally learn a residual relative to an average dynamics model.
Key results
- On MuJoCo Half-Cheetah and Ant, FE + NODE + Res gives accurate long-horizon predictions from 200 data points, outperforming NODE and FE + Res on Ant.
- On the PyBullet quadrotor, FE + NODE + Res outperforms competing approaches at long-horizon prediction and yields lower MPC slew rate than NODE.
- Ablations show insensitivity to number of basis functions around k=100 and to data points beyond 200 on Half-Cheetah.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the residuals method to FE + NODE (ablation) | FE + NODE · Half-Cheetah and Ant | long-horizon prediction accuracy | Helped |
| use FE + NODE + Res instead of NODE | dynamics prediction · PyBullet quadrotor with varying mass | long-horizon prediction accuracy | Helped |
| use FE + NODE or FE + NODE + Res instead of NODE | quadrotor MPC · PyBullet quadrotor | slew rate | Helped |
| combine basis-function gradients for one integration instead of integrating each basis function separately (ablation) | FE + NODE inference · dynamics prediction | prediction accuracy | Hurt |
| vary the number of basis functions around k=100 (ablation) | FE + NODE + Res · Half-Cheetah | model performance | No clear effect |
| reduce the number of basis functions toward 0 (ablation) | FE + NODE + Res · Half-Cheetah | model performance | Hurt |
| increase the number of example data points (ablation) | FE + NODE + Res · Half-Cheetah | model performance | No clear effect |
Surprising findings
- The residuals method performs best in both MuJoCo environments, while the Oracle NODE given hidden parameters has unstable long-horizon predictions.
- Gradient-based orthonormalization is not enforced; orthogonality emerges from the training loss, and the proposed sum-of-gradients integration trick was less accurate in practice.
Limitations
- Requires a large collection of example datasets to span the dynamics space, more data than a single dynamics model.
- Basis functions only trained on short intervals within the state domain; long-horizon integration may leave the training domain and become unpredictable.
- Integration overhead: k neural ODEs increase inference time or memory; RK4 used as fixed-step integrator.
Experimental setup
Datasets: Van der Pol oscillator trajectories MuJoCo Half-Cheetah trajectories with varying hidden parameters MuJoCo Ant trajectories with varying hidden parameters PyBullet quadrotor trajectories with varying mass
Benchmarks: Van der Pol oscillator MuJoCo Half-Cheetah MuJoCo Ant PyBullet quadrotor with varying mass
Metrics: long-horizon prediction MSE 10-step MSE slew rate of MPC control
Baselines: NODE FE + Res (function encoder with residuals method) Oracle NODE with hidden parameters as input
Builds on: neural ODE function encoders parameterized neural ODEs
Closest papers by meaning
- Zero-Shot Reinforcement Learning via Function Encoders (ICML 2024 · similarity 0.86)
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- How Deep Do We Need: Accelerating Training and Inference of Neural ODEs via Control Perspective (ICML 2024 · similarity 0.84)
- A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems (NeurIPS 2026 · similarity 0.83)
- Zero-Shot Robotic Manipulation with Pre-Trained Image-Editing Diffusion Models (ICLR 2024 · similarity 0.83)
- Unsupervised Zero-Shot Reinforcement Learning via Functional Reward Encodings (ICML 2024 · similarity 0.83)
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