Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts
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Proposes MetaKoopman, a Bayesian meta-learned MNIW prior over a latent Koopman operator with closed-form test-time updates, tempering, and a variational action encoder for sampling-based planning, evaluated on a 37.5-ton truck and simulated MuJoCo shifts.
Problem
Modeling and forecasting nonlinear dynamics under distribution shift with calibrated uncertainty and fast enough adaptation for real-time planning in safety-critical autonomous systems.
Approach
Places a Matrix Normal-Inverse Wishart prior over a latent Koopman operator, meta-learns the prior across tasks, and performs closed-form Bayesian updates from recent trajectory segments, with a meta-learned scalar tempering factor that rescales prior precision; a variational action encoder allows sampling latent actions directly from a Gaussian.
Key results
- On the Truck-Dataset, MetaKoopman reaches validation loss 0.0596 ± 0.0021 versus 0.0888 for Bayesian MAML and 0.0917 for GrBAL.
- On HalfCheetah-Slope, MetaKoopman reaches 0.7490 ± 0.0117 versus 0.8808 for Bayesian MAML, the next best method.
- The paper reports MetaKoopman achieving the highest uncertainty-error correlation across datasets, and an order-of-magnitude speedup in rollouts from latent action sampling (claimed).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MetaKoopman instead of BayesianMAML | Hopper dynamics prediction · Hopper | validation loss: 0.0475 $\pm$ 0.0027 -> 0.0369 $\pm$ 0.0019 | Helped |
| Use MetaKoopman instead of BayesianMAML | Truck-Dataset dynamics prediction · Truck-Dataset | validation loss: 0.0888 $\pm$ 0.0100 -> 0.0596 $\pm$ 0.0021 | Helped |
| Use MetaKoopman instead of BayesianMAML | HalfCheetah-Slope dynamics prediction · HalfCheetah-Slope | validation loss: 0.8808 $\pm$ 0.0104 -> 0.7490 $\pm$ 0.0117 | Helped |
| Use MetaKoopman instead of GrBAL | Ant-DisabledJoints dynamics prediction · Ant-DisabledJoints | validation loss: 0.29 $\pm$ 0.00 -> 0.21 $\pm$ 0.00 | Helped |
| Use MetaKoopman instead of BayesianMAML | HalfCheetah-Stationary dynamics prediction · HalfCheetah-Stationary | validation loss: 0.69 $\pm$ 0.02 -> 0.62 $\pm$ 0.00 | Helped |
| Use MetaKoopman instead of BayesianMAML | Walker-Friction dynamics prediction · Walker-Friction | validation loss: 0.54 $\pm$ 0.00 -> 0.52 $\pm$ 0.10 | Helped |
| Use MetaKoopman instead of BayesianMAML | Panda-Damping dynamics prediction · Panda-Damping | validation loss: 0.05 $\pm$ 0.0002 -> 0.035 $\pm$ 0.002 | Helped |
| Update the Koopman operator using recent trajectory data | MetaKoopman on the truck dataset · Truck-Dataset | normalized MSE | Helped |
| Adapt dynamics online instead of using a non-adaptive model | Truck planner in the snow obstacle scenario · Real-world evasive lane change on snow | collision avoidance | Helped |
Limitations
- Encoder is deterministic; uncertainty is modeled only over the Koopman operator, not representation-level uncertainty.
- Truck dataset and truck planning code are not released.
- Gaussian approximation of the Student-t predictive relies on large degrees of freedom.
Experimental setup
Datasets: Truck-Dataset (37.5-ton Scania truck-trailer winter driving logs) MuJoCo simulated environments (HalfCheetah-Slope, Hopper-Gravity, Walker-Friction, Ant-DisabledJoints, Panda-Damping, Ha
Benchmarks: HalfCheetah-Slope Hopper-Gravity Truck-Dataset Ant-DisabledJoints HalfCheetah-Stationary Walker-Friction Panda-Damping
Metrics: validation MSE final validation loss normalized MSE Pearson correlation between predicted uncertainty and square
Baselines: Deep Koopman Operator (DKO) GrBAL Bayesian MAML Bayesian Neural Network Ensemble MLP (EMLP) Neural ODE
Builds on: Koopman operator theory EDMD Bayesian MAML PEARL VAE
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