Zero-Shot Transfer of Neural ODEs

Abstract

Autonomous systems often encounter environments and scenarios beyond the scope of their training data, which underscores a critical challenge: the need to generalize and adapt to unseen scenarios in real time. This challenge necessitates new mathematical and algorithmic tools that enable adaptation and zero-shot transfer. To this end, we leverage the theory of function encoders, which enables zero-shot transfer by combining the flexibility of neural networks with the mathematical principles of Hilbert spaces. Using this theory, we first present a method for learning a space of dynamics spanned by a set of neural ODE basis functions. After training, the proposed approach can rapidly identify dynamics in the learned space using an efficient inner product calculation. Critically, this calculation requires no gradient calculations or retraining during the online phase. This method enables zero-shot transfer for autonomous systems at runtime and opens the door for a new class of adaptable control algorithms. We demonstrate state-of-the-art system modeling accuracy for two MuJoCo robot environments and show that the learned models can be used for more efficient MPC control of a quadrotor.

Figures (8)

• Figure 1: An illustration of our approach. The training phase uses a set of datasets $\mathcal{D}$ to train basis functions $\{g_1, ..., g_k\}$ to span $\mathcal{F}$. The zero-shot phase uses online data to identify the coefficients for a new function, which can be estimated as a linear combination of the basis functions.
• Figure 2: The approximated dynamics for different Van der Pol systems, where the parameter $\mu$ is varied. This plot shows that a NODE can only fit a single Van der Pol system, whereas FE + NODE + Res can fit a space of Van der Pol systems from $5000$ example data points.
• Figure 3: Model performance on predicting the dynamics of MuJoCo robotics environments with hidden parameters. $200$ example data points are given to identify dynamics. The results show that FE + NODE + Res. makes accurate, long-horizon predictions even in the presence of hidden parameters. Evaluation is over 5 seeds, shaded regions show the first and third quartiles around the median.
• Figure 4: Model performance on the PyBullet quadrotor environment with varying mass. Function encoders improve model performance across varying masses. Shaded region is $1^{\rm st}$ and $3^{\rm rd}$ quartiles over 200 trajectories (left) and over 5 trajectories (middle, right).
• Figure 5: Qualitative analysis of the difference in control between NODEs and our approach. Two trajectories with the same initial position but different masses are shown. NODE is unaware of the mass, and so its $z$ position requires constant correction. In contrast, FE + NODE (+Res) accounts for the mass through the coefficients, meaning it is more accurate and requires fewer corrections.