Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Models

TL;DR

This work tackles reliable trajectory prediction under unknown obstacle dynamics and distributional shift by combining conformal prediction with a plug-and-play physics-informed learning framework. When OOD dynamics are detected, a Gaussian-process distributed Port-Hamiltonian system (GP-dPHS) is activated to learn a physically consistent Hamiltonian and quantify predictive uncertainty, ensuring physics-compliant predictions. The approach is demonstrated on an oscillating spring, showing that CP effectively flags OOD cases and GP-dPHS outperforms purely data-driven baselines and retraining under limited observations. The proposed method offers a general, data-efficient way to inject physical priors into learning pipelines and provide reliable, uncertainty-aware predictions in robotic settings.

Abstract

The ability to predict trajectories of surrounding agents and obstacles is a crucial component in many robotic applications. Data-driven approaches are commonly adopted for state prediction in scenarios where the underlying dynamics are unknown. However, the performance, reliability, and uncertainty of data-driven predictors become compromised when encountering out-of-distribution observations relative to the training data. In this paper, we introduce a Plug-and-Play Physics-Informed Machine Learning (PnP-PIML) framework to address this challenge. Our method employs conformal prediction to identify outlier dynamics and, in that case, switches from a nominal predictor to a physics-consistent model, namely distributed Port-Hamiltonian systems (dPHS). We leverage Gaussian processes to model the energy function of the dPHS, enabling not only the learning of system dynamics but also the quantification of predictive uncertainty through its Bayesian nature. In this way, the proposed framework produces reliable physics-informed predictions even for the out-of-distribution scenarios.

Figures (6)

• Figure 1: The left panels in the fire scene indicate that the DNN reliably predicts outcomes when test-time dynamics resemble its training regime $\mathcal{D}_0$, while the right panels show that CP flags unreliable DNN outputs under OOD dynamics $D_1$. The red arrow indicates the direction of the object movement of the future, blue denotes the ground-truth future observation, which is outbound of the CP (white).
• Figure 2: Illustration of proposed PnP-PIML pipeline. We leverage conformal prediction to detect outlier dynamics and, in this case, apply a data-efficient Bayesian physics-informed learning method to provide reliable predictions.
• Figure 3: From left to right, the figure illustrates the process starting with the original video, skeletonization, and final denoised nonlinear movement data over time (overlay).
• Figure 4: The nonconformity score on observation $D_{1}$ of DNN trained on $D_{0}$ is significantly higher than the conformal quantile $C$, which indicates the existence of OOD. On the other hand, the majority of the sample scores from $D_{0}$ are lower than $C$ to demonstrate the ID case.
• Figure 5: Proposed PnP-PIML approach, in which the physics-consistent GP-dPHS (red) generalizes well on unseen test data marked by gray plane, leading to improved accuracy.