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

arXiv: https://arxiv.org/abs/2504.17966 · HTML: https://mlsanity.com/paper/2504.17966/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 24 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [On Adversarial Robustness of Trajectory Prediction for Autonomous Vehicles](https://mlsanity.com/paper/2201.05057/) (2022)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning](https://mlsanity.com/paper/2111.00998/) (2021)
- [Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior](https://mlsanity.com/paper/2305.09017/) (2023)
- [Robust Conformal Prediction for STL Runtime Verification under Distribution Shift](https://mlsanity.com/paper/2311.09482/) (2023)
- [Targeted Adversarial Attacks against Neural Network Trajectory Predictors](https://mlsanity.com/paper/2212.04138/) (2022)
- [Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)](https://mlsanity.com/paper/2406.03172/) (2024)
- [Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models](https://mlsanity.com/paper/2406.11809/) (2024)

## Built on by (most cited first, 1 of 1)

- [Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective](https://mlsanity.com/paper/2506.19805/) (2025)

## Abstract (arXiv)

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.