EPIC-PIML: Epistemic-Constructed Physics-Informed Machine Learning

Learning the dynamics of complex robotic systems via a hybrid physics-informed machine learning (HPIML) approach, which combines known physics with machine learning (ML), has shown promising performance in decision-making and optimal control tasks. However, under environmental uncertainty, HPIML is not necessarily a robust predictive model: the in-distribution region favors the ML term, while the out-of-distribution region favors the physics term. Therefore, adaptively weighing the outputs of these two terms across different environments or regions is important for an accurate and robust learning model. This paper proposes Epistemic-Constructed Physics-Informed Machine Learning (EPIC-PIML), which introduces an uncertainty mechanism that coordinates the outputs of physics and ML to produce a well-adjusted prediction from the HPIML model. Specifically, we attach an Epistemic Neural Network to a pre-trained HPIML model to estimate its epistemic uncertainty in closed form, and this uncertainty then drives the mechanism that determines the relative contribution of the physics and ML terms to the HPIML model's overall prediction. We prove that this mechanism converges to the correct trade-off as data and capacity grow, with a matching guarantee that its uncertainty estimate yields valid prediction sets even out-of-distribution. We further embed EPIC-PIML in a model predictive control framework, enabling closed-loop robotic control. We demonstrate our proposed method across two robotic systems at different scales: a quadrotor and an autonomous racing car. Across these experiments, the proposed model outperforms four baselines in system modeling and control performance.