HyPer-EP: Meta-Learning Hybrid Personalized Models for Cardiac Electrophysiology

Personalized virtual heart models have demonstrated increasing potential for clinical use, although the estimation of their parameters given patient-specific data remain a challenge. Traditional physics-based modeling approaches are computationally costly and often neglect the inherent structural errors in these models due to model simplifications and assumptions. Modern deep learning approaches, on the other hand, rely heavily on data supervision and lacks interpretability. In this paper, we present a novel hybrid modeling framework to describe a personalized cardiac digital twin as a combination of a physics-based known expression augmented by neural network modeling of its unknown gap to reality. We then present a novel meta-learning framework to enable the separate identification of both the physics-based and neural components in the hybrid model. We demonstrate the feasibility and generality of this hybrid modeling framework with two examples of instantiations and their proof-of-concept in synthetic experiments.

Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Framework

Modern applications increasingly require unsupervised learning of latent dynamics from high-dimensional time-series. This presents a significant challenge of identifiability: many abstract latent representations may reconstruct observations, yet do they guarantee an adequate identification of the governing dynamics? This paper investigates this challenge from two angles: the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification. We combine these two strategies in a novel framework for unsupervised meta-learning of hybrid latent dynamics (Meta-HyLaD) with: 1) a latent dynamic function that hybridize known mathematical expressions of prior physics with neural functions describing its unknown errors, and 2) a meta-learning formulation to learn to separately identify both components of the hybrid dynamics. Through extensive experiments on five physics and one biomedical systems, we provide strong evidence for the benefits of Meta-HyLaD to integrate rich prior knowledge while identifying their gap to observed data.