Abstract

The interest in leveraging physics-based inductive bias in deep learning has resulted in recent developments of hybrid deep generative models (hybrid-DGMs) that integrates known physics-based mathematical expressions in neural generative models. The identification of these hybrid-DGMs often involves the inference of the parameters of the physics-based component along with its neural component. The identfiability of these hybrid-DGM however has not yet been theoretically probed or established. While the (un)identfiability of DGMs has been investigated,  existing solutions often do not apply here as they require observed auxiliary labels about the underlying hybrid models. In this talk, we probe the theoretical identfiability of hybrid-DGMs, present meta-learning as a novel solution to construct identifiable hybrid-DGMs, and examine empirical evidence for on synthetic and real-data benchmarks. We further discuss the possibility to extend the identification of these hybrid-DGMs to unsupervised settings using high-dimensional observation data (e.g., image sequences), and its proof-of-concept application to digital twins for cardiac electrophysiology.