On the Identifiability of Hybrid Deep Generative Models: Meta-Learning as a Solution

Area of Science:

• Artificial Intelligence
• Machine Learning
• Physics-Informed Deep Learning

Background:

• Deep generative models (DGMs) are increasingly integrated with physics-based mathematical expressions to create hybrid-DGMs.
• The identifiability of these hybrid-DGMs, crucial for reliable parameter inference, remains theoretically unestablished.
• Existing DGMs face identifiability challenges, raising questions about their hybrid counterparts.

Purpose of the Study:

• To theoretically probe the identifiability of hybrid deep generative models (hybrid-DGMs).
• To investigate how general DGM un-identifiability theory applies to hybrid-DGMs.
• To propose and validate a novel approach for constructing identifiable hybrid-DGMs.

Main Methods:

• Theoretical analysis of identifiability in hybrid-DGMs.
• Application of meta-learning strategies to enhance hybrid-DGM identifiability.
• Empirical validation using synthetic and real-world datasets.

Main Results:

• Existing hybrid-DGMs with unconditional priors demonstrate significant un-identifiability.
• Meta-learning formulations of hybrid-DGMs exhibit strong identifiability.
• Empirical evidence supports the theoretical findings on identifiability.

Conclusions:

• Hybrid-DGMs face inherent identifiability challenges, particularly with unconditional priors.
• Meta-learning provides a robust framework for developing theoretically-proven identifiable hybrid-DGMs.
• The proposed meta-formulations offer a promising direction for reliable physics-informed deep learning.