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Updated: Jun 29, 2026

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

Yubo Ye1, Maryam Toloubidokhti2, Sumeet Vadhavkar2

  • 1Zhejiang University.

Advances in Neural Information Processing Systems
|June 26, 2026
PubMed
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This study investigates hybrid deep generative models (hybrid-DGMs) that combine physics and neural networks. Meta-learning offers a novel solution to ensure the identifiability of these complex models.

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.

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  • 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.