Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling (2102.13156v3)

Abstract: Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics models into deep generative models. In particular, we introduce an architecture of variational autoencoders (VAEs) in which a part of the latent space is grounded by physics. A key technical challenge is to strike a balance between the incomplete physics and trainable components such as neural networks for ensuring that the physics part is used in a meaningful manner. To this end, we propose a regularized learning method that controls the effect of the trainable components and preserves the semantics of the physics-based latent variables as intended. We not only demonstrate generative performance improvements over a set of synthetic and real-world datasets, but we also show that we learn robust models that can consistently extrapolate beyond the training distribution in a meaningful manner. Moreover, we show that we can control the generative process in an interpretable manner.

Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling

The paper by Takeishi and Kalousis introduces an advanced variational autoencoder (VAE) architecture that integrates incomplete physics models with deep generative models to improve robustness, extrapolation capabilities, and interpretability in machine learning applications. The primary focus of the research is on blending theory-driven physics models with data-driven neural networks within the latent space of VAEs. This integration is aimed at addressing challenges associated with ensuring meaningful use of the physics components, which are often overlooked or underutilized when combined with highly expressive neural networks.

Key Concepts and Technical Contribution

1. Physics-Driven Latent Space: The authors propose a design for variational autoencoders where a segment of the latent space is grounded in physics models. This grounding provides a semantic link between the latent variables and the domain-specific physical parameters.
2. Regularization Method: A novel regularized learning approach is introduced to maintain the intended semantic relationships and balance the influence between physics and neural network components. This methodology prevents dominant behavior by trainable components, thus ensuring that the physics models are utilized effectively.
3. Empirical Demonstrations: The architecture is shown to enhance generative modeling across synthetic and real-world datasets. The VAEs exhibit improved generalization, extrapolate meaningfully beyond the training data, and allow for interpretable control over the generation process.

Strong Numerical Results and Claims

• Generative Performance Improvement: The integrated model consistently outperformed conventional VAEs and physics-only models on various tasks, demonstrating superior robustness to variations outside the training distribution.
• Reduced Reconstruction Error: Quantitative assessments indicated lower reconstruction errors when compared to baselines, substantiating the unique benefits of physics integration in model architecture.
• Semantic Preservation: The proposed regularization method effectively preserved the semantics of latent variables, as evidenced by lower inference errors of physics parameters relative to baseline models.

Implications and Future Work

The integration of physics with machine learning models as presented holds substantial theoretical and practical implications. Not only does it promise advancements in interpretability and robustness, but it also sets the stage for future work in AI systems that require understanding complex physical environments and phenomena. This research may pave the way for developing hybrid models applicable in fields like physics-based simulations, weather modeling, biomechanics, and beyond.

Future explorations could involve tackling open challenges such as optimizing neural architecture search for hybrid models and consolidating numerical solver efficiency through neural network solutions. Moreover, expanding the framework to handle more complex simulations or stochastic scenarios could significantly contribute to scientific computing and machine learning disciplines.

In conclusion, the paper presents a sophisticated approach to incorporating physics in machine learning models, showcasing potential improvements in robustness, interpretability, and extrapolation capabilities of generative models.