arXiv:2410.10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework such that manifold geometries, subject to our geometric flow, embedded in Euclidean space are learned in the intermediary latent space developed by encoders and decoders. By tailoring the geometric flow in which the latent space evolves, we induce latent geometric properties of our choosing, which are refl
This research emerges as advanced AI systems increasingly tackle complex, high-dimensional data, pushing the boundaries of traditional VAE architectures into geometric and manifold learning.
Sophisticated latent space modeling with geometric flows allows for more robust and interpretable representations of physical systems and data, critical for scientific AI and real-world applications.
The development of VAE-DLM introduces a novel method for integrating geometric dynamics into variational autoencoders, potentially leading to more accurate and generalizable models for complex systems.
- · AI researchers
- · Scientific computing
- · Engineering design
- · Material science
- · Traditional VAE approaches for complex dynamics
- · Purely statistical latent models
Improved simulation and predictive modeling of physical phenomena using AI.
Accelerated discovery processes in fields like physics, chemistry, and materials science through better AI-driven insights.
Enhanced AI systems capable of understanding and generating complex, geometrically consistent data for new forms of engineering and design.
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Read at arXiv cs.LG