Speakers: Nicola Rares Franco, Politecnico di Milano

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy, room 138.

Deep autoencoders have become a central tool in scientific machine learning, especially in model order reduction and data-driven surrogate modeling for PDEs. Although previous work has investigated their theoretical foundations—from topological constraints on latent dimensions to expressivity results and sample-complexity considerations—many core questions remain open, particularly when compared to the classical and well-understood linear setting. In this talk, we will focus on recent progress concerning symmetric autoencoders (SAEs), a class of architectures whose structure enables a notably transparent theoretical analysis. We will introduce several families of symmetric designs and discuss their strengths and limitations. In particular, we will see that SAEs with orthonormality constraints admit a reconstruction-error characterization directly linked to the Eckart–Young–Schmidt theorem, opening the door to new interesting connections between nonlinear and classical linear reduction techniques. As we will discuss, these insights naturally lead to a novel initialization strategy tailored to SAE architectures, which is based on an iterated application of the Singular Value Decomposition. We refer to this as EYS initialization, in honor of the Eckart–Young–Schmidt theorem. We will conclude with numerical experiments that validate our findings and underscore the importance of model design and initialization.

Zoom link:
https://sissa-it.zoom.us/j/85158091056?pwd=b93RT9aRgakgRYutt3tLPSluUwTrCm.1