Speaker
Description
Nowadays, autoencoders play a major role in reduced order modeling as they allow to represent the solution manifold of complex parameterized PDEs using few latent coordinates, thanks to their nonlinear nature. Indeed, their expressive power enables them to overcome the limitations of linear reduction methods, such as proper orthogonal decomposition (POD), which cannot break the so-called linear Kolmogorov barrier.
However, unlike linear reduction methods, generic autoencoders are not usually endowed with a rich mathematical structure providing a solid theoretical framework for their analysis and interpretation. In this respect, within this talk, we propose to study a class of constrained autoencoders which we refer to as deep symmetric autoencoders, which bridge the expressive power of neural networks and the well-established structure of linear methods. In doing so, we provide error estimates and, building upon them, we derive an initialization strategy. Our theoretical apparatus is then complemented by a set of numerical experiments providing practical insights on deep symmetric autoencoders.
[1] Brivio, S., & Franco, N. R. (2025). Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective. arXiv preprint arXiv:2506.11641.
[2] Otto, S. E., Macchio, G. R., & Rowley, C. W. (2023). Learning nonlinear projections for reduced-order modeling of dynamical systems using constrained autoencoders. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(11).