arXiv Machine Learning
Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systems
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arXiv Machine Learning
Sep 1
Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction
arXiv:2608.29867v1 Announce Type: new Abstract: Autoencoders are widely used for nonlinear dimensionality reduction and manifold learning. While most common implementations rely on both nonlinear enc...
arXiv Machine Learning
Sep 1
Autoencoders in Function Space
The paper introduces function‑space versions of autoencoders (FAE) and variational autoencoders (FVAE), analysing their theoretical properties and practical deployment. It highlights that the FVAE objective is well‑defined only when the data distribution aligns with the generative model, a restriction often met when data come from stochastic differential equations. In contrast, the FAE objective remains well‑defined in many cases where FVAE fails, and both can be paired with neural operator architectures to enable tasks such as inpainting, super‑resolution, and generative modelling of scientific data.
arXiv Machine Learning
Jun 19
Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
arXiv Machine Learning
Aug 13
Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv Machine Learning
Jul 1
Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
arXiv:2605. 27756v2 Announce Type: replace-cross Abstract: Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span.
arXiv Machine Learning
Jul 2
Geometry-Preserving Neural Architectures on Manifolds with Boundary
arXiv:2602. 03082v2 Announce Type: replace Abstract: A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs.