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cs.LG2024
Proper Latent Decomposition
Daniel Kelshaw, Luca Magri
In this paper, we introduce the proper latent decomposition (PLD) as a generalization of the proper orthogonal decomposition (POD) on manifolds. PLD is a nonlinear reduced-order mo…
cs.LG2024
Computing distances and means on manifolds with a metric-constrained Eikonal approach
Daniel Kelshaw, Luca Magri
Computing distances on Riemannian manifolds is a challenging problem with numerous applications, from physics, through statistics, to machine learning. In this paper, we introduce…
physics.flu-dyn2024
Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations
Daniel Kelshaw, Luca Magri
We propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary…