4 papers
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…
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-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…
Manifold-augmented Eikonal Equations: Geodesic Distances and Flows on Differentiable Manifolds
Daniel Kelshaw, Luca Magri
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and pr…