4 citations · 7 across the 9 of their papers we have counts for
9 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…
Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach
Daniel Kelshaw, Luca Magri
We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial diff…
Uncovering solutions from data corrupted by systematic errors: A physics-constrained convolutional neural network approach
Daniel Kelshaw, Luca Magri
Information on natural phenomena and engineering systems is typically contained in data. Data can be corrupted by systematic errors in models and experiments. In this paper, we pro…
Short and Straight: Geodesics 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…
Physics-Informed CNNs for Super-Resolution of Sparse Observations on Dynamical Systems
Daniel Kelshaw, Georgios Rigas, Luca Magri
In the absence of high-resolution samples, super-resolution of sparse observations on dynamical systems is a challenging problem with wide-reaching applications in experimental set…
Physics-Informed Convolutional Neural Networks for Corruption Removal on Dynamical Systems
Daniel Kelshaw, Luca Magri
Measurements on dynamical systems, experimental or otherwise, are often subjected to inaccuracies capable of introducing corruption; removal of which is a problem of fundamental im…