4 citations · 7 across the 9 of their papers we have counts for
4 papers · 1 filter
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…