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Found 8 papers, 3 papers with code
Computing distances and means on manifolds with a metric-constrained Eikonal approach
In this paper, we introduce the metric-constrained Eikonal solver to obtain continuous, differentiable representations of distance functions on manifolds.
Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations
The task is to uncover from the biased data the true state, which is the solution of the PDE.
Manifold-augmented Eikonal Equations: Geodesic Distances and Flows on Differentiable Manifolds
Manifolds discovered by machine learning models provide a compact representation of the underlying data.
Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach
We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations.
Uncovering solutions from data corrupted by systematic errors: A physics-constrained convolutional neural network approach
We show that the solutions inferred from the PC-CNN are physical, in contrast to the data corrupted by systematic errors that does not fulfil the governing equations.
Short and Straight: Geodesics on Differentiable Manifolds
Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order modelling, statistical inference, and interpolation.
Physics-Informed CNNs for Super-Resolution of Sparse Observations on Dynamical Systems
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 settings.
Physics-Informed Convolutional Neural Networks for Corruption Removal on Dynamical Systems
Measurements on dynamical systems, experimental or otherwise, are often subjected to inaccuracies capable of introducing corruption; removal of which is a problem of fundamental importance in the physical sciences.
