Results 41 to 50 of about 24,182 (212)
Metrics for matrix-valued measures via test functions
, 2014 It is perhaps not widely recognized that certain common notions of distance between probability measures have an alternative dual interpretation which compares corresponding functionals against suitable families of test functions.
Georgiou, Tryphon T., Ning, Lipeng
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A Framework for Wasserstein-1-Type Metrics
, 2017 We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the Wasserstein-1 metric, and it includes several previous approaches from the literature as special cases.
Schmitzer, Bernhard, Wirth, Benedikt
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The Wasserstein metric in Factor Analysis [PDF]
, 2013 We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances –one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are sought between variables corrupted by independent measurement noise.
Lipeng Ning, Tryphon Georgiou
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The quadratic Wasserstein metric for earthquake location [PDF]
Journal of Computational Physics, 2018 25 pages, 13 ...
Chen, Jing +3 more
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Stein's method and Poisson process approximation for a class of Wasserstein metrics
, 2009 Based on Stein's method, we derive upper bounds for Poisson process approximation in the $L_1$-Wasserstein metric $d_2^{(p)}$, which is based on a slightly adapted $L_p$-Wasserstein metric between point measures.
Schuhmacher, Dominic
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Electromagnetic Full Waveform Inversion Based on Quadratic Wasserstein Metric
IEEE Transactions on Antennas and Propagation, 2022 Abstract: Electromagnetic full waveform inversion (FWI) is a high-resolution method to reveal the distribution of dielectric parameters of the medium. Traditionally, the electromagnetic FWI is usually performed using the L-2 norm misfit function, which suffers severely local minimum problems since the L-2 norm misfit function is nonconvex in the model ...
Jian Deng +5 more
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Advanced Intelligent Discovery, EarlyView.We investigate MACE‐MP‐0 and M3GNet, two general‐purpose machine learning potentials, in materials discovery and find that both generally yield reliable predictions. At the same time, both potentials show a bias towards overstabilizing high energy metastable states. We deduce a metric to quantify when these potentials are safe to use.
Konstantin S. Jakob +2 more
wiley +1 more source
Advanced Intelligent Discovery, EarlyView.This work presents a novel generative artificial intelligence (AI) framework for inverse alloy design through operations (optimization and diffusion) within learned compact latent space from variational autoencoder (VAE). The proposed work addresses challenges of limited data, nonuniqueness solutions, and high‐dimensional spaces.
Mohammad Abu‐Mualla +4 more
wiley +1 more source
Stability of the global attractor under Markov-Wasserstein noise [PDF]
, 2011 We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense.
Kell, Martin
core
Optimal Transport for Seismic Full Waveform Inversion
, 2016 Full waveform inversion is a successful procedure for determining properties of the earth from surface measurements in seismology. This inverse problem is solved by a PDE constrained optimization where unknown coefficients in a computed wavefield are ...
Engquist, Bjorn +2 more
core +1 more source