Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Recent developments in numerical methods for fully nonlinear second order partial differential equations
This article surveys the recent developments in computational methods for second order
fully nonlinear partial differential equations (PDEs), a relatively new subarea within …
fully nonlinear partial differential equations (PDEs), a relatively new subarea within …
Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion
Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function
is known to suffer from cycle-skip** issues that increase the risk of computing a local …
is known to suffer from cycle-skip** issues that increase the risk of computing a local …
Application of the Wasserstein metric to seismic signals
Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We
propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology …
propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology …
Numerical solution of the optimal transportation problem using the Monge–Ampère equation
A numerical method for the solution of the elliptic Monge–Ampère Partial Differential
Equation, with boundary conditions corresponding to the Optimal Transportation (OT) …
Equation, with boundary conditions corresponding to the Optimal Transportation (OT) …
A least-squares method for optimal transport using the Monge--Ampère equation
In this article we introduce a novel numerical method to solve the problem of optimal
transport and the related elliptic Monge--Ampère equation. It is one of the few numerical …
transport and the related elliptic Monge--Ampère equation. It is one of the few numerical …
Optimal transport on discrete domains
J Solomon - AMS Short Course on Discrete Differential Geometry, 2018 - ams.org
Many tools from discrete differential geometry (DDG) were inspired by practical
considerations in areas like computer graphics and vision. Disciplines like these require fine …
considerations in areas like computer graphics and vision. Disciplines like these require fine …
Convergent filtered schemes for the Monge--Ampère partial differential equation
The theory of viscosity solutions has been effective for representing and approximating weak
solutions to fully nonlinear partial differential equations such as the elliptic Monge--Ampère …
solutions to fully nonlinear partial differential equations such as the elliptic Monge--Ampère …
A numerical method for the elliptic Monge--Ampère equation with transport boundary conditions
BD Froese - SIAM Journal on Scientific Computing, 2012 - SIAM
The problem of optimal mass transport arises in numerous applications, including image
registration, mesh generation, reflector design, and astrophysics. One approach to solving …
registration, mesh generation, reflector design, and astrophysics. One approach to solving …
Fast Sinkhorn I: An O (N) algorithm for the Wasserstein-1 metric
The Wasserstein metric is broadly used in optimal transport for comparing two probabilistic
distributions, with successful applications in various fields such as machine learning, signal …
distributions, with successful applications in various fields such as machine learning, signal …