• Corpus ID: 244896285

Fast $L^2$ optimal mass transport via reduced basis methods for the Monge-Amp$\grave{\rm e}$re equation

@inproceedings{Hou2021FastO,
  title={Fast \$L^2\$ optimal mass transport via reduced basis methods for the Monge-Amp\$\grave\{\rm e\}\$re equation},
  author={Shi-Cheng Hou and Yanlai Chen and Yinhua Xia},
  year={2021}
}
Repeatedly solving the parameterized optimal mass transport (pOMT) problem is a frequent task in applications such as image registration and adaptive grid generation. It is thus critical to develop a highly efficient reduced solver that is equally accurate as the full order model. In this paper, we propose such a machine learning-like method for pOMT by adapting a new reduced basis (RB) technique specifically designed for nonlinear equations, the reduced residual reduced over-collocation (R2… 

References

SHOWING 1-10 OF 52 REFERENCES

A Numerical Method for the Elliptic Monge-Ampère Equation with Transport Boundary Conditions

TLDR
This paper proposes a method for solving the transport problem by iteratively solving a Monge-Amp\`ere equation with Neumann boundary conditions and extends an earlier discretization of the equation to allow for right-hand sides that depend on gradients of the solution.

L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations

TLDR
This paper augment and extend the EIM approach as a direct solver, as opposed to an assistant, for solving nonlinear pPDEs on the reduced level, and the resulting method, called Reduced Over-Collocation method (ROC), is stable and capable of avoiding the efficiency degradation inherent to a traditional application of EIM.

Mixed Finite Element Methods for the Fully Nonlinear Monge-Ampère Equation Based on the Vanishing Moment Method

TLDR
A family of Hermann-Miyoshi-type mixed finite element methods for approximating the solution of the regularized fourth-order problem, which computes simultaneously $u^\varepsilon$ and the moment tensor $\sigma^ \varePSilon:=D^2u^⩽𝕂𝕽$, is developed.

Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge-Ampère Equation in Dimensions Two and Higher

TLDR
This article builds a wide stencil finite difference discretization for the Monge-Ampere equation and proves convergence of Newton's method and provides a systematic method to determine a starting point for the Newton iteration.

Optimal mass transport for higher dimensional adaptive grid generation

Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap

TLDR
This method provides an efficient, robust and accurate approach for multi-scale non-rigid point cloud registration.

An Efficient Numerical Method for the Solution of the L2 Optimal Mass Transfer Problem

TLDR
A new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping is presented, employing a direct variational method.

Optimal Mass Transport for Registration and Warping

TLDR
This paper presents a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport, and shows how this approach leads to practical algorithms, and demonstrates the method with a number of examples, including those from the medical field.
...