scholarly journals Subspace Detours Meet Gromov–Wasserstein

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 366
Author(s):  
Clément Bonet ◽  
Titouan Vayer ◽  
Nicolas Courty ◽  
François Septier ◽  
Lucas Drumetz
Keyword(s):  
Shape Matching ◽  
Optimal Transport ◽  
Matching Problem ◽  
Optimal Plan ◽  
Specific Cost ◽  
First Finding ◽  
Whole Space ◽  
Transport Plan ◽  
Specific Geometry

In the context of optimal transport (OT) methods, the subspace detour approach was recently proposed by Muzellec and Cuturi. It consists of first finding an optimal plan between the measures projected on a wisely chosen subspace and then completing it in a nearly optimal transport plan on the whole space. The contribution of this paper is to extend this category of methods to the Gromov–Wasserstein problem, which is a particular type of OT distance involving the specific geometry of each distribution. After deriving the associated formalism and properties, we give an experimental illustration on a shape matching problem. We also discuss a specific cost for which we can show connections with the Knothe–Rosenblatt rearrangement.

scholarly journals Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs

2015 ◽  
Vol 67 (2) ◽  
pp. 350-368 ◽  
Author(s):  
Maria Colombo ◽  
Luigi De Pascale ◽  
Simone Di Marino
Keyword(s):  
Density Functional ◽  
Optimal Transport ◽  
Qualitative Properties ◽  
Optimal Plan ◽  
Functional Theory ◽  
One Dimensional ◽  
Transport Plan ◽  
Optimal Transportation Problem ◽  
Transport Maps ◽  
Multimarginal Optimal Transportation

AbstractWe study a multimarginal optimal transportation problem in one dimension. For a symmetric, repulsive cost function, we show that, given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose optimal transport problem is strictly related to the strong interaction limit of Density Functional Theory. In this last setting, our result justifies some qualitative properties of the potentials observed in numerical experiments.

scholarly journals Guiding the One-to-One Mapping in CycleGAN via Optimal Transport

2019 ◽  
Vol 33 ◽  
pp. 4432-4439 ◽  
Author(s):  
Guansong Lu ◽  
Zhiming Zhou ◽  
Yuxuan Song ◽  
Kan Ren ◽  
Yong Yu
Keyword(s):  
Cost Function ◽  
Feasible Solution ◽  
Optimal Transport ◽  
Solution Space ◽  
Specific Cost ◽  
Data Translation ◽  
One To One ◽  
The One

CycleGAN is capable of learning a one-to-one mapping between two data distributions without paired examples, achieving the task of unsupervised data translation. However, there is no theoretical guarantee on the property of the learned one-to-one mapping in CycleGAN. In this paper, we experimentally find that, under some circumstances, the one-to-one mapping learned by CycleGAN is just a random one within the large feasible solution space. Based on this observation, we explore to add extra constraints such that the one-to-one mapping is controllable and satisfies more properties related to specific tasks. We propose to solve an optimal transport mapping restrained by a task-specific cost function that reflects the desired properties, and use the barycenters of optimal transport mapping to serve as references for CycleGAN. Our experiments indicate that the proposed algorithm is capable of learning a one-to-one mapping with the desired properties.

A theoretical study of surface‐to‐borehole electromagnetic logging in cased holes

Geophysics ◽  
1989 ◽  
Vol 54 (1) ◽  
pp. 90-99 ◽  
Author(s):  
A. M. Augustin ◽  
W. D. Kennedy ◽  
H. F. Morrison ◽  
K. H. Lee
Keyword(s):  
Theoretical Study ◽  
Enhanced Recovery ◽  
Field Studies ◽  
Drill Hole ◽  
Repeated Measurements ◽  
Low Frequencies ◽  
First Finding ◽  
Horizontal Stratification ◽  
Whole Space ◽  
Logging Tool

A new electromagnetic logging method, in which the source is a horizontal loop coaxial with a cased drill hole and the secondary axial fields are measured at depth within the casing, has been analyzed. The analysis, which is for an idealized model of an infinite pipe in a conductive whole space, has shown that the casing and formation are uncoupled at the low frequencies that would be used in field studies. The field inside the casing may be found by first finding the field in the formation and then using this field as an incident field for the pipe alone. This result permits the formation response to be recovered from the measured field in the borehole by applying a correction for the known properties of the casing. If the casing response cannot be accurately predicted, a separate logging tool employing a higher frequency transmitter could be used to determine the required casing parameters in the vicinity of the receiver. This logging technique shows excellent sensitivity to changes in formation conductivity, but it is not yet known how well horizontal stratification can be resolved. One of its most promising applications will be in monitoring, through repeated measurements, changes in formation conductivity during production or enhanced recovery operations.

scholarly journals Targeted Adversarial Learning Optimized Sampling

2019 ◽  
Author(s):  
Jun Zhang ◽  
Yi Isaac Yang ◽  
Frank Noé
Keyword(s):  
Deep Learning ◽  
Optimal Transport ◽  
Dimensional Space ◽  
Optimization Techniques ◽  
Free Energy Barrier ◽  
Adversarial Learning ◽  
Bias Potential ◽  
Novel Approach ◽  
Transport Plan ◽  
Sampling Problem

<div>Boosting transitions of rare events is critical to modern-day simulations of complex dynamic systems. We present a novel approach to modify the potential energy surface in order to drive the system to a user-defined target distribution where the free energy barrier is lowered. The new approach, called targeted adversarial learning optimized sampling (TALOS), cross-fertilizes statistical mechanics and deep learning. By casting the enhanced sampling problem as a competing game between a real sampling engine and a virtual discriminator, TALOS enables unsupervised construction of bias potential on an arbitrary dimensional space and seeks for an optimal transport plan that transforms the system into target. Through multiple experiments we show that on-the-fly training of TALOS benefits from the state-of-art optimization techniques in deep learning, thus is efficient, robust and interpretable. TALOS can also simultaneously learn to extract good reaction coordinate from a high-dimensional space where bias potential is being constructed. Additionally, TALOS is shown to be closely related to reinforcement learning, giving rise to a new framework of manipulating Hamiltonian in order to fulfill user-specified tasks via deep learning.</div>

Targeted Adversarial Learning Optimized Sampling

2019 ◽  
Author(s):  
Jun Zhang ◽  
Yi Isaac Yang ◽  
Frank Noé
Keyword(s):  
Deep Learning ◽  
Optimal Transport ◽  
Dimensional Space ◽  
Optimization Techniques ◽  
Free Energy Barrier ◽  
Adversarial Learning ◽  
New Approach ◽  
Novel Approach ◽  
Transport Plan ◽  
Sampling Problem

<div>Abstract Boosting transitions of rare events is critical to modern-day simulations of complex dynamic systems. We present a novel approach to modify the potential energy surface in order to drive the system to a user-defined target distribution where the free energy barrier is lowered. The new approach, called targeted adversarial learning optimized sampling (TALOS) combines the strengths of statistical mechanics and deep learning. By casting the enhanced sampling problem as a competing game between a real sampling engine and a virtual discriminator, TALOS enables unsupervised construction of bias potential on an arbitrary dimensional space and seeks for an optimal transport plan that transforms the system into target. Through multiple experiments we show that on-the-fly training of TALOS benefits from the state-of-art optimization techniques in deep learning, thus is efficient, robust and interpretable. Additionally, TALOS is closely connected to actor-critic reinforcement learning, giving rise to a new approach to manipulating the Hamiltonian systems via deep learning.</div>

scholarly journals An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains

2020 ◽  
Vol 12 (2) ◽  
pp. 687 ◽  
Author(s):  
Svetla Stoilova
Keyword(s):  
Objective Function ◽  
Optimal Transport ◽  
Hybrid Methods ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Transport Plan ◽  
The Impact ◽  
Constraint Method

The development of the transport plan must take into account various criteria impacting the transport process. The main objective of the study is to propose an integrated approach to determine the transport plan of passenger trains. The methodology consists of five steps. In the first step, the criteria for optimization of the transport plan were defined. In the second step, variants of the transport plan were formulated. In the third step, the weights of the criteria are determined by applying the step-wise weight assessment ratio analysis method (SWARA) multi-criteria method. The multi-objective optimization was conducted in the fourth step. The following multi-objective optimization approaches were used and compared: weighted sum method (WSM), compromise programming method (CP), and the epsilon–constraint method (EC). The study proposes a modified epsilon–constraint method (MEC) by applying normalization of each objective function according to the maximal value of the solution by individual optimization for each objective function, and hybrid methods: hybrid WSM and EC, hybrid WSM and MEC, hybrid CP and EC, and Hybrid CP and MEC. The impact of the variation of passenger flows on the choice of an optimal transport plan was studied in the fifth step. The Laplace’s criterion, Hurwitz’s criterion, and Savage’s criterion were applied to come to a decision. The approbation of the methodology was demonstrated through the case study of Bulgaria’s railway network. Suitable variant of transport plan is proposed.

scholarly journals Solving the Cross-Subject Parcel Matching Problem Using Optimal Transport

2018 ◽  
pp. 836-843 ◽  
Author(s):  
Guillermo Gallardo ◽  
Nathalie T. H. Gayraud ◽  
Rachid Deriche ◽  
Maureen Clerc ◽  
Samuel Deslauriers-Gauthier ◽  
...  
Keyword(s):  
Optimal Transport ◽  
Matching Problem ◽  
The Cross

Targeted Adversarial Learning Optimized Sampling

2019 ◽  
Author(s):  
Jun Zhang ◽  
Yi Isaac Yang ◽  
Frank Noé
Keyword(s):  
Deep Learning ◽  
Optimal Transport ◽  
Dimensional Space ◽  
Optimization Techniques ◽  
Free Energy Barrier ◽  
Adversarial Learning ◽  
New Approach ◽  
Novel Approach ◽  
Transport Plan ◽  
Sampling Problem

<div>Abstract Boosting transitions of rare events is critical to modern-day simulations of complex dynamic systems. We present a novel approach to modify the potential energy surface in order to drive the system to a user-defined target distribution where the free energy barrier is lowered. The new approach, called targeted adversarial learning optimized sampling (TALOS) combines the strengths of statistical mechanics and deep learning. By casting the enhanced sampling problem as a competing game between a real sampling engine and a virtual discriminator, TALOS enables unsupervised construction of bias potential on an arbitrary dimensional space and seeks for an optimal transport plan that transforms the system into target. Through multiple experiments we show that on-the-fly training of TALOS benefits from the state-of-art optimization techniques in deep learning, thus is efficient, robust and interpretable. Additionally, TALOS is closely connected to actor-critic reinforcement learning, giving rise to a new approach to manipulating the Hamiltonian systems via deep learning.</div>

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