scholarly journals Detecting changes in forced climate attractors with Wasserstein distance

2017 ◽  
Vol 24 (3) ◽  
pp. 393-405 ◽  
Author(s):  
Yoann Robin ◽  
Pascal Yiou ◽  
Philippe Naveau
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Warming Trend ◽  
Wasserstein Distance ◽  
Mean Values ◽  
External Forcings ◽  
Attractor Dynamics ◽  
Important Challenge ◽  
Natural Building ◽  
Optimal Transport Theory

Abstract. The climate system can been described by a dynamical system and its associated attractor. The dynamics of this attractor depends on the external forcings that influence the climate. Such forcings can affect the mean values or variances, but regions of the attractor that are seldom visited can also be affected. It is an important challenge to measure how the climate attractor responds to different forcings. Currently, the Euclidean distance or similar measures like the Mahalanobis distance have been favored to measure discrepancies between two climatic situations. Those distances do not have a natural building mechanism to take into account the attractor dynamics. In this paper, we argue that a Wasserstein distance, stemming from optimal transport theory, offers an efficient and practical way to discriminate between dynamical systems. After treating a toy example, we explore how the Wasserstein distance can be applied and interpreted to detect non-autonomous dynamics from a Lorenz system driven by seasonal cycles and a warming trend.

scholarly journals Detecting Changes in Forced Climate Attractors with Wasserstein Distance

2017 ◽  
Author(s):  
Yoann Robin ◽  
Pascal Yiou ◽  
Philippe Naveau
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Warming Trend ◽  
Wasserstein Distance ◽  
Mean Values ◽  
External Forcings ◽  
Attractor Dynamics ◽  
Important Challenge ◽  
Natural Building ◽  
Optimal Transport Theory

Abstract. The climate system can been described by a dynamical system and its associated attractor. The dynamics of this attractor depends on the external forcings that influence the climate. Such forcings can affect the mean values or variances, but regions of the attractor that are seldom visited can also be affected. It is an important challenge to measure how the climate attractor responds to different forcings. Currently, the Euclidean distance or similar measures like the Mahalanobis distance have been favoured to measure discrepancies between two climatic situations. Those distances do not have a natural building mechanism to take into account the attractor dynamics. In this paper, we argue that a Wasserstein distance, stemming from optimal transport theory, offers an efficient and practical way to discriminate between dynamical systems. After treating a toy example, we explore how the Wasserstein distance can be applied and interpreted to detect non-autonomous dynamics from a Lorenz system driven by seasonal cycles and a warming trend.

scholarly journals Optimal transport for variational data assimilation

2018 ◽  
Vol 25 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Nelson Feyeux ◽  
Arthur Vidard ◽  
Maëlle Nodet
Keyword(s):  
Data Assimilation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Wasserstein Distance ◽  
Variational Data Assimilation ◽  
Water Model ◽  
Position Errors ◽  
Optimal Transport Theory ◽  
The Cost ◽  
Model Trajectory

Abstract. Usually data assimilation methods evaluate observation-model misfits using weighted L2 distances. However, it is not well suited when observed features are present in the model with position error. In this context, the Wasserstein distance stemming from optimal transport theory is more relevant.This paper proposes the adaptation of variational data assimilation for the use of such a measure. It provides a short introduction of optimal transport theory and discusses the importance of a proper choice of scalar product to compute the cost function gradient. It also extends the discussion to the way the descent is performed within the minimization process.These algorithmic changes are tested on a nonlinear shallow-water model, leading to the conclusion that optimal transport-based data assimilation seems to be promising to capture position errors in the model trajectory.

scholarly journals Unsupervised collaborative learning based on Optimal Transport theory

2021 ◽  
Vol 30 (1) ◽  
pp. 698-719
Author(s):  
Fatima-Ezzahraa Ben-Bouazza ◽  
Younès Bennani ◽  
Guénaël Cabanes ◽  
Abdelfettah Touzani
Keyword(s):  
Collaborative Learning ◽  
Transport Theory ◽  
Optimal Transport ◽  
Wasserstein Distance ◽  
Data Sets ◽  
Multiple Data ◽  
Novel Approach ◽  
Multiple Data Sets ◽  
Optimal Transport Theory ◽  
The Right

Abstract Collaborative learning has recently achieved very significant results. It still suffers, however, from several issues, including the type of information that needs to be exchanged, the criteria for stopping and how to choose the right collaborators. We aim in this paper to improve the quality of the collaboration and to resolve these issues via a novel approach inspired by Optimal Transport theory. More specifically, the objective function for the exchange of information is based on the Wasserstein distance, with a bidirectional transport of information between collaborators. This formulation allows to learns a stopping criterion and provide a criterion to choose the best collaborators. Extensive experiments are conducted on multiple data-sets to evaluate the proposed approach.

scholarly journals Optimal Transport for Variational Data Assimilation

2017 ◽  
Author(s):  
Nelson Feyeux ◽  
Arthur Vidard ◽  
Maëlle Nodet
Keyword(s):  
Data Assimilation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Wasserstein Distance ◽  
Variational Data Assimilation ◽  
Initial Condition ◽  
Geometrical Properties ◽  
Euclidean Distances ◽  
Optimal Transport Theory ◽  
The Impact

Abstract. Variational data assimilation methods are designed to estimate an unknown initial condition of a model using observations. To do so, one needs to compare model outputs and observations. This is generally performed using Euclidean distances. This paper investigates another distance choice: the Wasserstein distance, stemming from optimal transport theory. We develop a variational data assimilation method using this distance. We investigate the impact of the scalar product, the 5 gradient choice as well as the minimization algorithm. With appropriate choices, we show successful results on preliminary experiments. Optimal-transport-based optimization seems to be promising to preserve the geometrical properties of the estimated initial condition.

scholarly journals Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory

2021 ◽  
Vol 11 (9) ◽  
pp. 4070
Author(s):  
Rabiul Hasan Kabir ◽  
Kooktae Lee
Keyword(s):  
Detection Rate ◽  
Transport Theory ◽  
Optimal Transport ◽  
Position Estimation ◽  
Wildlife Monitoring ◽  
High Detection Rate ◽  
Monitoring Strategies ◽  
Spatio Temporal ◽  
Optimal Transport Theory ◽  
Multi Uav

This paper addresses a wildlife monitoring problem using a team of unmanned aerial vehicles (UAVs) with the optimal transport theory. The state-of-the-art technology using UAVs has been an increasingly popular tool to monitor wildlife compared to the traditional methods such as satellite imagery-based sensing or GPS trackers. However, there still exist unsolved problems as to how the UAVs need to cover a spacious domain to detect animals as many as possible. In this paper, we propose the optimal transport-based wildlife monitoring strategy for a multi-UAV system, to prioritize monitoring areas while incorporating complementary information such as GPS trackers and satellite-based sensing. Through the proposed scheme, the UAVs can explore the large-size domain effectively and collaboratively with a given priority. The time-varying nature of wildlife due to their movements is modeled as a stochastic process, which is included in the proposed work to reflect the spatio-temporal evolution of their position estimation. In this way, the proposed monitoring plan can lead to wildlife monitoring with a high detection rate. Various simulation results including statistical data are provided to validate the proposed work. In all different simulations, it is shown that the proposed scheme significantly outperforms other UAV-based wildlife monitoring strategies in terms of the target detection rate up to 3.6 times.

Schrödinger dynamics and optimal transport of measures

2021 ◽  
pp. 2150016
Author(s):  
Lorenzo Zanelli
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Time Dependent ◽  
Probability Measures ◽  
Flat Torus ◽  
Optimal Transport Theory

In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrödinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.

Multi-projection of unequal dimension optimal transport theory for Generative Adversary Networks

2020 ◽  
Vol 128 ◽  
pp. 107-125
Author(s):  
Judy Yangjun Lin ◽  
Shaoyan Guo ◽  
Longhan Xie ◽  
Gu Xu
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Optimal Transport Theory
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