Optimal Transport Research Articles

LPOT: Locality-Preserving Gromov-Wasserstein Discrepancy for Nonrigid Point Set Registration.

The main problems in point registration involve recovering correspondences and estimating transformations, especially in a fully unsupervised way without any feature descriptors. In this work, we propose a robust point matching method using discrete optimal transport (OT), which is a natural and useful approach for assignment tasks, to recover the underlying correspondences and improve the nonrigid registration in the presence of unknown global transformations. Specifically, we cast the registration problem as a joint estimation over local transport couplings and global transformations, observing that the local neighborhood topology structures should be preserved strongly and stably for nonrigid transformations. By solving the Gromov-Wasserstein discrepancy, a smooth assignment matrix from one point set to another can be recovered in a fully unsupervised way. Registration performance can be improved by applying an unsupervised map to guide the transformation estimate under the alternating optimization. Experimental results on several datasets reveal how the presented method is superior to the state-of-the-art methods when facing large data degradations.

Model order reduction by convex displacement interpolation

We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure introduced in [Iollo, Taddei, J. Comput. Phys., 2022] to multi-dimensional parameter domains and to datasets of several snapshots. Given a library of high-fidelity simulations, we rely on a scalar testing function and on a point set registration method to identify coherent structures of the solution field in the form of sorted point clouds. Given a new parameter value, we exploit a regression method to predict the new point cloud; then, we resort to a boundary-aware registration technique to define bijective mappings that deform the new point cloud into the point clouds of the neighboring elements of the dataset, while preserving the boundary of the domain; finally, we define the estimate as a weighted combination of modes obtained by composing the neighboring snapshots with the previously-built mappings. We present several numerical examples for compressible and incompressible, viscous and inviscid flows to demonstrate the accuracy of the method. Furthermore, we employ the nonlinear interpolation procedure to augment the dataset of simulations for linear-subspace projection-based model reduction: our data augmentation procedure is designed to reduce offline costs — which are dominated by snapshot generation — of model reduction techniques for nonlinear advection-dominated problems.

A distributionally robust optimization approach for the potassium fertilizer product transportation considering transshipment through crossdocks

Potassium fertilizer is an essential input for agricultural productivity, and plays a critical role in various plant processes, influencing water uptake, enzyme activation, and photosynthesis. The efficient delivery of potassium fertilizer products to the end-users, typically farmers and agricultural enterprises, is of utmost importance. Due to the long traveling distance between the supplier and customers, decision makers of supplier normally set up multiple crossdocks to aid in transition and storage of potassium fertilizer products. In this situation, making an optimal transportation plan as well as the inventory level of crossdocks will directly enhance the efficiency and effectiveness of long-distance transportation. In this study, we model this problem as a dynamic transportation problem with transshipment considering the uncertain time-varying customers’ demand. To characterize the demand information, we first construct an ambiguity set of customers’ demand based in limited historical data and then develop a distributionally robust optimization-based (DRO) framework to optimize the transportation plan and related inventory level of crossdocks simultaneously. We also propose a general approach to overcome the computational challenges of DRO by transforming the original DRO into a second-order cone programming based on duality theory. Additionally, we introduce linear decision rules to adjust the optimization strategy based on the new observed demand, thus lead the model to handle the dynamic information flow in real time. In case study, all involved data are collected or derived from a real potassium fertilizer company located at Western China. The results show our model reduces the cost by 18.07% compared to stochastic model (sample average approximation), indicating a significant effectiveness of our model on the improvement of delivery efficiency and cost saving in real dynamic logistic systems. Also, we conclude the managerial insight that decision-makers should develop a comprehensive strategy, including improving communication to ensure order status updates, planning rationally to evenly distribute orders, and proactively allocating resources to meet operational demands.

Techno-Economic Analysis of Clean Hydrogen Production Plants in Sicily: Comparison of Distributed and Centralized Production

This paper presents an assessment of the levelized cost of clean hydrogen produced in Sicily, a region in Southern Italy particularly rich in renewable energy and where nearly 50% of Italy’s refineries are located, making a comparison between on-site production, that is, near the end users who will use the hydrogen, and centralized production, comparing the costs obtained by employing the two types of electrolyzers already commercially available. In the study for centralized production, the scale factor method was applied on the costs of electrolyzers, and the optimal transport modes were considered based on the distance and amount of hydrogen to be transported. The results obtained indicate higher prices for hydrogen produced locally (from about 7 €/kg to 10 €/kg) and lower prices (from 2.66 €/kg to 5.80 €/kg) for hydrogen produced in centralized plants due to economies of scale and higher conversion efficiencies. How-ever, meeting the demand for clean hydrogen at minimal cost requires hydrogen distribution pipelines to transport it from centralized production sites to users, which currently do not exist in Sicily, as well as a significant amount of renewable energy ranging from 1.4 to 1.7 TWh per year to cover only 16% of refineries’ hydrogen needs.

Optimal Transport Map With Prescribed Direction Indicator for Seismic Full‐Waveform Inversion

AbstractThe quadratic Wasserstein (W2) metric has been proposed as a promising misfit function to mitigate cycle‐skipping phenomena in full‐waveform inversion. Mathematically, we demonstrate that the smoothness of the W2‐based adjoint source is two orders of magnitude higher than that based on L2‐norm, which guarantees a larger convergence radius of related inverse problems. However, the oscillatory characteristics of seismic signals and subsequent operations of transforming them into probability densities would decrease the accuracy of the optimal transport map T(t) and exacerbate the nonconvexity of the misfit function. To tackle these challenges, we propose the concept of prescribed direction indicator, which indicates the properly matching direction from predictions to observations, in order to correct inaccurate T(t). 1D synthetic examples suggest that reasonable bijection can be constructed through the proposed method. Numerical experiments demonstrate that it works well during optimization procedures, including enlarging the convergence radius of the inverse problem, improving the computational efficiency and enhancing the reliability of inversion results.

Approximate Bayesian computation for inferring Waddington landscapes fromsingle-cell data.

Single-cell technologies allow us to gain insights into cellular processes at unprecedented resolution. In stem cell and developmental biology snapshot data allow us to characterize how the transcriptional states of cells change between successive cell types. Here, we show how approximate Bayesian computation (ABC) can be employed to calibrate mathematical models against single-cell data. In our simulation study, we demonstrate the pivotal role of the adequate choice of distance measures appropriate for single-cell data. We show that for good distance measures, notably optimal transport with the Sinkhorn divergence, we can infer parameters for mathematical models from simulated single-cell data. We show that the ABC posteriors can be used (i) to characterize parameter sensitivity and identify dependencies between different parameters and(ii) to construct representations of the Waddington or epigenetic landscape, which forms a popular and interpretable representation of the developmental dynamics. In summary, these results pave the way for fitting mechanistic models of stem cell differentiation to single-cell data.

Assessing Coriolis meter performance in multicomponent carbon dioxide-rich mixtures

Accurate flow measurement plays a pivotal role in monitoring CO2 flows across the CCS value chain. This not only bolsters the overall business model of the CCS industry, but also ensures adherence to environmental legislations and regulatory requirements. Unlike other industrial process fluids, such as water, oil & natural gas, it is unclear whether current commercially available metering technologies can meet the requisite accuracy levels, specifically the ±2.5 % recommended within the EU/UK European Trading Scheme for CO2 mass transfer. Accordingly, the aim of this work was to gain a comprehensive understanding of CO2 flow measurement within the context of CCS transport conditions. Firstly, GERG-2008 equation of state was implemented on REFPROP v10 to predict the optimal transport conditions for CO2-rich mixtures and to understand the influence of non-condensable gas impurities in CCS flow operations. Then, a dedicated laboratory-scale gravimetric flow facility was designed and used to evaluate the performance of a Coriolis flow meter under gas, liquid, and supercritical flow conditions. The results indicate that the impurities have a relatively minor impact on the measurement performance of the meter, with maximum mean absolute measurement errors of 0.25 %, 0.12 %, and 0.28 % observed in gas, liquid, and supercritical CO2 flow conditions, respectively. The findings support the use of Coriolis metering technology as a reliable option for CCS metering, underscoring its suitability for accurate measurements in single-phase CO2 transport applications.

Semi-supervised prototype network based on compact-uniform-sparse representation for rotating machinery few-shot class incremental fault diagnosis

Distinct from the ideal ‘closed-set’ assumption of comprehensive fault types and arbitrary data access, the entangled challenges of labeled instance paucity and fault increasing with operation are difficult to circumvent in industrial diagnostics. However, conventional deep learning-based diagnostic models lack the capacity for dynamic and incremental acceptance of new faults under limited labeled instances. When confronted with this more industrially realistic diagnostic task, their performance is constrained by overfitting, imbalance, and catastrophic forgetting, thus diminish the feasibility of engineering deployment. In this research, we define this task as a few-shot class incremental fault diagnosis (FS-CIFD) problem and develop a semi-supervised prototype network based on compact-uniform-sparse representation (CUS-SSPN) for this purpose. Structurally, CUS-SSPN incorporates the designed compact-uniform-sparse (CUS) composite loss, optimal transport (OT)-based semi-supervised strategy, and multi-level knowledge distillation (KD) strategy into the prototype network. With the CUS composite loss and OT-based semi-supervised strategy, CUS-SSPN can assign representative prototypes for each incremental fault and form an intra-class compact and inter-class uniform and sparse representation space. This allows the model to incrementally learn new faults while effectively suppressing the overfitting triggered by instance paucity and the biased diagnosis triggered by unbalanced labeling. Combining the designed multi-level KD strategy to convey category centroid information and classification decision knowledge from both prototype and logits levels, catastrophic forgetting of known faults can be effectively mitigated. Extensive FS-CIFD tasks are constructed on both publicly available dataset and practical wind turbine dataset to validate the effectiveness of CUS-SSPN and the feasibility of engineering diagnostics.

Optimized transportation scheduling for precast concrete components considering heterogeneous vehicle-size matching

Recently, prefabricated construction has been vigorously promoted, resulting in high demand for precast concrete (PC) components. The transportation scheduling optimization problem of PC components with various kinds from multiple projects arises. Unlike conventional cargo, PC components are characterized by shape heterogeneity, large volume, and strict delivery time limits. Based on three characteristics, a heterogeneous fixed fleet vehicle routing problem (HFFVRP) for PC components is introduced, where heterogeneous vehicles, allocation of PC components to size-matching vehicles, and hybrid time windows are considered. Then a two-stage solution strategy based on the improved ant colony optimization (ACO) and Dijkstra algorithm is designed to obtain optimal vehicle routes under minimum transportation costs. The results indicate that the improved ACO-Dijkstra algorithm outperforms in obtaining optimal transportation plans for heterogeneous vehicles compared with manual decision-making and other heuristic algorithms. Sensitivity analysis denotes that utilizing heterogeneous vehicles contributes to reductions in transportation costs, and vehicle configuration should be adjusted along with demand scales. The proposed model and algorithm extend the theoretical basis of construction industrial applications.

A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains

We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on curved triangle meshes. To address this challenge, we leverage a splitting integrator combined with a convex optimization step to solve these PDE. Our machinery can be used to compute entropic approximation of optimal transport distances on geometric domains, overcoming the numerical limitations of the state-of-the-art method. In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion and front propagation tasks in geometry processing.

Multi-scale information transport generative adversarial network for human pose transfer

Human pose transfer, a challenging image generation task, aims to transfer a source image from one pose to another. Existing methods often struggle to preserve details in visible regions or predict reasonable pixels for invisible regions due to inaccurate correspondences. In this paper, we design a novel multi-scale information transport generative adversarial network, composed of Information Transport (IT) blocks to establish and refine the correspondences progressively. Specifically, we compute a transport matrix to warp the source image features by integrating an optimal transport solver in our proposed IT block, and use IT blocks to refine the correspondences in different resolutions to preserve rich details of the source image features. The experimental results and applications demonstrate the effectiveness of our proposed method. We further present an image-specific optimization using only a single image. The code is available for research purposes athttps://github.com/Zhangjinso/OT-POSE.

Evolution of the network structure and voltage loss of anode electrode with the polymeric dispersion in PEM water electrolyzer

Exploring the intrinsic relationship between the network structure and the performance of catalyst layer (CL) by rational design its structure is of paramount importance for proton exchange membrane (PEM) electrolyzers. This study reveals the relative effect of polymeric dispersion evolution on oxygen evolution reaction (OER) performance and cell voltage loss and linked to CL network structure. The results show that although the dispersed particle size of the ionomer and ink increases with increasing the solubility parameter (δ) difference between the mixed solvent and the ionomer, MeOH-cat (ink from MeOH aqueous solution) has the largest ionomer and ink particle size resulting in the poorest stability, but has comparable OER overpotential to that of IPA-cat (249 mV@10 mA cm−2), which has the smallest dispersed size. While at 100 mA cm−2, the overpotential of the ink rises as the particle size increases, suggesting that the electrode structure becomes more influential as the current density increases. Quantitatively analyzed the electrolyzers’ voltage losses and determined that the CL from MeOH-cat has the lowest kinetic overpotential. However, its performance is the worst because of the insufficient network structure of CL, resulting in an output of 1.96 V at 1.5 A cm−2. Comparatively, the CL from IPA-cat has the highest kinetic overpotential yet can achieve the greatest performance of 1.76 V at 2 A cm−2 due to its homogeneous network structure and optimal mass transport. Furthermore, the performance variation becomes more pronounced as current density rises. Hence, this study highlights the significant impact of CL structure on electrolyzer’s performance. To improve performance in PEM water electrolysis technology, especially for large work current density, it is crucial to enhance the CL’s network structure.

Wasserstein local slow feature analysis and its application to process monitoring

Abstract Complex industrial processes are commonly characterized by dynamics, which results from the fact that there exists compensation of the closed-loop control and complex reflux during process operations. In this work, we propose a new method termed Wasserstein local slow feature analysis approach (WLSFA) used for monitoring the dynamic process, which can learn slowly varying information to capture the trend of process variations and characterize dynamics. Specifically, Wasserstein graph embedding based on optimal transport is proposed to preserve the local geometrical structure of raw data so that the reduced-dimensional representations can more faithfully reveal the underlying information of data, enhancing monitoring performance. Moreover, the l_2 -norm orthogonal constraint is incorporated into the objective function to improve generalization ability and alleviate the false alarm rate. On the basis of WLSFA model, a contribution plot in the sense of reconstruction is developed to locate the fault variables, which is beneficial to regulate abnormal conditions towards normal levels. Finally, the efficiency of the proposed approach is illustrated by a benchmark process and the application to a real-world fractionation process.

Randomized Methods for Computing Optimal Transport Without Regularization and Their Convergence Analysis

Randomized Methods for Computing Optimal Transport Without Regularization and Their Convergence Analysis

Optimal transport for automatic alignment of untargeted metabolomic data.

Untargeted metabolomic profiling through liquid chromatography-mass spectrometry (LC-MS) measures a vast array of metabolites within biospecimens, advancing drug development, disease diagnosis, and risk prediction. However, the low throughput of LC-MS poses a major challenge for biomarker discovery, annotation, and experimental comparison, necessitating the merging of multiple datasets. Current data pooling methods encounter practical limitations due to their vulnerability to data variations and hyperparameter dependence. Here, we introduce GromovMatcher, a flexible and user-friendly algorithm that automatically combines LC-MS datasets using optimal transport. By capitalizing on feature intensity correlation structures, GromovMatcher delivers superior alignment accuracy and robustness compared to existing approaches. This algorithm scales to thousands of features requiring minimal hyperparameter tuning. Manually curated datasets for validating alignment algorithms are limited in the field of untargeted metabolomics, and hence we develop a dataset split procedure to generate pairs of validation datasets to test the alignments produced by GromovMatcher and other methods. Applying our method to experimental patient studies of liver and pancreatic cancer, we discover shared metabolic features related to patient alcohol intake, demonstrating how GromovMatcher facilitates the search for biomarkers associated with lifestyle risk factors linked to several cancer types.

Optimal transport for automatic alignment of untargeted metabolomic data

Untargeted metabolomic profiling through liquid chromatography-mass spectrometry (LC-MS) measures a vast array of metabolites within biospecimens, advancing drug development, disease diagnosis, and risk prediction. However, the low throughput of LC-MS poses a major challenge for biomarker discovery, annotation, and experimental comparison, necessitating the merging of multiple datasets. Current data pooling methods encounter practical limitations due to their vulnerability to data variations and hyperparameter dependence. Here, we introduce GromovMatcher, a flexible and user-friendly algorithm that automatically combines LC-MS datasets using optimal transport. By capitalizing on feature intensity correlation structures, GromovMatcher delivers superior alignment accuracy and robustness compared to existing approaches. This algorithm scales to thousands of features requiring minimal hyperparameter tuning. Manually curated datasets for validating alignment algorithms are limited in the field of untargeted metabolomics, and hence we develop a dataset split procedure to generate pairs of validation datasets to test the alignments produced by GromovMatcher and other methods. Applying our method to experimental patient studies of liver and pancreatic cancer, we discover shared metabolic features related to patient alcohol intake, demonstrating how GromovMatcher facilitates the search for biomarkers associated with lifestyle risk factors linked to several cancer types.

Entropic Approximation of ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\infty $$\\end{document}-Optimal Transport Problems

We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\infty $$\\end{document}-cyclically monotone plans at the limit. We also present some numerical illustrations performed with Sinkhorn’s algorithm.

Energy Saving and Emission Reduction Optimization of Enterprise Hazardous Waste Recycling Management System based on Hybrid Genetic Algorithm

This research proposes a new path planning model for hazardous waste recycling transportation to effectively manage the hazardous waste recycling transportation, improving the transportation efficiency, while considering the actual road conditions. The new model adopts the conservation algorithm and hybrid genetic algorithm, which makes the new model better meet the complex needs of hazardous waste recycling. The new approach enables optimal transportation path planning for hazardous waste recycling while ensuring safety and compliance. The results showed that the hybrid algorithm outperformed the other two algorithms in terms of path optimization, cost reduction, accuracy improvement and error reduction. The hybrid algorithm had the best path optimization effect, which can get the optimal path with the lowest cost and highest efficiency. The hybrid algorithm had the highest accuracy of 95.62%. It also had the lowest root mean square error and average percentage error, indicating that it had less error. Finally, the hybrid algorithm had the highest loss function value, which indicated that the model had the best stability and better performance. The new hybrid genetic algorithm performed better than the single traditional algorithm, which is more efficient for hazardous waste recycling.

Optimal Transport Distances to Characterize Electronic Excitations.

Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very useful in a plethora of classification problems and, therefore, seem a natural tool to try to tackle this challenge. We propose and investigate a new diagnostic Θ based on the Sinkhorn divergence from optimal transport. We evaluate a k-NN classification algorithm on Θ, the popular Λ diagnostic, and their combination, and assess their performance in labeling excitations, finding that (i) the combination only slightly improves the classification, (ii) Rydberg excitations are not separated well in any setting, and (iii) Θ breaks down for charge transfer in small molecules. We then define a length-scale-normalized version of Θ and show that the result correlates closely with Λ for results obtained with Gaussian basis functions. Finally, we discuss the orbital dependence of our approach and explore an orbital-independent version. Using an optimized combination of the optimal transport and overlap diagnostics together with a different metric is in our opinion the most promising for future classification studies.

Incremental Confidence Sampling with Optimal Transport for Domain Adaptation.

Domain adaptation is a subfield of statistical learning theory that takes into account the shift between the distribution of training and test data, typically known as source and target domains, respectively. In this context, this paper presents an incremental approach to tackle the intricate challenge of unsupervised domain adaptation, where labeled data within the target domain is unavailable. The proposed approach, OTP-DA, endeavors to learn a sequence of joint subspaces from both the source and target domains using Linear Discriminant Analysis (LDA), such that the projected data into these subspaces are domain-invariant and well-separated. Nonetheless, the necessity of labeled data for LDA to derive the projection matrix presents a substantial impediment, given the absence of labels within the target domain in the setting of unsupervised domain adaptation. To circumvent this limitation, we introduce a selective label propagation technique grounded on optimal transport (OTP), to generate pseudo-labels for target data, which serve as surrogates for the unknown labels. We anticipate that the process of inferring labels for target data will be substantially streamlined within the acquired latent subspaces, thereby facilitating a self-training mechanism. Furthermore, our paper provides a rigorous theoretical analysis of OTP-DA, underpinned by the concept of weak domain adaptation learners, thereby elucidating the requisite conditions for the proposed approach to solve the problem of unsupervised domain adaptation efficiently. Experimentation across a spectrum of visual domain adaptation problems suggests that OTP-DA exhibits promising efficacy and robustness, positioning it favorably compared to several state-of-the-art methods.