Potential Flow Generator With L 2 Optimal Transport Regularity for Generative Models
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Computer Science↗
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Results for “Optimal transport”
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Minimizing Optimal Transport for Functions with Fixed-Size Nodal Sets
Consider the class of zero-mean functions with fixed L ∞ and L 1 norms and exactly N ϵ N nodal points. Which functions f minimize W p (f + ,f – ), the Wasserstein distance between the measures whose densities are the positive and negative parts? We provide a complete solution to this minimization problem on the line and the circle, which provides sharp constants for previously proven “uncertainty principle”-type inequalities, i.e., lower bounds on N • W p (f + ,f – ). We further show that, while such inequalities hold in many metric measure spaces, they are no longer sharp when the non-branching assumption is violated; indeed, for metric star-graphs, the optimal lower bound on W p (f + ,f – ) is not inversely proportional to the size of the nodal set, N. Here, based on similar reductions, we make connections between the analogous problem of minimizing W p (f + ,f – ) for f defined on Ω C R d with an equivalent optimal domain partition problem.
97 MATHEMATICS AND COMPUTING↗
Optimizing Transportation Networks for E-Waste Reverse Logistics: A Multi-Modal Cost Allocation and Pricing Strategy
The exponential growth of electronic waste (e-waste) poses critical challenges for sustainable reverse logistics and transportation network optimization. This study develops a dual-channel transportation framework for e-waste logistics that integrates dynamic freight pricing, cost allocation mechanisms, and game-theoretic coordination. The model captures interactions between centralized hubs and distributed processing networks, accounting for freight rate elasticity, volume allocation, and capacity constraints. Using Stackelberg game theory and cost-sharing strategies, the framework optimizes transportation efficiency and profit distribution across logistics channels. Numerical simulations show that the dual-channel structure increases centralized hub profit by 226.8% compared to baseline single-channel operations, while boosting total transported volume by 1.2% and nearly doubling freight collector profit under cost-sharing. Scenario analyses across regional infrastructures reveal that network density, policy incentives, and logistics costs shape routing efficiency and profit allocation. These findings suggest that coordinated strategies combining dynamic pricing, targeted infrastructure investment, and strategic cost allocation are needed to design efficient, resilient, and regionally adaptable e-waste transportation systems.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Accelerating template generation in resonant anomaly detection searches with optimal transport
We introduce Resonant Anomaly Detection with Optimal Transport (RAD-OT), a method for generating signal templates in resonant anomaly detection searches. RAD-OT leverages the fact that the samples from the conditional probability density of the target features vary approximately linearly along the optimal transport path connecting the resonant feature. This does not assume that the conditional density itself is linear with the resonant feature, allowing RAD-OT to efficiently capture multimodal relationships, changes in resolution, etc. By solving the optimal transport problem, RAD-OT can quickly build a template by interpolating between the background distributions in two sideband regions. We demonstrate the performance of RAD-OT using the LHC Olympics R&D dataset, where we find comparable sensitivity and improved stability with respect to deep learning-based approaches.
Automation↗
Computational optimal transport for molecular spectra: The semi-discrete case
Comparing a discrete molecular spectrum to a continuous molecular spectrum in a quantitative manner is a challenging problem, for example, when attempting to fit a theoretical stick spectrum to a continuous spectrum. In this paper, the use of computational optimal transport is investigated for such a problem. In the optimal transport literature, the comparison of a discrete and a continuous spectrum is referred to as semi-discrete optimal transport and is a situation where a metric such as least-squares may be difficult to define except under special conditions. The merits of an optimal transport approach for this problem are investigated using the transport distance defined for the semi-discrete case. A tutorial on semi-discrete optimal transport for molecular spectra is included in this paper, and several well-chosen synthetic spectra are investigated to demonstrate the utility of computational optimal transport for the semi-discrete case. Among several types of investigations, we include calculations showing how the frequency resolution of the continuous spectrum affects the transport distance between a discrete and a continuous spectrum. We also use the transport distance to measure the distance between a continuous experimental electronic absorption spectrum of SO 2 and a theoretical stick spectrum for the same system. The comparison of the theoretical and experimental SO 2 spectra also allows us to suggest a theoretical value for the band origin that is closer to the observed band origin than previous theoretical values.
74 ATOMIC AND MOLECULAR PHYSICS↗
Computational optimal transport for molecular spectra: The fully discrete case
In this study, the use of computational optimal transport is investigated as a tool for comparing two molecular spectra. Unlike other techniques for comparing molecular spectra in a pattern-recognition framework, transport distances simultaneously encode information about line positions and intensities. In addition, it is shown that transport distances are a useful alternative to Euclidean distances as Euclidean distances are based on line-by-line comparisons, while transport distances reflect broader features of molecular spectra and adequately compare spectra with different resolutions. This paper includes a tutorial on the use of optimal transport and investigates several well-chosen examples to illustrate the utility of computational optimal transport for comparing molecular spectra.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Computational optimal transport for molecular spectra: The fully continuous case
Computational optimal transport is used to analyze the difference between pairs of continuous molecular spectra. It is demonstrated that transport distances which are derived from this approach may be a more appropriate measure of the difference between two continuous spectra than more familiar measures of distance under many common circumstances. Associated with the transport distances is the transport map which provides a detailed analysis of the difference between two molecular spectra and is a key component of our study of quantitative differences between two continuous spectra. The use of optimal transport for comparing molecular spectra is developed in detail here with a set of model spectra, so that the discussion is self-contained. The difference between the transport distance and more common definitions of distance is elucidated for some well-chosen examples and it is shown where transport distances may be very useful alternatives to standard definitions of distance. The transport distance between a theoretical and experimental electronic absorption spectrum for SO 2 is studied and it is shown how the theoretical spectrum can be modified to fit the experimental spectrum better adjusting the theoretical band origin and the resolution of the theoretical spectrum. In conclusion, this analysis includes the calculation of transport maps between the theoretical and experimental spectra suggesting future applications of the methodology.
74 ATOMIC AND MOLECULAR PHYSICS↗
Quantum Computing in Next-Generation Transportation Optimization
We explore how quantum computing (QC) can advance transportation optimization, with a focus on two high-impact areas: traffic signal control and vehicle electrification with grid integration. As transportation systems grow in complexity, classical optimization methods increasingly struggle to deliver scalable and efficient solutions, particularly for real-time, data-rich environments. This work identifies key challenges within these two domains where QC may offer advantages, particularly in handling combinatorial decision spaces and dynamic constraints. We begin by outlining the limitations of classical approaches for traffic signal control optimization and electric vehicle charging coordination, highlighting where computational limitations arise. Previous quantum formulations are presented and new formulations are proposed to demonstrate how emerging quantum algorithms, including quantum annealing and the Quantum Approximation Optimization Algorithm, could be leveraged to reformulate and address these problems. We also evaluate the suitability of current quantum hardware and discuss recent trends that indicate when QC may become a viable tool for transportation applications. While acknowledging the present limitations of QC technologies, this poster emphasizes the importance of preparing quantum-compatible models today. By reviewing and establishing formulations that align with the strengths of quantum algorithms, researchers and practitioners can better position themselves to take advantage of QC advancements as they occur. This work aims to provide a practical, forward-looking perspective on the near-term potential of quantum computing in transportation optimization.
33 ADVANCED PROPULSION SYSTEMS↗
Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference
In this work, we present two neural network approaches that approximate the solutions of static and dynamic conditional optimal transport (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference—particularly in the simulation-based (“likelihood-free”) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.
97 MATHEMATICS AND COMPUTING↗
Optimal Transport Based Control of Granular Imaging System in Space
"Orbiting Rainbows” is a paradigm for creating a space-based observatory (telescope) from confined and aligned granular media. The overall objective is to construct a very large and lightweight aperture in space using a cloud of micron-sized particles held in position and aligned by the application of external electromagnetic fields, thus alleviating the extreme expense of deploying and stabilizing large monolithic telescopes by reducing the mass of the primary aperture. Adaptive optics techniques for wavefront stabilization and computational imaging techniques are then used to remove the optical noise from the scattering reflections of the granular medium, and finally producing clean images within the diffraction limit. In this paper, we address one of the key challenges of this new paradigm, namely controlling the position and orientation of the granules or particles so that the cloud of particles achieves the desired shape of an ultra-lightweight telescope and points into the right orientation. A further complication arises due to the fact that the particles do not have any onboard actuators. A number of external electric-field-based actuators are used to control all the particles simultaneously. Moreover, the number of actuators are orders-of-magnitude smaller than the number of particles, making this system largely under-actuated. Since the cloud of particles in any plausible configuration can be modeled as a probability distribution over the workspace, we formulate this control challenge as an optimal transport problem and then show that our optimal transport based control law drives the cloud of particles from any initial distribution to the desired position distribution (optical surface) and angular distribution (polarization state). Simulation results demonstrate the effectiveness of our approach.
Bandyopadhyay, Saptarshi↗
Optimizing Transportation for People, Communities, and Businesses,
The document provides a vision on how future air transportation could be optimized for better living and business needs rather than current system where living and business have to accommodate transportation considerations in location strategies.
Parimal Hemchandra Kopardekar↗
Equity-driven Planning of Distributed Solar PV using Optimal Transport
Typically, distribution system planning processes do not explicitly incorporate energy equity considerations, such as identifying consumers most affected by energy costs and determining how investments in the distribution system can address existing energy burden imbalances. This paper proposes a novel optimal transport (OT)-based method to improve the energy burden distribution of consumers. The approach involves the strategic siting and sizing of solar PV in order to assist customers with high energy burden and improve the overall energy burden distribution of the community. The desired energy burden distribution is defined using the equal distribution equivalent (EDE) concept. The OT-based method is then used to estimate the distributed solar PV capacity to be installed at various locations and the tariffs to be adjusted, all while improving the energy burden distribution and providing valuable insights into distributed generation (DG) planning. The results on IEEE 37 bus test system demonstrate how DG planning, considering EDE and OT, can help reduce the energy burden of low-income consumers. Additionally, the approach also reveals optimal tariff adjustments needed to ensure revenue neutrality for distribution utilities.
Optimal transport, equal distribution equivalent, ↗
A continuous calibration of the ATLAS flavour-tagging classifiers via optimal transportation maps
A calibration of the ATLAS flavour-tagging algorithms using a new calibration procedure based on optimal transportation maps is presented. Simultaneous, continuous corrections to the b-jet, c-jet, and light-flavour jet classification probabilities from jet-tagging algorithms in simulation are derived for b-jets using $t\bar{t} \rightarrow e\mu \nu \nu bb$ data. After application of the derived calibration maps, closure between simulation and observation is achieved for jet flavour observables used in ATLAS analyses of Large Hadron Collider (LHC) Run 2 proton-proton collision data. This continuous calibration opens up new possibilities for the future use of jet flavour information in LHC analyses and also serves as a guide for deriving high-dimensional corrections to simulation via transportation maps, an important development for a broad range of inference tasks.
Aad, G. [Aix-Marseille Université] (ORCID:00000002↗
AlignOT: An Optimal Transport Based Algorithm for Fast 3D Alignment With Applications to Cryogenic Electron Microscopy Density Maps
Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, called AlignOT, which relies on the use of computational optimal transport (OT) to align EM maps in 3D space. By embedding a fast estimation of OT maps within a stochastic gradient descent algorithm, our method searches for a rotation that minimizes the Wasserstein distance between two maps, represented as point clouds. Here, we quantify the impact of various parameters on the precision and accuracy of the alignment, and show that AlignOT can outperform the standard local alignment methods, with an increased range of rotation angles leading to proper alignment. We further benchmark AlignOT on various pairs of experimental maps, which account for different types of conformational heterogeneities and geometric properties. As our experiments show good performance, we anticipate that our method can be broadly applied to align 3D EM maps.
3D alignment↗
Optimal Transport for Super Resolution Applied to Astronomy Imaging
Super resolution is an essential tool in optics, especially on interstellar scales, due to physical laws restricting possible imaging resolution. We propose using optimal transport and entropy for super resolution applications. We prove that the reconstruction is accurate when sparsity is known and noise or distortion is small enough. We prove that the optimizer is stable and robust to noise and perturbations. We compare this method to a state of the art convolutional neural network and get similar results for much less computational cost and greater methodological flexibility.
Rawson, Michael G.↗
High-fidelity holographic beam shaping with optimal transport and phase diversity
A phase-only spatial light modulator (SLM) provides a powerful way to shape laser beams into arbitrary intensity patterns but at the cost of a hard computational problem of determining an appropriate SLM phase. Here, we show that optimal transport methods can generate approximate solutions to this problem that serve as excellent initializations for iterative phase retrieval algorithms, yielding vortex-free solutions with superior accuracy and efficiency. Additionally, we show that analogous algorithms can be used to measure the intensity and phase of the input beam incident upon the SLM via phase diversity imaging. These techniques furnish flexible and convenient solutions to the computational challenges of beam shaping with an SLM.
47 OTHER INSTRUMENTATION↗
Optimal transport for 𝑒/𝜋 0 particle classification in LArTPC neutrino experiments
The efficient classification of electromagnetic activity from 𝜋 0 and electrons remains an open problem in the reconstruction of neutrino interactions in liquid argon time projection chamber (LArTPC) detectors. We address this problem using the mathematical framework of optimal transport (OT), which has been successfully employed for event classification in other high energy physics contexts and is ideally suited to the high-resolution calorimetry of LArTPCs. Using a publicly available simulated dataset from the MicroBooNE Collaboration, we show that OT methods achieve state-of-the-art reconstruction performance in 𝑒/𝜋 0 classification. The success of this first application indicates the broader promise of OT methods for LArTPC-based neutrino experiments.
Neutrino detection↗
Optimal Transport for $e/\pi^0$ Particle Classification in LArTPC Neutrino Experiments
The efficient classification of electromagnetic activity from $\pi^0$ and electrons is a notoriously challenging problem in the reconstruction of neutrino interactions in Liquid Argon Time Projection Chamber (LArTPC) detectors. We address this problem using the mathematical framework of Optimal Transport (OT), which has been successfully employed for event classification in other HEP contexts and is ideally suited to the high-resolution calorimetry of LArTPCs. Using a publicly available simulated dataset from the MicroBooNE collaboration, we show that OT methods achieve state-of-the-art reconstruction performance in $e/\pi^0$ classification. The success of this first application indicates the broader promise of OT methods for LArTPC-based neutrino experiments. This work motivates integrating OT in the reconstruction frameworks of LArTPC experiments such as SBN and DUNE more broadly. Since $\pi^0$s are a significant background for both oscillation experiments and BSM searches, OT can lead to sizeable improvements in the selection efficiency for these analyses by introducing a novel method with which to achieve $\pi^0$ rejection.
Caratelli, David [UC, Santa Barbara]↗