Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematical optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

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]↗
DOE OSTI2026

A Hierarchical Optimization Method for Electric Vertical Takeoff and Landing Aircraft Network Design

Electric vertical takeoff and landing aircraft (eVTOLs) are expected to serve urban air mobility in a station-to-station configuration, which makes the optimal network design of eVTOL stations a critical question to explore. Existing approaches often face limitations, such as the inability to interact station locations with demand or difficulty in finding the optimal solution for large study regions. Here, this paper first proposes a mathematical model to generate optimal eVTOL station locations while considering associated potential eVTOL demand, and then proposes a heuristic algorithm, Hierarchical Optimization MEthod (HOME), to efficiently solve the model. With a case study of Southern California, HOME was compared to 1) directly solving the original integer linear programming-based network design problem, and 2) employing the widely used genetic algorithm. Results suggest that HOME can find optimal solutions with limited computational resources. The proposed framework powered by HOME provides a computationally efficient way to support urban air mobility planning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Minimization of Measurement Uncertainty in Optical Frequency Domain Reflectometry

Optical frequency domain reflectometry (OFDR) is a technique for interrogating optical fiber sensors to generate relative, quasi-distributed measurements. Although Optical frequency domain reflectometry (OFDR) is increasingly being adopted for aerospace, energy production, and structural monitoring applications, the quantification of uncertainty for OFDR measurements has not been developed beyond sparse empirical relationships. To address this knowledge gap, an uncertainty metric for OFDR measurements was developed. This uncertainty metric was applied to weight the edges between OFDR measurements on directed correlation graphs and analyzed to minimize the cumulative uncertainty. In conclusion, this work is the first to propose an uncertainty metric for OFDR and provides a generalized mathematical framework for optimizing OFDR hardware selection, optical fiber sensor selection, and postprocessing strategy.

42 ENGINEERING↗
DOE OSTI2024

Generating Euler Diagrams Through Combinatorial Optimization

Abstract Can a given set system be drawn as an Euler diagram? We present the first method that correctly decides this question for arbitrary set systems if the Euler diagram is required to represent each set with a single connected region. If the answer is yes, our method constructs an Euler diagram. If the answer is no, our method yields an Euler diagram for a simplified version of the set system, where a minimum number of set elements have been removed. Further, we integrate known wellformedness criteria for Euler diagrams as additional optimization objectives into our method. Our focus lies on the computation of a planar graph that is embedded in the plane to serve as the dual graph of the Euler diagram. Since even a basic version of this problem is known to be NP‐hard, we choose an approach based on integer linear programming (ILP), which allows us to compute optimal solutions with existing mathematical solvers. For this, we draw upon previous research on computing planar supports of hypergraphs and adapt existing ILP building blocks for contiguity‐constrained spatial unit allocation and the maximum planar subgraph problem. To generate Euler diagrams for large set systems, for which the proposed simplification through element removal becomes indispensable, we also present an efficient heuristic. We report on experiments with data from MovieDB and Twitter. Over all examples, including 850 non‐trivial instances, our exact optimization method failed only for one set system to find a solution without removing a set element. However, with the removal of only a few set elements, the Euler diagrams can be substantially improved with respect to our wellformedness criteria.

Computer Science↗
DOE OSTI2025

Clifford Circuit-Based Heuristic Optimization of Fermion-To-Qubit Mappings

Simulation of interacting Fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analyzing Fermionic systems with a quantum computer hinges on the efficiency of Fermion-to-qubit mappings that encode nonlocal Fermionic degrees of freedom in local qubit degrees of freedom. While recent studies have highlighted the importance of designing Fermion-to-qubit mappings that are tailored to specific problem Hamiltonians, the methods proposed so far either are restricted to a narrow class of mappings or they use computationally expensive and unscalable brute-force search algorithms. Here, in this work, we address this challenge by designing a heuristic numerical optimization framework for Fermion-to-qubit mappings. To this end, we first translate the Fermion-to-qubit mapping problem to a Clifford circuit optimization problem and then use simulated annealing to optimize the average Pauli weight of the problem Hamiltonian. For all Fermionic Hamiltonians we have considered, the numerically optimized mappings outperform their conventional counterparts, including ternary-tree-based mappings that are known to be optimal for single creation and annihilation operators. We find that our optimized mappings yield between 15% and 40% improvements on the average Pauli weight when the simulation Hamiltonian has an intermediate level of complexity. Most remarkably, the optimized mappings improve the average Pauli weight for 6 × 6 nearest-neighbor hopping and Hubbard models by more than 40% and 20%, respectively. Surprisingly, we also find specific interaction Hamiltonians for which the optimized mapping outperforms any ternary-tree-based mapping. Our results establish heuristic numerical optimization as an effective method for obtaining mappings tailored for specific Fermionic Hamiltonian.

Hamiltonians↗
DOE OSTI2025

Classical Preoptimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications

The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work, we report the implementation and performance of ADAPT-VQE with our recently developed sparse wave function circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and a larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. Furthermore, by preoptimizing a quantum simulation with a parametrized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.

ADAPT-VQE↗
DOE OSTI2024

PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments

This article describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to “enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.” This article provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate the potential of the package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Randomized Federated Learning Methods for Nonsmooth, Nonconvex, and Hierarchical Optimization (Final Technical Report)

This final technical report summarizes the outcomes of a DOE-funded project on federated scientific machine learning (FL) under nonsmooth, nonconvex, and hierarchical optimization settings. The project develops new mathematical models, algorithms, and theoretical guarantees for decentralized stochastic, bilevel, and minimax optimization problems arising in DOE mission-relevant applications. A unified framework of randomized and zeroth-order federated optimization methods is introduced, providing provable convergence, communication efficiency, and sample-complexity guarantees. The report documents algorithmic design, theoretical analysis, and empirical validation of the proposed federated learning methods. The project also contributes to workforce development through graduate training and dissemination of results via publications and seminars.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

DONKEY: A Flexible and Accurate Algorithm for Clustering

We propose an accurate clustering algorithm suitable for the varied and multidimensional data sets that correspond to temporal snapshots from on-the-fly nonadiabatic trajectory-based simulations of photoexcited dynamics. The algorithm approximates the underlying probability density function using variable kernel density estimation, with local maxima corresponding to cluster centers. Each data point is then assigned to one of the maxima by employing a maximization procedure. Finally, clusters artificially separated by minor fluctuations in the probability density are merged. The algorithm does not require parameter tuning, which ensures flexibility and reduces the risk of bias. It is tested on several synthetic data sets, where it consistently outperforms conventional clustering algorithms. As a final example, the algorithm is applied to the excited dynamics of the norbornadiene ⇌ quadricyclane (C 7 H 8 ) molecular photoswitch, demonstrating how distinct reaction pathways can be identified.

algorithms↗
DOE OSTI2024

EF-Hand Battle Royale: Hetero-ion Complexation in Lanmodulin

The lanmodulin (LanM) protein has emerged as an effective means for rare earth element (REE) extraction and separation from complex feedstocks without the use of organic solvents. Whereas the binding of LanM to individual REEs has been well characterized, little is known about the thermodynamics of mixed metal binding complexes (i.e., heterogeneous ion complexes), which limits the ability to accurately predict separation performance for a given metal ion mixture. In this paper, we employ the law of mass action to establish a theory of perfect cooperativity for LanM-REE complexation at the two highest-affinity binding sites. The theory is then used to derive an equation that explains the nonintuitive REE binding behavior of LanM, where separation factors for binary pairs of ions vary widely based on the ratio of ions in the aqueous phase, a phenomenon that is distinct from single-ion-binding chemical chelators. We then experimentally validate this theory and perform the first quantitative characterization of LanM complexation with heterogeneous ion pairs using resin-immobilized LanM. Importantly, the resulting homogeneous and heterogeneous constants enable accurate prediction of the equilibrium state of LanM in the presence of mixtures of up to 10 REEs, confirming that the perfect cooperativity model is an accurate mechanistic description of REE complexation by LanM. We further employ the model to simulate separation performance over a range of homogeneous and heterogeneous binding constants, revealing important insights into how mixed binding differentially impacts REE separations based on the relative positioning of the ion pairs within the lanthanide series. In addition to informing REE separation process optimization, these results provide mathematical and experimental insight into competition dynamics in other ubiquitous and medically relevant, cooperative binding proteins, such as calmodulin.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Dynamic Model Development of a Wind Power Plant Using Neural Net Method to Forecast Wind Power Output (CRADA Final Report)

This project is intended to model wind power plant based on monitored data at the wind power plant. This project will promote the university research in Renewable Energy area and trains the future highly qualified engineers. The dynamic model will be based on neural net model with the input from the two met towers (12 inputs), and the number of turbines in operation (one input). The overall input will be 13 inputs to drive the simulations. The output power at the point of interconnection will be used to tune the neural net weight coefficients. Two neural net concepts will be investigated (the back propagation neural net and the dynamic recurrent neural net with feedback).

17 WIND ENERGY↗
DOE OSTI2024

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

MethodOpt: a Shiny-based graphical user interface for multivariate optimization of sampling and analytical instrumentation

Method optimization is an important step in producing useful data in various experimental settings involving the use of sampling and analytical instrumentation, such as gas-chromatography mass-spectrometry or other analytical techniques. However, traditional optimization techniques often lack the sophistication of more modern optimization techniques developed in areas of applied mathematics. A graphical user interface has been developed that implements a multivariate, multi-objective optimization technique for spectra-generating sampling and analytical instrumentation, which saves substantial time and resources compared to the more traditional approaches to method development.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal Design Approaches for Cost-Effective Manufacturing & Deployment of Chemical Process Families with Economies of Numbers

This work builds on our optimization formulation for process family design and extends it to explicitly include the benefits of economies of numbers. Economies of numbers (sometimes referred to as economies of learning) is a well-documented cost saving phenomenon. It characterizes the manufacturing cost savings due to standardization; in particular, it is capturing the correlation between cost reduction and the number of times a particular product has been manufactured. Following an approach similar to that in Gazzaneo et al. (2022), we develop a costing expression that captures material costs and manufacturing costs as a function of the number of unit modules produced. If the platform has a small number of unit module designs, we will be manufacturing a large number of each of these designs and gaining increased benefits from economies of numbers. However, increasing the number of unit module designs in the platform gives each process variant more choices to consider (at the cost of reducing economies of numbers). The optimization formulation in Stinchfield et al. (2023) pre-specified the number of unit module designs to be included in the platform. Here, by including the economies of numbers explicitly, we allow the mathematical programming formulation to determine the optimal number of unit module designs to include in the platform. We demonstrate this approach on multiple case studies, including MEA-based carbon capture and water desalination.

Stinchfield, Georgia↗
DOE OSTI2025

Physics-Informed Neural Networks for PDE-Constrained Optimization and Control

The goal of optimal control is to determine a sequence of inputs for maximizing or minimizing a given performance criterion subject to the dynamics and constraints of the system under observation. This work introduces Control Physics-Informed Neural Networks (PINNs), which simultaneously learn both the system states and the optimal control signal in a single-stage framework that leverages the system’s underlying physical laws. While prior approaches often follow a two-stage process-modeling, the system first and then devising its control—the presented novel framework embeds the necessary optimality conditions directly into the network architecture and loss function. We demonstrate the effectiveness of the novel methodology by solving various open-loop optimal control problems governed by analytical, one-dimensional, and two-dimensional partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗