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DOE OSTI2024

Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Abstract Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library , and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Oles, Vladyslav (ORCID:0000000188727463)↗

DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗

DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints

Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.

augmented Lagrangian↗

DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗

DOE OSTI2024

Decomposing a renewable energy design and dispatch model

We address a mixed-integer linear programming model which selects a cost-minimizing set of available technologies with which to design a renewable energy system and prescribe their associated dispatch decisions. Realistically sized instances of such models pose computational challenges. To this end, we develop a Lagrangian heuristic based on a decomposition methodology which partitions the model into blocks and optimizes these more manageable, smaller subproblems. It also provides a lower bound to assess solution quality. In conclusion, we apply this methodology to the National Renewable Energy Laboratory's Renewable Energy Integration and Optimization (REopt TM ) model to generate near-optimal solutions to realistic instances containing, on average, approximately 300,000 variables and at least as many constraints, with a mean 30% optimality gap improvement using a five-minute solution time limit, compared to directly solving the original monolith.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Memory-efficient nonsmooth dynamic optimization using adaptive randomized compression

Dynamic optimization problems arise in many applications including flow control, full waveform inversion, and medical imaging. These problems are plagued by significant computational challenges. One such challenge — and the focus of this work — is the memory limitation induced by the size of the underlying dynamical system. In particular, the entire dynamic trajectory is required for derivative computation and therefore must be stored or recomputed using, e.g., checkpointing. Although recent work demonstrated the use of adaptive randomized sketching to overcome the memory challenge, that work only applies to smooth unconstrained problems, prohibiting its use for nonsmooth regularized and constrained problems. The inclusion of nonsmooth regularizers and constraints is critical as they often arise in an attempt to preserve certain physical properties or to promote sparsity. To solve these problems, we introduce a trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function that leverages randomized sketching to compress the dynamical system trajectories and adaptively adjust the sketch rank to satisfy a gradient inexactness condition. We prove convergence of this algorithm and demonstrate that it achieves substantial memory reduction on three discretized PDE-constrained optimization applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Consequential improvement acquisition function for efficient multi-fidelity Bayesian optimization

Abstract Surrogate-based Bayesian optimization has been widely applied in design optimization to increase sampling efficiency. However, the cost for each evaluation of the objective function can still be very high when physical experiments or large-scale simulations are involved. Multi-fidelity Bayesian optimization is the new approach to further improve the sampling efficiency by reducing the number of expensive samples at the highest fidelity level and supplementing them with less expensive ones at low-fidelity levels. In this paper, a new consequential improvement (CI) acquisition function is proposed to allow for the simultaneous selection of the solution and the fidelity level in problems with a known hierarchy of fidelity levels. The new CI acquisition function incorporates the consequential effectiveness of objective improvement with the considerations of cost, accuracy, and validity differences between high- and low-fidelity samples in engineering practice. The new method of multi-fidelity Bayesian optimization based on the CI is demonstrated with several analytical and simulation-based design examples. In the simulation-based design optimization example, the results show that the CI acquisition function has a decisive advantage in the sampling efficiency over the other methods of multi-fidelity Bayesian optimization with simultaneous selection. The results indicate that the proposed method is particularly advantageous in solving high-dimensional problems and when large cost ratios between high- and low-fidelity evaluations exist and high-fidelity validation is mandatory. Furthermore, the method robustly avoids the prevalent issue of over sampling at low-fidelity levels.

Aydogdu, Ibrahim [Georgia Institute of Technology,↗

DOE OSTI2025

Machine learning models for segmentation and classification of cyanobacterial cells

Abstract Timelapse microscopy has recently been employed to study the metabolism and physiology of cyanobacteria at the single-cell level. However, the identification of individual cells in brightfield images remains a significant challenge. Traditional intensity-based segmentation algorithms perform poorly when identifying individual cells in dense colonies due to a lack of contrast between neighboring cells. Here, we describe a newly developed software package called Cypose which uses machine learning (ML) models to solve two specific tasks: segmentation of individual cyanobacterial cells, and classification of cellular phenotypes. The segmentation models are based on the Cellpose framework, while classification is performed using a convolutional neural network named Cyclass. To our knowledge, these are the first developed ML-based models for cyanobacteria segmentation and classification. When compared to other methods, our segmentation models showed improved performance and were able to segment cells with varied morphological phenotypes, as well as differentiate between live and lysed cells. We also found that our models were robust to imaging artifacts, such as dust and cell debris. Additionally, the classification model was able to identify different cellular phenotypes using only images as input. Together, these models improve cell segmentation accuracy and enable high-throughput analysis of dense cyanobacterial colonies and filamentous cyanobacteria.

Huffine, Clair A.↗

DOE OSTI2025

Toward computing bounds for Ramsey numbers using quantum annealing

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems, such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum annealing as a tool for use in exploring combinatorial mathematics research problems. We consider the monochromatic triangle problem and the Ramsey number problem, both examples of graph coloring. Conversion to quadratic unconstrained binary optimization (QUBO) form is required to run on quantum hardware. While the monochromatic triangle problem is quadratic by nature, the Ramsey number problem requires the use of order reduction methods for a quadratic formulation. The goal is to provide a method for producing special colorings of graphs which if successful would provide lower bounds for certain Ramsey numbers. We discuss implementations, limitations, and results when running on the D-Wave Advantage quantum annealer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Eco-driving Profile Optimization by Dynamic Programming for Battery Electric Vehicles

Although full automation has not yet been achieved, automated vehicles are a valid research area. Not only would automated vehicles provide ultimate driver convenience, but they would maximize energy efficiency by eliminating undesired human driving behaviors and optimally controlling the powertrain. From the perspective of control related to energy saving, speed profile optimization is important for improving system efficiency and satisfying passenger demands. This study employs Dynamic Programming (DP) to solve the constrained optimal problem for travel time, distance, and speed limit by exploring all possible control options. The solutions obtained by DP demonstrate consistent control patterns combining four control modes-acceleration, cruising, coasting, and braking, with cruising or coasting being selective depending on the boundary conditions. Further, this study introduces DP-based simulation results and attempts to provide comprehensive interpretations of the optimal policy by analyzing the essential factors that affect the control problem, including boundary conditions, road load, and powertrain characteristics. Based on these interpretations, the control concepts can be explained as the optimal policy selecting the best control option based on system efficiency and boundary conditions. The results of DP are compared with a human-like driver model to show that the optimal speed profiles can effectively reduce energy consumption.

Autonomous vehicles↗

DOE OSTI2024

Composite coatings from polycarbosilane derived SiC and Al/SiC cermet active fillers as protective barriers against steel corrosion

Stainless steel is used throughout the world as a structural material. However, it undergoes corrosion damage when exposed to extremely corrosive media, such as the marine environment. An alternative to solve this problem lies in the development of coatings that can withstand extreme conditions but also be easily deposited with inherently corrosion-resistant materials such as silicon carbide (SiC). The present study shows a simple method to produce Al/SiC cermet powders by attrition milling. The resulting cermet powders with a metallic matrix and hemispherical morphology, were employed as fillers in polycarbosilane (PCS) solutions that were sprayed on A304 stainless steel substrates. Al/SiC composite coatings were produced after heating the sprayed suspensions at 700 °C for 1 h in Ar atmosphere. The resulting composite coatings exhibited low surface energies (< 35 mN/m), water contact angles of 53°, and adhesion strength of up to 30 MPa. Finally, corrosion tests were performed in a cyclic corrosion test chamber, showing that these coatings effectively reduced the corrosion rate of stainless steel by 87%, reaching corrosion rate values of 0.007 g/cm 2 year.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Utilization of Hemp Processing Waste for 3D Printing of Biocomposites

Unlike stem biomass, the residues after the extraction of cannabidiol (CBD) oil from hemp flower are challenging to utilize because of their high extractive content (~ 40%, mainly lipids) and are typically considered waste and landfilled. This study presented a novel approach to effectively valorize this underutilized hemp processing waste via chemical processing for three-dimensional (3D) printing applications. Hemp processing waste was processed with sodium hydroxide (NaOH) to control extractives for solving nozzle clogging and then applied as a biofiller in polylactic acid (PLA) composites to improve the mechanical strength. The novelty of this work lies in demonstrating that controlled extractive removal via NaOH treatment not only improves processability but also enhances mechanical performance in 3D-printed biocomposites. We systematically investigated the effect of the processed biofiller content (2.5–10 wt%) on the mechanical and thermal properties of the biocomposites. The decrease in the content of extractives reduced the non-structural components and improved the surface compatibility of the hemp waste with the PLA matrix, thereby enhancing the polymer-biofiller interactions. The best performance was achieved at 2.5 wt% loading, where Young’s modulus increased from 2.3 GPa to 2.6 GPa and tensile strength from 42.7 MPa to 48.8 MPa. Interestingly, the complete removal of extractives also reduced the mechanical strength of their biocomposites, indicating the interfacial adhesion effects of extractives. Furthermore, this study provides new insights into balancing extractive content for optimal mechanical properties, offering a sustainable solution for waste valorization in additive manufacturing.

Additive manufacturing↗

DOE OSTI2025

Asymmetrical cavity design that bypasses mode mixings in axion haloscope experiments

Microwave cavities used in axion haloscope experiments typically employ a tuning rod as a means to widen the range of resonance frequencies at which it is sensitive to axion-to-photon conversion. A realistic tuning mechanism requires a gap between the cavity end caps and the tuning rod to ensure movement, and causes some modes to hybridize with the resonant mode that is being tracked for the experiment. These so-called mode mixings lead to gaps in the frequency range that practically lose sensitivity to axions. Here, to solve this problem, we present a cavity design which, for two tuning rod configurations corresponding to a lower and higher frequency range, have a dielectric rod inserted at a specific location that makes the cavity asymmetrical. Moving the tuning rod closer to the dielectric insert changes the location and frequency of the mode mixing compared to when it is farther away from it. This design is easily realizable in practical experiments and makes possible an axion dark matter search with minimal loss in sensitivity due to mode mixings. We also show that the same design has the same desired effect when cavity dimensions are scaled down to be smaller and are at higher resonance frequencies.

Axion↗

DOE OSTI2025

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy↗

DOE OSTI2026

Optimization of the FRIB beam dump: a hybrid genetic algorithm and reinforcement learning approach

The operational envelope of high-power-density systems, such as particle accelerators and advanced nuclear energy systems, is critically constrained by the need to manage extreme thermal loads. To address this, we present a novel hybrid optimization framework combining a genetic algorithm (GA) with a soft actor-critic (SAC) deep reinforcement learning agent. This framework was applied to a practical high-heat-flux problem: redesigning the beam dump at the Facility for Rare Isotope Beams (FRIB) for a power upgrade from 20 kW to 50 kW. The resulting design, validated by three-dimensional conjugate heat transfer simulations, suppresses hazardous hot spots and yields a markedly more uniform temperature distribution. This provides a robust operating margin, increasing the average power-handling capability by 72% relative to the current design, demonstrating the framework’s potential to solve complex thermal management challenges in both accelerator technology and advanced nuclear systems.

Accelerator↗

DOE OSTI2024

Formulation of a one-dimensional electrostatic plasma model for testing the validity of kinetic theory

Here, we present a one-dimensional (1-D) model composed of aligned, electrostatically interacting charged disks, conceived to address in a computable model the validity of the Bogoliubov assumption on the decay of particle correlations in the Born–Bogoliubov–Green–Kirkwood–Yvon hierarchy. This assumption is a basic premise of plasma kinetic theory. The disk model exhibits spatially 1-D features at short distances, but retains 3-D features at large distances. Here the collective dynamics of this model plasma is investigated by solving the corresponding Vlasov equation. In addition, the implementation of the model for the numerical validation of the Bogoliubov assumption is formulated.

1-D plasma model↗