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DOE OSTI2021

Learning-Accelerated ADMM for Distributed DC Optimal Power Flow

We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118- and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.

alternating direction method of multipliers↗

DOE OSTI2022

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

OPFLearnData: Dataset for Learning AC Optimal Power Flow

The datasets are resulting from OPFLearn.jl, a Julia package for creating AC OPF datasets. The package was developed to provide researchers with a standardized way to efficiently create AC OPF datasets that are representative of more of the AC OPF feasible load space compared to typical dataset creation methods. The OPFLearn dataset creation method uses a relaxed AC OPF formulation to reduce the volume of the unclassified input space throughout the dataset creation process. The dataset contains load profiles and their respective optimal primal and dual solutions. Load samples are processed using AC OPF formulations from PowerModels.jl. More information on the dataset creation method can be found in our publication, "OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets" and in the package website: https://github.com/NREL/OPFLearn.jl.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Advanced Transmission Technologies – GETs and HPCs Session 2: Advanced Power Flow Control and Transmission Topology Optimization

The INL TADA GETs Cohort Session 2, held on November 7, 2025, conducted in collaboration with ScottMadden, focused on two core Advanced Transmission Technologies (ATTs): Advanced Power Flow Control (APFC) and Transmission Topology Optimization (TTO). These technologies are pivotal in enhancing grid flexibility, reliability, and cybersecurity resilience. APFC, particularly through modular FACTS devices like Modular Static Synchronous Series Compensators (M-SSSCs), enables dynamic voltage injection to reroute power flows. The session highlighted the deployment benefits of APFC, such as rapid installation, minimal civil works, and re-deployability. Regulatory drivers like FERC Order 2023 mandate the inclusion of Grid-Enhancing Technologies (GETs) in interconnection studies. Case studies from Central Hudson, CAISO, and National Grid (UK) demonstrated APFC’s effectiveness in congestion relief and cost savings. The session also addressed cybersecurity concerns, including firmware vulnerabilities, SCADA integration risks, and supply chain dependencies. Participants engaged in interactive exercises to rank cybersecurity and supply chain risks, emphasizing the need for robust digital assurance strategies. TTO involves software-based reconfiguration of transmission networks to optimize power flow without new infrastructure. The session showcased its operational value, with examples from SPP, PJM, and MISO showing significant congestion cost reductions. Cybersecurity vulnerabilities were discussed, particularly in API security and software supply chains, referencing incidents like SolarWinds and attacks on Danish utilities. Digital assurance exercises explored worst-case scenarios, attack paths, and mitigation responsibilities between vendors and utilities. Reliability challenges such as algorithm stability, vendor dependency, and operator trust were also examined. Cross-cutting themes emphasized the importance of digital assurance tools, including Software Bills of Materials (SBOMs) and hardware-in-loop testing. Human performance, training, and operational confidence were identified as critical enablers of technology adoption. The session concluded with a preview of Session 3, which will focus on High Performance Conductors (HPCs) and risk-based cybersecurity tools. Session 2 of 3.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Crossbreeding Effect of Chalcogenation and Iodination on Benzene Additives Enables Optimized Morphology and 19.68% Efficiency of Organic Solar Cells

Volatile solid additives have attracted increasing attention in optimizing the morphology and improving the performance of currently dominated non-fullerene acceptor-based organic solar cells (OSCs). However, the underlying principles governing the rational design of volatile solid additives remain elusive. Herein, a series of efficient volatile solid additives are successfully developed by the crossbreeding effect of chalcogenation and iodination for optimizing the morphology and improving the photovoltaic performances of OSCs. Five benzene derivatives of 1,4-dimethoxybenzene (DOB), 1-iodo-4-methoxybenzene (OIB), 1-iodo-4-methylthiobenzene (SIB), 1,4-dimethylthiobenzene (DSB) and 1,4-diiodobenzene (DIB) are systematically studied, where the widely used DIB is used as the reference. The effect of chalcogenation and iodination on the overall property is comprehensively investigated, which indicates that the versatile functional groups provided various types of noncovalent interactions with the host materials for modulating the morphology. Among them, SIB with the combination of sulphuration and iodination enabled more appropriate interactions with the host blend, giving rise to a highly ordered molecular packing and more favorable morphology. As a result, the binary OSCs based on PM6:L8-BO and PBTz-F:L8-BO as well as the ternary OSCs based on PBTz-F:PM6:L8-BO achieved impressive high PCEs of 18.87%, 18.81% and 19.68%, respectively, which are among the highest values for OSCs.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Modular supply chain optimization considering demand uncertainty to manage risk

Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. We report the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.

42 ENGINEERING↗

DOE OSTI2020

Optimization of leaf morphology in relation to leaf water status: A theory

The leaf economic traits such as leaf area, maximum carbon assimilation rate, and venation are all correlated and related to water availability. Furthermore, leaves are often broad and large in humid areas and narrower in arid/semiarid and hot and cold areas. We use optimization theory to explain these patterns. We have created a constrained optimization leaf model linking leaf shape to vein structure that is integrated into coupled transpiration and carbon assimilation processes. The model maximizes net leaf carbon gain (NPPleaf) over the loss of xylem water potential. Modeled relations between leaf traits are consistent with empirically observed patterns. As the results of the leaf shape-venation relation, our model further predicts that a broadleaf has overall higher NPPleaf compared to a narrowleaf. In addition, a broadleaf has a lower stomatal resistance compared to a narrowleaf under the same level of constraint. With the same leaf area, a broadleaf will have, on average, larger conduits and lower total leaf xylem resistance and thus be more efficient in water transportation but less resistant to cavitation. By linking venation structure to leaf shape and using water potential as the constraint, our model provides a physical explanation for the general pattern of the covariance of leaf traits through the safety-efficiency trade-off of leaf hydraulic design.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

State elimination for mixed‐integer optimal control of partial differential equations by semigroup theory

Abstract Mixed‐integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Optimized Substrates and Measurement Approaches for Raman Spectroscopy of Graphene Nanoribbons

The on-surface synthesis of graphene nanoribbons (GNRs) allows for the fabrication of atomically precise narrow GNRs. Despite their exceptional properties which can be tuned by ribbon width and edge structure, significant challenges remain for GNR processing and characterization. In this work, Raman spectroscopy is used to characterize different types of GNRs on their growth substrate and track their quality upon substrate transfer. A Raman-optimized (RO) device substrate and an optimized mapping approach are presented that allow for the acquisition of high-resolution Raman spectra, achieving enhancement factors as high as 120 with respect to signals measured on standard SiO 2 /Si substrates. This approach is well suited to routinely monitor the geometry-dependent low-frequency modes of GNRs. In particular, the radial breathing-like mode (RBLM) and the shear-like mode (SLM) for 5-, 7-, and 9-atom-wide armchair GNRs (AGNRs) are tracked and their frequencies are compared with first-principles calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design

Access to reliable, clean energy sources is a major concern for national security. Much research is focused on the “grand challenge” of producing energy via controlled fusion reactions in a laboratory setting. For fusion experiments, specifically inertial confinement fusion (ICF), to produce sufficient energy, the fusion reactions in the ICF fuel need to become self-sustaining and burn deuterium-tritium (DT) fuel efficiently. The recent record-breaking NIF ignition shot was able to achieve this goal as well as produce more energy than used to drive the experiment. This achievement brings self-sustaining fusion-based power systems closer than ever before, capable of providing humans with access to secure, renewable energy. In order to further progress toward the actualization of such power systems, more ICF experiments need to be conducted at large laser facilities such as the United States's National Ignition Facility (NIF) or France's Laser Mega-Joule. The high cost per shot and limited number of shots that are possible per year make it prohibitive to perform large numbers of experiments. As such, experimental design relies heavily on complex predictive physics simulations for high-fidelity “preshot” analysis. These multidimensional, multi-physics, high-fidelity simulations have to account for a variety of input parameters as well as modeling the extreme conditions (pressures and densities) present at ignition. Such simulations (especially in 3D) can become computationally prohibitive to turn around for each ICF experiment. In this work, we explore using Bayesian optimization with Gaussian processes (GPs) to find optimal designs for ICF double shell targets, while keeping computational costs to manageable levels. These double shell targets have an inner shell that grades from beryllium on the outer surface to the higher Z material molybdenum, as opposed to the nominally used tungsten, on the inside in order to trade off between the high performance associated with high density inner shells and capsule stability. We describe our results for “capsule-only” xRAGE simulations to study the physics between different capsule designs, inner shell materials, and potential for future experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Spatial‐Uniformity–Driven Bayesian Optimization for Rapid Development of Printed Perovskite Solar Cells

Printed metal halide perovskites can enable rapid, roll-to-roll manufacturing of a broad class of optoelectronics—flexible solar cells and imagers among them—while promising cost and speed advantages over incumbent silicon. However, though current methods offer high throughput and patterning capabilities, perovskite films’ spatial heterogeneity remains a challenge for large-area devices. Here, a spatial-uniformity-driven Bayesian optimization (BO) approach is leveraged to accelerate the development of printed perovskite solar cells and improve large-area device performance. Using a BO surrogate model, a 6D design space of ink chemistry and printing physics is explored via extensive iterative experimentation (≈100) informed by an objective function capturing spatial photoluminescence (PL) variance. It is discovered that optimizing for uniformity drives rapid advances in photovoltaic performance, yielding ≈20% power conversion efficiency (PCE) for small area (0.134 cm 2 ) devices and > 16% for large area (1 cm 2 ) devices. This machine-learning approach simultaneously enables rheological comparison of ink formulations that accelerate the leveling of Saffman-Taylor artifacts and improve film uniformity. Here, this showcases uniformity-driven BO as an efficient approach for uncovering the key printing physics and mitigating spatial heterogeneity to enable device scaling beyond small cell areas.

14 SOLAR ENERGY↗

DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗

DOE OSTI2025

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗

DOE OSTI2021

hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm

In this study, we present an $hr$ -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as $hr$ -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of $hr$ -adaptivity over both r - and $h$ -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that $hr$ -adaptivity can help satisfy geometric targets even when $r$ -adaptivity fails to do so, due to the topology of the initial mesh.

42 ENGINEERING↗

DOE OSTI2024

Topological Optimization with Big Steps

Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and backpropagate gradients only onto the simplices involved in particular pairs. We show how the cycles and chains used in the persistence calculation can be used to prescribe gradients to larger subsets of the domain. In particular, we show that in a special case, which serves as a building block for general losses, the problem can be solved exactly in linear time. This relies on another contribution of this paper, which eliminates the need to examine a factorial number of permutations of simplices with the same value. Here, we present empirical experiments that show the practical benefits of our algorithm: the number of steps required for the optimization is reduced by an order of magnitude.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2023

Multistage robust optimization for the day-ahead scheduling of hybrid thermal-hydro-wind-solar systems

The integration of large-scale uncertain and uncontrollable wind and solar power generation has brought new challenges to the operations of modern power systems. In a power system with abundant water resources, hydroelectric generation with high operational flexibility is a powerful tool to promote a higher penetration of wind and solar power generation. In this paper, we study the day-ahead scheduling of a thermal-hydro-wind-solar power system. The uncertainties of renewable energy generation, including uncertain natural water inflow and wind/solar power output, are taken into consideration. We explore how the operational flexibility of hydroelectric generation and the coordination of thermal-hydro power can be utilized to hedge against uncertain wind/solar power under a multistage robust optimization (MRO) framework. To address the computational issue, mixed decision rules are employed to reformulate the original MRO model with a multi-level structure into a bi-level one. Column-and-constraint generation (C &CG) algorithm is extended into the MRO case to solve the bi-level model. The proposed optimization approach is tested in three real-world cases. Furthermore, the computational results demonstrate the capability of hydroelectric generation to promote the accommodation of uncertain wind and solar power.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

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↗