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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Convex Optimization with Smart Grid Examples

In this talk, we give an overview of the field of convex optimization and work through four canonical problems that relate to electrical power systems and smart grids. The purpose of these examples is to demonstrate the breadth of applications of convex optimization in energy research and to show that toy versions of these problems can be solved in just a few lines of code, indicating the scale and complexity of problems that can be tackled with a more detailed treatment. We emphasize the cvxpy modeling language as a foundational technology that enables rapid development and prototyping of convex optimization problems, allowing researchers to focus on model development rather than get caught in the weeds of numerical and code implementation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Using Convex Optimization to Efficiently Apportion Tracer and Pollutant Sources From Point Concentration Observations

Abstract Rivers transport elements, minerals, chemicals, and pollutants produced in their upstream basins. A sample from a river is a mixture of all of its upstream sources, making it challenging to pinpoint the contribution from each individual source. Here, we show how a nested sample design and convex optimization can be used to efficiently unmix downstream samples of a well‐mixed, conservative tracer in a steady state system into the contributions of their upstream sources. Our approach is significantly faster than previous methods. We represent the river's sub‐catchments, defined by sampling sites, using a directed acyclic graph. This graph is used to build a convex optimization problem which, thanks to its convexity, can be quickly solved to global optimality—in under a second on desktop hardware for data sets of ∼100 samples or fewer. Uncertainties in the upstream predictions can be generated using Monte Carlo resampling. We provide an open‐source implementation of this approach in Python. The inputs required are straightforward: a table containing sample locations and observed tracer concentrations, along with a D8 flow‐direction raster map. As a case study, we use this method to map the elemental geochemistry of sediment sources for rivers draining the Cairngorms mountains, UK. This method could be extended to non‐conservative and non‐steady state tracers. We also show, theoretically, how multiple tracers could be simultaneously inverted to recover upstream run‐off or erosion rates as well as source concentrations. Overall, this approach can provide valuable insights to researchers in various fields, including water quality, geochemical exploration, geochemistry, hydrology, and wastewater epidemiology.

Barnes, Richard↗
DOE OSTI2024

Convex optimization of contour deformations

We discuss various formal aspects of contour deformations used to alleviate sign problems; most importantly, relating these contour deformations to a certain convex optimization problem. As a consequence of this connection we describe a general method for proving upper bounds on the average phase achievable by the contour deformation method. Using this method we show that Abelian lattice Yang-Mills in two spacetime dimensions possesses, for many values of the complex coupling, an exponential sign problem that cannot be removed via any contour deformation. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Parallel hybrid quantum-classical machine learning for kernelized time-series classification

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. Here, in this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a timeseries Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗
DOE OSTI2024

Automatic Loss Factor Modeling and Attribution on Unlabeled PV Energy Data

We present a novel approach for modeling the loss factors of photovoltaic power generation systems (PV systems). This method is a white-box machine learning model built on convex optimization that is fast, interpretable, and auditable. It takes as an input the measured daily energy produced by the system, over a multi-year period, and returns a multiplicative decomposition model of the daily energy signal and full attribution of the total energy loss to each feature. The methods section of this paper has two major components: (1) the description of the signal decomposition (SD) model, expressed in the SD framework, and (2) the attribution of total energy losses via Shapley values. We validate the method on synthetic and open-source data sets and compare to similar methods from the literature.

artificial intelligence↗
DOE OSTI2025

Optimizing on-ramp merging for connected and automated vehicles: A hierarchical approach using deep reinforcement learning and optimal control

On-ramp merging for Connected and Automated Vehicles (CAVs) presents significant challenges in dynamic traffic environments. Traditional methods and recent learning-based approaches often fail to simultaneously address decision-making complexity and execution precision under fluctuating conditions. This study introduces a novel hierarchical framework that combines: (1) a high-level Deep Reinforcement Learning (DRL) module that coordinates merging sequences through Virtual Traffic Signals (VTS) with Yield/Green phases and (2) a low-level optimal controller generating collision-free speed trajectories via pseudospectral convex optimization. A convolutional autoencoder compresses high-dimensional traffic states to enhance responsiveness. Extensive simulations demonstrate a 12.5% improvement in mainline throughput a 28% reduction in emergency braking events, and 31.66% lower fuel consumption compared to baseline methods. Furthermore, the framework’s effectiveness in coordinating CAV merges highlights its potential for real-world deployment. Future work will extend validation to multi-lane scenarios with mixed traffic and large-scale multiple merging points.

Connected and automated vehicles↗
DOE OSTI2024

ACOPF Transmission Switching Using Open-Source MINLP Solvers

The optimal transmission switching (OTS) problem with AC physics represents a mixed integer non-linear non-convex optimization problem which can provide benefits to transmission level power system operations. In this paper we benchmark a set of open-source mixed integer non-linear programming (MINLP) solvers on the OTS problem with AC physics using the pglib set of power system test cases. Results characterizing the performance of the different solvers are reported and discussed.

ACOPF↗
DOE OSTI2026

ZEUS: An Efficient GPU Optimization Method Integrating PSO, BFGS, and Automatic Differentiation

We introduce a novel, efficient computational method, ZEUS, for numerical optimization, and provide an open-source implementation. It has four key ingredients: (1) particle swarm optimization (PSO), (2) the use of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, (3) automatic differentiation (AD), and (4) GPUs. Our approach addresses the computational challenges inherent in high-dimensional, non-convex optimization problems. In the first phase of the algorithm, we get a potentially good set of starting points using PSO. Thereafter, we run BFGS independently in parallel from these starting points. BFGS is one of the best-performing algorithms for numerical optimization. However, it requires the gradient of the function being optimized. ZEUS integrates automatic differentiation into BFGS thus avoiding the need for the user to calculate derivatives explicitly. The use of GPUs allows ZEUS to speed up the calculations substantially. We carry out systematic studies to explore the trade-offs between the number of PSO iterations taken, starting points, and BFGS iteration depth. We show that a handful of iterations of PSO can improve global convergence when combined with BFGS. We also present performance studies using common test functions. The source code can be found at https://github.com/fnal-numerics/global-optimizer-gpu.

Soos, Dominik [Old Dominion U.]↗
DOE OSTI2024

An OpenStreetMaps based tool to study the energy demand and emissions impact of electrification of medium and heavy-duty freight trucks

In this paper, we present the mathematical formulation of an OpenStreetMaps (OSM) based tool that compares the costs and emissions of long-haul medium and heavy-duty (M&HD) electric and diesel freight trucks, and determines the spatial distribution of added energy demand due to M&HD EVs. The optimization utilizes a combination of information on routes from OSM, utility rate design data across the United States, and freight volume data, to determine these values. In order to deal with the computational complexity of this problem, we formulate the problem as a convex optimization problem that is scalable to a large geographic area. In our analysis, we further evaluate various scenarios of utility rate design (energy charges) and EV penetration rate across different geographic regions and their impact on the operating cost and emissions of the freight trucks. Our approach determines the net emissions reduction benefits of freight electrification by considering the primary energy source in different regions. Such analysis will provide insights to policy makers in designing utility rates for electric vehicle supply equipment (EVSE) operators depending upon the specific geographic region and to electric utilities in deciding infrastructure upgrades based on the spatial distribution of the added energy demand of M&HD EVs. To showcase the results, a case study for the U.S. state of Texas is conducted.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗
DOE OSTI2025

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.

bilevel optimization↗
DOE OSTI2026

An information-matching approach to optimal experimental design and active learning

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher information matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. Here, we demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an active learning (AL) loop for materials science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly AL in large machine-learning models.

Materials science↗
DOE OSTI2024

Interpretable Net Load Forecasting Using Smooth Multiperiodic Features

We consider the problem of forecasting net load over a horizon such as one day, using a trailing window of past net load values as well as date and time. We focus on three variations on this problem: point forecasts, marginal quantile forecasts, and generating conditional samples of the future value. We propose a method that relies on linear regression using some custom engineered time-based features to capture multiple periodicities, such as daily, weekly, and seasonal, and their interactions. Our proposed models are readily interpretable, and rely on efficient and reliable convex optimization [1] to fit. We illustrate our method on four years worth of hourly net load data, comparing predictions made with various subsets of the features.

Ogut, Mehmet G↗
DOE OSTI2024

Time Dilated Bundt Cake Analysis of PV Output [Poster]

We present a novel method for modeling time-dependent statistics in the power signal generated by a photovoltaic (PV) system. Our white-box machine learning method is interpretable and auditable, based on principles of multiperiodic basis functions and convex optimization. Our proposed method of time dilating the daily signal to remove night time values results in a novel representation of PV power signals, evocative of a ‘Bundt cake’. The proposed model describes the marginal distribution of power output as a function of date and time. The resulting probabilistic model of a PV system can be used to perform a variety of tasks, and here, we demonstrate the application of clear sky detection.

14 SOLAR ENERGY↗