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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 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 OSTI2023

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗
DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗
DOE OSTI2021

On a nonlocal Cahn–Hilliard model permitting sharp interfaces

A nonlocal Cahn–Hilliard model with a non-smooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg–Landau energy functional is defined which recovers the classical (local) model as the extent of nonlocal interactions vanish. In contrast to the local Cahn–Hilliard problem that always leads to diffuse interfaces, the proposed nonlocal model can lead to a strict separation into pure phases of the substance. In this work, the lack of smoothness of the potential is essential to guarantee the aforementioned sharp-interface property. Mathematically, this introduces additional inequality constraints that, in a weak formulation, lead to a coupled system of variational inequalities which at each time instance can be restated as a constrained optimization problem. We prove the well-posedness and regularity of the semi-discrete and continuous in time weak solutions, and derive the conditions under which pure phases are admitted. Moreover, we develop discretizations of the problem based on finite element methods and implicit–explicit time-stepping methods that can be realized efficiently. Finally, we illustrate our theoretical findings through several numerical experiments in one and two spatial dimensions that highlight the differences in features of local and nonlocal solutions and also the sharp interface properties of the nonlocal model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Non-cooperative Game-based Approach to Distributed Beam Scheduling in Millimeter-Wave Networks

We consider the distributed beam scheduling problem in mm-Wave networks where the base stations may belong to different operators and there is no centralized coordination among them. Our goal is to design distributed beam scheduling algorithms such that the network utility, which is defined as a logarithm function of the average throughput of the user equipment, can be maximized. We propose a non-cooperative game-based scheduling approach where the base stations are modeled as players that greedily maximize their own utilities. The Nash Equilibrium (NE) then provides a distributed solution to the network utility maximization problem. By employing the Lyapunov optimization, the asymptotic optimality of the proposed scheduling can be guaranteed. We prove the existence and provide sufficient conditions which guarantee the uniqueness of the NE by establishing an equivalence to the Variational Inequality (VI) problem. We also propose a parallel power adaptation algorithm which is proved to converge to the NE. Numerical results show the superiority of the proposed scheduling over several distributed baseline schemes.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2021

TAO Users Manual (Rev. 3.15)

The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints. The development of TAO was motivated by the scattered support for parallel computations and the lack of reuse of external toolkits in current optimization software. Our aim is to produce high-quality optimization software for computing environments ranging from workstations and laptops to massively parallel high-performance architectures. Our design decisions are strongly motivated by the challenges inherent in the use of large-scale distributed memory architectures and the reality of working with large, often poorly structured legacy codes for specific applications.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Can socio-economic indicators of vulnerability help predict spatial variations in the duration and severity of power outages due to tropical cyclones?

Abstract Tropical cyclones are the leading cause of major power outages in the U.S., and their effects can be devastating for communities. However, few studies have holistically examined the degree to which socio-economic variables can explain spatial variations in disruptions and reveal potential inequities thereof. Here, we apply machine learning techniques to analyze 20 tropical cyclones and predict county-level outage duration and percentage of customers losing power using a comprehensive set of weather, environmental, and socio-economic factors. Our models are able to accurately predict these outage response variables, but after controlling for the effects of weather conditions and environmental factors in the models, we find the effects of socio-economic variables to be largely immaterial. However, county-level data could be overlooking effects of socio-economic disparities taking place at more granular spatial scales, and we must remain aware of the fact that when faced with similar outage events, socio-economically vulnerable communities will still find it more difficult to cope with disruptions compared to less vulnerable ones.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Solar cities: A case study analysis of city-level enablers of expanded solar energy access

Rooftop solar photovoltaic (PV) adoption can benefit households by reducing electricity bills and enhancing energy resiliency. Low and moderate-income (LMI) households have been less likely to adopt PV and experience these benefits in the United States than higher-income households. Adopter income trends are often explored through quantitative analysis with limited explanatory power. Our quantitative analysis only explains around one-third of city-level variation in LMI adoption trends through socioeconomic factors such as median home values and income inequality and PV market factors such as cumulative adoption and incentives. We implement semi-structured interviews in three case studies of cities with relatively high rates of LMI PV adoption to better understand the factors that explain PV adopter income trends. The case studies partly reiterate findings from quantitative analysis, such as the role of PV incentives. The case studies reveal a broader set of LMI adoption drivers that are missed in quantitative analyses. The case studies show how city contexts can affect LMI adoption, such as the role of supportive city governments. The case studies also reveal the importance of partnerships, such as partnerships between city governments and state LMI PV program implementers. Finally, interviewees emphasized the importance of building trust among prospective LMI PV adopters. Interviewees suggested that partnerships, outreach, and consumer protection measures were crucial to building trust in PV installers among LMI households.

Adoption↗
DOE OSTI2024

Assessment of U.S. Urban Surface Temperature Using GOES-16 and GOES-17 Data: Urban Heat Island and Temperature Inequality

Abstract This study utilizes hourly land surface temperature (LST) data from the Geostationary Operational Environmental Satellite (GOES) to analyze the seasonal and diurnal characteristics of surface urban heat island intensity (SUHII) across 120 largest U.S. cities and their surroundings. Distinct patterns emerge in the classification of seasonal daytime SUHII and nighttime SUHII. Specifically, the enhanced vegetation index (EVI) and albedo (ALB) play pivotal roles in influencing these temperature variations. The diurnal cycle of SUHII further reveals different trends, suggesting that climate conditions, urban and nonurban land covers, and anthropogenic activities during nighttime hours affect SUHII peaks. Exploring intracity LST dynamics, the study reveals a significant correlation between urban intensity (UI) and LST, with LST rising as UI increases. Notably, populations identified as more vulnerable by the social vulnerability index (SVI) are found in high UI regions. This results in discernible LST inequality, where the more vulnerable communities are under higher LST conditions, possibly leading to higher heat exposure. This comprehensive study accentuates the significance of tailoring city-specific climate change mitigation strategies, illuminating LST variations and their intertwined societal implications.

Environmental Sciences & Ecology↗
DOE OSTI2020

Primal interface debonding formulation for finite strain isotropic plasticity

In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.

42 ENGINEERING↗
DOE OSTI2024

Urban Land Surface Temperature Downscaling in Chicago: Addressing Ethnic Inequality and Gentrification

In this study, we developed a XGBoost-based algorithm to downscale 2 km-resolution land surface temperature (LST) data from the GOES satellite to a finer 70 m resolution, using ancillary variables including NDVI, NDBI, and DEM. This method demonstrated a superior performance over the conventional TsHARP technique, achieving a reduced RMSE of 1.90 °C, compared to 2.51 °C with TsHARP. Our approach utilizes the geostationary GOES satellite data alongside high-resolution ECOSTRESS data, enabling hourly LST downscaling to 70 m—a significant advancement over previous methodologies that typically measure LST only once daily. Applying these high-resolution LST data, we examined the hottest days in Chicago and their correlation with ethnic inequality. Our analysis indicated that Hispanic/Latino communities endure the highest LSTs, with a maximum LST that is 1.5 °C higher in blocks predominantly inhabited by Hispanic/Latino residents compared to those predominantly occupied by White residents. This study highlights the intersection of urban development, ethnic inequality, and environmental inequities, emphasizing the need for targeted urban planning to mitigate these disparities. The enhanced spatial and temporal resolution of our LST data provides deeper insights into diurnal temperature variations, crucial for understanding and addressing the urban heat distribution and its impact on vulnerable communities.

Lee, Jangho (ORCID:0000000289421092)↗
DOE OSTI2024

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

97 MATHEMATICS AND COMPUTING↗