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Results for “gradient-based optimization”

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

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189 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
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 OSTI2026

Adaptive Cybersecurity for Distributed Energy Resources (AdCyDER): Online Reinforcement Learning with Stackelberg-Optimized Defenses — Pipeline Architecture, Evaluation Methodology, and Findings from a Synthetic-Data Evaluation

This report documents the design and evaluation of an integrated online-learning pipeline developed within the AdCyDER project for Distributed Energy Resource (DER) cybersecurity. The pipeline couples a Reinforcement Learning (RL) attack classifier — which produces an attack-type probability distribution — with a Stackelberg game-theoretic (GT) defense selector that consumes those distributions alongside SME-encoded priors over (defense, attack) effectiveness pairings and perdefense costs to choose grid-health-preserving defenses. The objective is not attack classification per se but production of distributions that drive effective defense selection through the Stackelberg layer, learned from delayed grid-health feedback rather than labeled attack data. AdCyDER as a whole is broader than the work presented here; this report covers the specific RL/GT loop integration and its evaluation. We present the integrated pipeline (SCADA telemetry with Fronius inverter physics, Suricata IDS, time-windowed aggregation, per-facility LSTM classifier, Stackelberg optimizer, OpenC2 actuators), an experimental campaign of 28 eight-hour iterations across three baseline modes, and a pipeline-ordered diagnostic protocol. The protocol identifies two distinct failure modes within the loop: paired supervised ceilings on the same features establish that the deployed online RL classifier (macro F1 ≈ 0.07) sits at least 4.7× below a same-architecture supervised LSTM (≈ 0.34) and 10–11× below a linear feature-signal ceiling (≈ 0.70–0.79 depending on per-facility isolation), localizing the dominant failure to the training procedure; and the reward signal driving online updates carries weak directional coupling with classifier correctness in the methodology-expected direction (multi-lens convergent: top-decile P(true) records produce more frequent state changes and slightly larger improvements, top-vs-bot Cohen’s 𝑑 ≈ −0.19), but at effect magnitudes too small to drive gradient-based learning at the campaign sample size. The original learning hypothesis is not supported by the data. The primary contributions are the diagnostic methodology — proposed as a transferable falsification protocol for online RL/GT defense pipelines learning from delayed environmental reward — and the open, reproducible experimental infrastructure. We outline reward reformulation as the highest-priority aspirational next step given the underpowered-but-aligned Q6 reading, with hardware-in-the-loop evaluation as the broadest scope-expansion option.

Blakely, Benjamin [Argonne National Laboratory (AN↗
DOE OSTI2025

A direct-adjoint approach for material point model calibration with application to plasticity

Here, this paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton–Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

17 WIND ENERGY↗
DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗
NASA NTRS1992

Observations on computational methodologies for use in large-scale, gradient-based, multidisciplinary design incorporating advanced CFD codes

How a combination of various computational methodologies could reduce the enormous computational costs envisioned in using advanced CFD codes in gradient based optimized multidisciplinary design (MdD) procedures is briefly outlined. Implications of these MdD requirements upon advanced CFD codes are somewhat different than those imposed by a single discipline design. A means for satisfying these MdD requirements for gradient information is presented which appear to permit: (1) some leeway in the CFD solution algorithms which can be used; (2) an extension to 3-D problems; and (3) straightforward use of other computational methodologies. Many of these observations have previously been discussed as possibilities for doing parts of the problem more efficiently; the contribution here is observing how they fit together in a mutually beneficial way.

Newman, P. A.↗
NASA NTRS1992

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Madyastha, Raghavendra K.↗
DOE OSTI2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator↗