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Results for “Second-order 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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
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

Endogenous Interface Pricing for Consistent Transmission–Distribution Co-Optimization With Discrete Distribution Controls

This paper proposes an endogenous interface pricing model for day-ahead transmission–distribution co-optimization that co-determines the interface locational marginal price (LMP) and the transmission–distribution exchange, ensuring price–dispatch consistency while optimally scheduling discrete distribution controls. The formulation couples a DC optimal power flow (OPF) with a branch-flow AC OPF that schedules distributed energy resources (DERs), tap-changer settings, capacitor banks (CBs), and multi-period energy storage systems (ESSs) under feeder voltage and current limits, and is solved as a mixed-integer second-order cone program (MISOCP). In a T14–D33 system, coordinated device scheduling recovers about 90% of the distribution-to-transmission export achievable in a reference case that ignores distribution network (DN) limits, while satisfying a 1.05 p.u. voltage upper bound. In a T39–D34/D37/D123 system, a sequential decoupled benchmark produces interface LMP distortions up to 12.5% and a 7.28% mismatch in net export energy, whereas the proposed model removes these distortions and the associated settlement mismatches. Second-order cone (SOC) relaxation gaps remain below $10^{-3}$ in all cases.

Noh, Seung-Gil↗
NASA NTRS1979

Analysis and design of an adaptive multi-loop controlled two winding buck/boost regulator

Small signal low frequency linear average model is derived for a multi-loop controlled two-winding buck/boost converter employing average techniques and the describing function method. The model reveals that a well-designed multi-loop control can provide a second-order zero adaptive to output filter parameter changes due to component tolerances, temperature changes, aging, and the effect of duty cycle modulation. It also can provide stabilization effect by shifting the positive zero to the left-half S-plane. Design guidelines are formulated to optimize regulator-loop dependent characteristics.

Mahmoud, M. F.↗
NASA NTRS1972

Criteria for the optimal design of experimental tests

Some of the basic concepts are unified that were developed for the problem of finding optimal approximating functions which relate a set of controlled variables to a measurable response. The techniques have the potential for reducing the amount of testing required in experimental investigations. Specifically, two low-order polynomial models are considered as approximations to unknown functionships. For each model, optimal means of designing experimental tests are presented which, for a modest number of measurements, yield prediction equations that minimize the error of an estimated response anywhere inside a selected region of experimentation. Moreover, examples are provided for both models to illustrate their use. Finally, an analysis of a second-order prediction equation is given to illustrate ways of determining maximum or minimum responses inside the experimentation region.

Canavos, G. C.↗
DOE OSTI2025

Simulating quantum-classical interfaces via the Lindblad master equation

In hybrid quantum systems, the interface between quantum and classical domains is essential for the generation, control, and measurement of quantum states. Quantum-classical interfaces (QCIs) are ubiquitous in devices such as optical modulators, quantum sensors, and signal processors, where classical signals influence quantum dynamics. In this paper, we employ the Lindblad master equation to simulate the evolution of a quantum system interacting with a classical control system. Our model captures both linear and nonlinear interactions by incorporating first- and second-order susceptibilities, and it quantifies the influence of externally applied control parameters on decoherence and state evolution. As an illustrative example, we analyze an optical modulator and demonstrate how variations in material response and drive conditions affect photon statistics, coherence, and phase-space distributions. In conclusion, the findings offer a path to an all-encompassing model for understanding and optimizing QCIs, with wide-ranging implications for the performance, design, and robustness of next-generation quantum devices.

Quantum engineering↗
DOE OSTI2026

Two datasets are better than one: method of double moments for 3D reconstruction in cryo-EM

Cryo-electron microscopy is a powerful imaging technique for reconstructing three-dimensional molecular structures from noisy tomographic projection images of randomly oriented particles. We introduce a new data fusion framework, termed the method of double moments, which reconstructs molecular structures from two instances of the second-order moment of projection images obtained under distinct orientation distributions: one uniform, the other non-uniform and unknown. We prove that these moments generically uniquely determine the underlying structure, up to a global rotation and reflection, and we develop a convex-relaxation-based algorithm that achieves accurate recovery using only second-order statistics. Our results demonstrate the advantage of collecting and modeling multiple datasets under different experimental conditions, illustrating that leveraging dataset diversity can substantially enhance reconstruction quality in computational imaging tasks.

Kam’s method↗
DOE OSTI2026

Deep learning-assisted modeling for χ (2) nonlinear optics

Modeling second-order (χ(2)) nonlinear optical processes remains computationally expensive due to the need to resolve fast field oscillations and simulate wave propagation using methods such as the split-step Fourier method (SSFM). This can become a bottleneck in real-time applications, such as high-repetition-rate laser systems requiring rapid feedback and control. We present a long short-term memory-based surrogate model trained on SSFM simulations generated from a start-to-end model of the photocathode drive laser at SLAC National Accelerator Laboratory’s Linac Coherent Light Source II. The model achieves over 250× speedup while maintaining high fidelity, enabling future real-time optimization and laying the foundation for data-integrated modeling frameworks and digital twins of laser systems.

Accelerator Physics (physics.acc-ph)↗
DOE OSTI2026

Correlation of Surface Acoustic Wave (SAW) force myography sensor output with elbow joint torque

Accurate assessment of skeletal muscle forces and net joint torque is essential for preventing fatigue-related injuries, optimizing physical training, and monitoring disease progression in neuromuscular conditions. However, existing joint torque evaluation techniques are hindered by limited portability and high operational costs, confining their use to controlled laboratory or clinical settings. Despite substantial advances in wearable joint torque estimation systems, ongoing challenges such as power constraints, bulky wired setups, and susceptibility to environmental or motion artifacts underscore the urgent need for truly batteryless, wireless solutions deployable in real-world settings. This paper proposes a novel surface acoustic wave (SAW)-based force myography (FMG) system for noninvasive measurement of joint torque, validated against a gold-standard electromechanical dynamometer. The approach uses a single SAW sensor embedded in an armband to detect volumetric biceps brachii changes, with a second-order polynomial mapping sensor output and elbow angle to torque. Seven participants were tested in both isometric (15°–90°) and isokinetic (10°/s and 20°/s) supinated elbow flexion tasks. Under isometric conditions, subject-specific calibration achieved a normalized root-mean-square error (NRMSE) of 13.6% ± 6.0% and R 2 = 0.834 ± 0.180, while a group-level model yielded 14.4% ± 6.8% and 0.808 ± 0.208, respectively. For isokinetic trials, the group model produced an NRMSE of 24.1% ± 6.6% at 10°/s and 24.9% ± 08.9% at 20°/s, highlighting the feasibility of using a single-sensor SAW-FMG setup across different speeds. Because SAW devices support wireless, battery-free operation, the proposed system offers a pathway to portable, real-time monitoring for sports medicine, rehabilitation, and clinical diagnostics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2026

Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2025

Using Separation-Enhanced Isotope Ratio Mass Spectrometry to Enable Increased Renewable Carbon Content in Transportation Fuels (CRADA 525)

Stable isotope ratio measurements of carbon atoms using isotope ratio mass spectrometry (IRMS) can be an effective tool for quantifying biogenic carbon in co-processed fuels, with results approaching the precision and accuracy of accelerator mass spectrometry (AMS). The lower cost of an IRMS may enable deployment to refineries, improving access and analysis turnaround times (≤2 hours), and, by extension, provide data that can allow process optimization to maximize renewable carbon in desired refinery products. This project explored the integration of chemical separation with IRMS analyses to enable highly detailed tracking of biogenic carbon into fuel product streams separated by boiling point range, chemical class, or specific compound. Forty-nine fuels and fuel components of fossil and biogenic origin, spanning gasoline and diesel boiling point ranges, were received from three refiners and were analyzed for their δ 13 C values via IRMS. Results spanned a 13 C range from ca. 10‰ to 44‰ and reflect materials derived from sustainable sources (e.g., C4 or C3 plants, animal-based pathways, syngas) or from fossil-derived fuels. Common ranges are approximately 18‰ to 9‰ and approximately 30‰ to 20‰ for C4 and C3 plants, respectively, and approximately 34‰ to 24‰ and approximately 70‰ to 33‰ for petroleum-derived fuels and methane, respectively. Fuel-like standards were developed and tested using direct-injection elemental analyzer (EA) IRMS for liquid fuels. This method was compared with the published methods, yielding statistically similar results. Four blend curve sets were produced ranging from 0% to 100% of a fuel containing biogenic carbon, focusing on 0% to 10% biogenic carbon. Linear fits were the most applicable for two of the four blend curve sets; however, two sets were found to exhibit slightly quadratic behavior, which was more pronounced in low biogenic blend samples, necessitating second-order fits. The origin of the slight quadratic behavior remains unclear; however, the discussion points to possible interpretations. CanmetENERGY thoroughly characterized a majority of the samples using one- and two-dimensional gas chromatography (GC and GC×GC, respectively) and other analyses. Selected samples were subjected to solid phase extraction (SPE) for saturate, olefin, aromatic, and polar (SOAP) analysis, and the resulting solvent-diluted fractions containing saturates and aromatics were returned to Pacific Northwest National Laboratory (PNNL), where the solvent was removed via evaporation or physical separation using GC techniques. Characterization and separations provided an understanding of saturate and aromatic content, as well as boiling point ranges for each sample and sample fraction. Samples resulting from SPE were examined using EA-IRMS and gas chromatography combustion IRMS (GC-C-IRMS) analyses. Both approaches suggest that the range in values between end-members can be increased by selecting the paraffinic or aromatic fraction of the end-member or by selecting among individual compounds resulting from GC separation of the paraffinic fractions. Considerable work remains to put these approaches into practice and statistically validate the benefit for using a fraction or individual compound over bulk analysis of a sample. However, initial results suggest that separations provide advantages for samples having blend ratios of less than 10% biogenic blendstocks. 13 C results showed statistically similar biofuel blend results to those obtained at PNNL, although additional work is needed to obtain better reproducibility. Select samples were sent to Los Alamos National Laboratory (LANL) for IRMS measurements and Beta Analytics for AMS measurements. This work suggests that IRMS and AMS yield closely comparable results and in some circumstances, IRMS could serve as a surrogate for AMS. While additional work is needed to better resolve statistical advantages for separations and better show the comparable nature of IRMS and AMS in both the biogenic carbon analysis of bulk chemical classes, initial results from this study suggest that these should be pursued in order to proliferate this approach for quantifying biogenic carbon in transportation fuels to the refinery level, thereby potentially enabling process optimization in co-processing scenarios.

09 BIOMASS FUELS↗
DOE OSTI2026

An efficient level set method for tracking many materials

Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗
DOE OSTI2025

Efficient near-field ptychography reconstruction using the Hessian operator

X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.

Carlsson, Marcus [Lund Univ. (Sweden)] (ORCID:0000↗
NASA NTRS1972

On optimizing the treatment of exchange perturbations.

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Hirschfelder, J. O.↗