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Results for “Nonlinear reduction”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification

Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Parametric Finite Element Analysis of Naturally Corroded Steel Specimens Using 3D Surface Laser Scans

Corrosion is considered a uniform thickness reduction design guideline of the maritime industry. However, additionally, the corroded and irregular morphology of the surface affects the steel's load-bearing capacity and its impact on the strength and elongation behaviour of the steel is not yet fully understood. These effects on the local behaviour of steel structures under tensile loading were investigated with tensile tests on naturally corroded steel specimens and nonlinear finite element simulations including the corroded surface morphology with a uniform surface idealation. The models also include the deformed specimen shape. The developed approach led to highly accurate parametric finite element models predicting the ultimate tensile strength and longitudinal position of fracture. The results show that all included aspects are essential for accurate simulations, while solely the maximum available surface resolution was not as decisive.

corrosion↗
DOE OSTI2021

Electrocatalytic Reduction of CO 2 to CO over Ag(110) and Cu(211) Modeled by Grand-Canonical Density Functional Theory

We report the results of modeling CO 2 reduction (CO 2 R) to CO over Ag(110) and Cu(211) surfaces at different applied potentials using grand-canonical density functional theory (GC-DFT), a method specifically designed to accurately model electrochemical systems. In addition to demonstrating GC-DFT’s ability to accurately model electrochemical processes, we also compare it with the computational hydrogen electrode (CHE) approach. GC-DFT predicts that the geometries of these reacting systems strongly depend on the applied potential and the Helmholtz free energies vary nonlinearly with the applied potential, which contradicts a central assumption of the CHE approach. The CHE approach neglects the change in the number of electrons on the electrode surface at different applied potentials, which reduces its accuracy as the potential changes from the potential of zero charge. Our results further demonstrate that the grand free energies of the reaction intermediates not only depend on the value of the applied potential but also on the metal surface type, adsorption site, and adsorbate. GC-DFT’s ability to predict the effect of the applied potential on adsorbate geometry enables it to evaluate different possible reaction mechanisms at different applied potentials. For instance, GC-DFT predicts that the first step of CO2R likely switches from proton-coupled electron transfer to sequential electron transfer and then proton transfer at more reducing potentials, a result that cannot be determined by the CHE because it assumes that all electron transfers are coupled to proton transfers and neglects the effect of the applied potential on the adsorbate geometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Probing lithium mobility at a solid electrolyte surface

Abstract Solid-state electrolytes overcome many challenges of present-day lithium ion batteries, such as safety hazards and dendrite formation 1,2 . However, detailed understanding of the involved lithium dynamics is missing due to a lack of in operando measurements with chemical and interfacial specificity. Here we investigate a prototypical solid-state electrolyte using linear and nonlinear extreme-ultraviolet spectroscopies. Leveraging the surface sensitivity of extreme-ultraviolet-second-harmonic-generation spectroscopy, we obtained a direct spectral signature of surface lithium ions, showing a distinct blueshift relative to bulk absorption spectra. First-principles simulations attributed the shift to transitions from the lithium 1 s state to hybridized Li- s /Ti- d orbitals at the surface. Our calculations further suggest a reduction in lithium interfacial mobility due to suppressed low-frequency rattling modes, which is the fundamental origin of the large interfacial resistance in this material. Our findings pave the way for new optimization strategies to develop these electrochemical devices via interfacial engineering of lithium ions.

25 ENERGY STORAGE↗
DOE OSTI2021

Investigation of UV filaments and their applications

UV laser pulses at 266 nm with 170 ps duration and up to 300 mJ energy create UV filaments. The effects of different beam preparation scenarios on UV filamentation are discussed. Beam preparation by focusing in vacuum and launching into the atmosphere through an aerodynamic window establishes the existence of filaments as self-guided non-diffracting entities. In addition, focusing through the aerodynamic window converts the initial super-Gaussian into a parabolic beam profile at the edge of the nonlinear medium (air). The shock-wave generated by the UV filament is investigated via shadowgraphy techniques. The shock-wave is cylindrically symmetric, leaving a low density channel behind, which is well-sustained for 1 ms, as it propagates outward. This low density channel is a waveguide that can be used for guiding purposes. Applications of UV filaments including guiding, remote sensing, and drag reduction for supersonic aircrafts are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Multigrid Reduction in Time for Chaotic Dynamical Systems

As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a significant bottleneck, as many types of simulations require large numbers of time-steps which must be computed sequentially. Parallel-in-time schemes, such as the Multigrid Reduction in Time (MGRIT) method, remedy this by parallelizing across time-steps and have shown promising results for parabolic problems. However, chaotic problems have proved more difficult, since chaotic initial value problems (IVPs) are inherently ill-conditioned. MGRIT relies on a hierarchy of successively coarser time-grids to iteratively correct the solution on the finest time-grid, but due to the nature of chaotic systems, small inaccuracies on the coarser levels can be greatly magnified and lead to poor coarse-grid corrections. Here we introduce a modified MGRIT algorithm based on an existing quadratically converging nonlinear extension to the multigrid Full Approximation Scheme (FAS), as well as a novel time-coarsening scheme. Together, these approaches better capture long-term chaotic behavior on coarse-grids and greatly improve convergence of MGRIT for chaotic IVPs. Further, we introduce a novel low-memory variant of the algorithm for solving chaotic PDEs with MGRIT which not only solves the IVP, but also provides estimates for the unstable Lyapunov vectors of the system. Finally, we provide supporting numerical results for the Lorenz system and demonstrate parallel speedup for the chaotic Kuramoto–Sivashinsky PDE over a significantly longer time-domain than in previous works.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Evidence for a thermally driven charge-density-wave transition in 1T-TaS 2 thin-film devices: Prospects for GHz switching speed

We report on the room-temperature switching of 1T-TaS 2 thin-film charge-density-wave devices, using nanosecond-duration electrical pulsing to construct their time-resolved current–voltage characteristics. The switching action is based upon the nearly commensurate to incommensurate charge-density-wave phase transition in this material, which has a characteristic temperature of 350 K at thermal equilibrium. For sufficiently short pulses, with rise times in the nanosecond range, self-heating of the devices is suppressed, and their current–voltage characteristics are weakly nonlinear and free of hysteresis. This changes as the pulse duration is increased to ~200 ns, where the current develops pronounced hysteresis that evolves nonmonotonically with the pulse duration. By combining the results of our experiments with a numerical analysis of transient heat diffusion in these devices, we clearly reveal the thermal origins of their switching. In spite of this thermal character, our modeling suggests that suitable reduction of the size of these devices should allow their operation at GHz frequencies.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effects of hydrogen isotope species on ITG microturbulence in LHD

Abstract The linear and nonlinear effects of hydrogen isotope species on ion temperature gradient (ITG) instability in the Large Helical Device (LHD) stellarator are studied using radially global gyrokinetic simulation. We found that the coupling range of linear toroidal harmonics depends on the ion mass of the hydrogen isotope. The growth rates of ITG mode are almost the same for H, D, and T plasmas, indicating a gyro-Bohm scaling of ion-mass dependence. The nonlinear electrostatic simulations show that the zonal flow breaks the radially elongated eigenmode structures and reduces the size of the turbulence eddies, which suppresses the turbulence and the ion heat transport in the LHD. The turbulence amplitude without the zonal flow is almost the same for H, D, and T plasmas, while it decreases with increasing ion mass of the hydrogen isotope when the zonal flow is present. The reduction of the turbulent transport with larger ion mass is mostly due to the enhancement of zonal flows by larger ion mass. The ion heat conductivity deviates from the gyro-Bohm scaling for both cases with and without the zonal flow.

Physics↗
DOE OSTI2021

Applying Time-Parallelization to Turbulent Flows

Parallelization of the temporal domain is explored for the solution of turbulent flows. Multigrid reduction-in-time (MGRIT) is used to advance the large-scale fluid dynamics in time sequentially on the coarsest space-time grid but propagate the information in time parallel on all other levels. The goal of this process is to accurately and efficiently resolve the coarse-scale turbulence structure and use that to drive the fine-scales of the turbulent flow. The extra forcing from nonlinear multigrid facilitates the coupling and interaction between fine and coarse scales, through which the multiscale nonlinear physics is properly captured. Adaptive mesh refinement is employed to finely resolve only the regions with strong gradients, which provides further computational efficiency. The underlying computational fluid dynamics solver is a fourth-order finite-volume scheme with the standard 4-stage Runge-Kutta method. An advanced approach is devised and implemented to enable MGRIT to solve highly turbulent flows successfully. Furthermore, the method is applied to solve a Taylor-Green vortex problem and a doubleshear-layer turbulent mixing flow. Results are promising, validating that MGRIT with the filtering approach has the potential to efficiently solve general turbulent flows.

Computational Fluid Dynamics↗
DOE OSTI2025

Unraveling Hydrogen Induced Geochemical Reaction Mechanisms through Coupled Geochemical Modeling and Machine Learning

Underground hydrogen storage (UHS) provides a promising large-scale, long-term energy storage solution. A reasonable recovery of stored hydrogen is critical for a successful storage scheme. However, in subsurface reservoirs hydrogen is subject to active geochemical reactions that might result in hydrogen loss. In this study, we implemented a geochemical modeling approach coupled with an unsupervised machine learning technique called non-negative matrix factorization (NMF) to unravel the complex brine-rock-H 2 geochemical processes responsible for hydrogen losses, with particular focus on sulfate reduction reactions. NMF is applied to modeled mineral evolution and fluid component profiles to retrieve profiles that can be interpreted to more easily assess competing processes. NMF decouples simulated competing equilibrium reactions. This facilitates separation of overlapping reaction profiles from redox processes, dissolution fronts, and secondary precipitation while considering the effects of simulation parameters such as salinity, temperature, and total H 2 pressure. NMF successfully discriminates these competing effects in nonlinear ways, allowing robust interpretation. In addition, NMF reveals subtle coupled mineral associations and reaction fronts that are invisible to conventional model analysis. This integrated approach strengthens the conceptual understanding of complex nonlinear hydrogen-brine-rock interactions and advances geochemical research on UHS systems to resolve complexities in modeled geochemical systems without the need for direct experiments or prior knowledge. Furthermore, this study highlights the efficacy of combining geochemical modeling with machine learning techniques to enhance the interpretability of the intricate geochemical simulation output through deciphering the overlapping reaction path that cannot be achieved only using conventional analysis of geochemical models alone.

08 HYDROGEN↗
DOE OSTI2022

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr 3 ) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

INTEGRATE - Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements

The INTEGRATE (Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements) project is developing a new inverse-design capability for the aerodynamic design of wind turbine rotors using invertible neural networks. This AI-based design technology can capture complex non-linear aerodynamic effects while being 100 times faster than design approaches based on computational fluid dynamics. This project enables innovation in wind turbine design by accelerating time to market through higher-accuracy early design iterations to reduce the levelized cost of energy. INVERTIBLE NEURAL NETWORKS Researchers are leveraging a specialized invertible neural network (INN) architecture along with the novel dimension-reduction methods and airfoil/blade shape representations developed by collaborators at the National Institute of Standards and Technology (NIST) learns complex relationships between airfoil or blade shapes and their associated aerodynamic and structural properties. This INN architecture will accelerate designs by providing a cost-effective alternative to current industrial aerodynamic design processes, including: - Blade element momentum (BEM) theory models: limited effectiveness for design of offshore rotors with large, flexible blades where nonlinear aerodynamic effects dominate - Direct design using computational fluid dynamics (CFD): cost-prohibitive - Inverse-design models based on deep neural networks (DNNs): attractive alternative to CFD for 2D design problems, but quickly overwhelmed by the increased number of design variables in 3D problems AUTOMATED COMPUTATIONAL FLUID DYNAMICS FOR TRAINING DATA GENERATION - MERCURY FRAMEWORK The INN is trained on data obtained using the University of Marylands (UMD) Mercury Framework, which has with robust automated mesh generation capabilities and advanced turbulence and transition models validated for wind energy applications. Mercury is a multi-mesh paradigm, heterogeneous CPU-GPU framework. The framework incorporates three flow solvers at UMD, 1) OverTURNS, a structured solver on CPUs, 2) HAMSTR, a line based unstructured solver on CPUs, and 3) GARFIELD, a structured solver on GPUs. The framework is based on Python, that is often used to wrap C or Fortran codes for interoperability with other solvers. Communication between multiple solvers is accomplished with a Topology Independent Overset Grid Assembler (TIOGA). NOVEL AIRFOIL SHAPE REPRESENTATIONS USING GRASSMAN SPACES We developed a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation as an analytic generative model, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data , (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes. TECHNOLOGY TRANSFER DEMONSTRATION - COUPLING WITH NREL WISDEM Researchers have integrated the inverse-design tool for 2D airfoils (INN-Airfoil) into WISDEM (Wind Plant Integrated Systems Design and Engineering Model), a multidisciplinary design and optimization framework for assessing the cost of energy, as part of tech-transfer demonstration. The integration of INN-Airfoil into WISDEM allows for the design of airfoils along with the blades that meet the dynamic design constraints on cost of energy, annual energy production, and the capital costs. Through preliminary studies, researchers have shown that the coupled INN-Airfoil + WISDEM approach reduces the cost of energy by around 1% compared to the conventional design approach. This page will serve as a place to easily access all the publications from this work and the repositories for the software developed and released through this pr...

aerodynamics↗
DOE OSTI2023

Active Site Engineering via Optimizing the Heterogeneous Support Structure for Single-Atom Catalysis

Supported single-atom catalysts show a large range of activities and selectivities that depend on the local environment of the catalytic sites. Here a theory-based optimization strategy is presented that is based on a density functional theory determination of the transition states and intermediates for a low-dimensional coordinate representation of the heterogeneity of the active sites. The approach is applied to a vanadium catalyst on an amorphous SiO 2 support that involves a large kinetic network described using a full chemistry model. Without assuming a priori scaling relations or mechanism reduction, the optimal state of heterogeneity is found to lie at atomic configurations where the activation energies for two distinct key chemical processes are equal. It is found a posteriori that the behavior of the system is consistent with linear free energy scaling relations in the randomness parameters. The energetic span theory proves quite useful in reducing the full chemistry model to a small number of key reactions. The use of a nonlinear optimization algorithm in combination with energetic span theory provides significant simplification in treating disordered systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II

Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Machine learning-based ethylene and carbon monoxide estimation, real-time optimization, and multivariable feedback control of an experimental electrochemical reactor

Electrochemical reduction of CO 2 gas is a novel CO 2 utilization technique that has the potential to mitigate the global climate crisis caused by anthropogenic CO 2 emissions, and enable the large-scale storage of energy generated from renewable sources in the form of carbon-based chemicals and fuels. However, due to the complexity of the electrochemical reactions, the explicit first-principles models for CO2 reduction are not available yet, and there has been a limited effort to develop process modeling, optimization and control of CO 2 electrochemical reactors. To this end, a rotating cylinder electrode (RCE) reactor has been constructed at UCLA to understand the mass transfer and reaction kinetics effects separately on the productivity. In the RCE reactor, the applied potential strongly influences the reaction energetics and the electrode rotation speed affects the hydrodynamic boundary layer and modifies the film mass transfer coefficient, which involves convective and diffusive transport. Further, the present work aims to develop a multi-input multi-output (MIMO) control scheme for the RCE reactor that integrates techniques from artificial and recurrent neural network modeling, nonlinear optimization, and process controller design. Specifically, production rates of two products from the experimental reactor, ethylene and carbon monoxide, are controlled by manipulating two inputs, applied potential and catalyst rotation speed. Process dynamics and controllability are analyzed, a feedback control strategy is designed and the controllers are tuned accordingly. The experimental electrochemical cell is employed to gather data for process modeling and implement the multivariable control system. Finally, the experimental results are presented which demonstrate excellent closed-loop performance by the control system and regulation of the outputs at three different set-points including an economically-optimal set-point.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Data-driven simultaneous process optimization and adsorbent selection for vacuum pressure swing adsorption

Technologies for post-combustion carbon capture are essential for the reduction of greenhouse gas emissions to the atmosphere. However, they are still associated with high costs and energy consumption. Intensified processes for carbon capture have the potential to overcome these challenges due to their higher efficiency, lower capital cost, and increased operational flexibility. Here, this work investigates simultaneous optimization of process conditions and adsorbent selection for a modular Vacuum Pressure-Swing Adsorption system designed for CO 2 capture. Both surrogate-based Nonlinear Programming and Mixed-Integer Nonlinear Programming approaches are applied and compared in terms of computational efficiency and solution accuracy. Moreover, process performance results are examined by applying several data analytics techniques to gain insights into the material-process correlations. Data-driven classifiers and neural networks can accurately predict whether a material is likely to satisfy purity, recovery, and energy constraints when operated at optimal process conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗