Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “model order 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47

An analytic modeling and system identification study of rotor/fuselage dynamics at hover

A combination of analytic modeling and system identification methods have been used to develop an improved dynamic model describing the response of articulated rotor helicopters to control inputs. A high-order linearized model of coupled rotor/body dynamics including flap and lag degrees of freedom and inflow dynamics with literal coefficients is compared to flight test data from single rotor helicopters in the near hover trim condition. The identification problem was formulated using the maximum likelihood function in the time domain. The dynamic model with literal coefficients was used to generate the model states, and the model was parametrized in terms of physical constants of the aircraft rather than the stability derivatives resulting in a significant reduction in the number of quantities to be identified. The likelihood function was optimized using the genetic algorithm approach. This method proved highly effective in producing an estimated model from flight test data which included coupled fuselage/rotor dynamics. Using this approach it has been shown that blade flexibility is a significant contributing factor to the discrepancies between theory and experiment shown in previous studies. Addition of flexible modes, properly incorporating the constraint due to the lag dampers, results in excellent agreement between flight test and theory, especially in the high frequency range.

Hong, Steven W.↗

An analytic modeling and system identification study of rotor/fuselage dynamics at hover

A combination of analytic modeling and system identification methods have been used to develop an improved dynamic model describing the response of articulated rotor helicopters to control inputs. A high-order linearized model of coupled rotor/body dynamics including flap and lag degrees of freedom and inflow dynamics with literal coefficients is compared to flight test data from single rotor helicopters in the near hover trim condition. The identification problem was formulated using the maximum likelihood function in the time domain. The dynamic model with literal coefficients was used to generate the model states, and the model was parametrized in terms of physical constants of the aircraft rather than the stability derivatives, resulting in a significant reduction in the number of quantities to be identified. The likelihood function was optimized using the genetic algorithm approach. This method proved highly effective in producing an estimated model from flight test data which included coupled fuselage/rotor dynamics. Using this approach it has been shown that blade flexibility is a significant contributing factor to the discrepancies between theory and experiment shown in previous studies. Addition of flexible modes, properly incorporating the constraint due to the lag dampers, results in excellent agreement between flight test and theory, especially in the high frequency range.

Hong, Steven W.↗

NASA Langley Low Speed Aeroacoustic Wind Tunnel: Background Noise and Flow Survey Results Prior to FY05 Construction of Facilities Modifications

The NASA Langley Research Center Low Speed Aeroacoustic Wind Tunnel is a premier facility for model-scale testing of jet noise reduction concepts at realistic flow conditions. However, flow inside the open jet test section is less than optimum. A Construction of Facilities project, scheduled for FY 05, will replace the flow collector with a new design intended to reduce recirculation in the open jet test section. The reduction of recirculation will reduce background noise levels measured by a microphone array impinged by the recirculation flow and will improve flow characteristics in the open jet tunnel flow. In order to assess the degree to which this modification is successful, background noise levels and tunnel flow are documented, in order to establish a baseline, in this report.

Booth, Earl R., Jr.↗

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗

Modeling the Transmission of Optical Lightning Signals Through Complex 3‐D Cloud Scenes

Abstract Space‐based lightning imagers have shown that complex cloud scenes consisting of multiple tall convective features, anvil clouds, and warm boundary cloud layers are illuminated by lightning in many different ways depending on where the lightning occurs and how energetic it is. Modifications to the optical lightning signals from radiative transfer in the cloud medium can lead to reductions in detection efficiency and location accuracy for these instruments and can also cause some of the optical signals that are detected to have unexpected spatial energy distributions. In this study, we perform Monte Carlo radiative transfer simulations of optical lightning emissions in clouds with complex 3‐D geometries to shed some light on the origins of certain irregular radiance patterns that have been recorded from orbit. We show that diffuse reflections off nearby cloud faces can explain lightning signals in nonelectrified clouds, tall clouds can result in poor optical transmission and suppressed radiances that could lead to missed events and that particularly favorable viewing conditions can cause otherwise normal lightning to produce a superbolt that is orders of magnitude brighter than the same flash seen from a different angle.

54 ENVIRONMENTAL SCIENCES↗

Separating Physics and Dynamics Grids for Improved Computational Efficiency in Spectral Element Earth System Models

Previous studies have shown that atmospheric models with a spectral element grid can benefit from putting physics calculations on a relatively coarse finite volume grid. Here we demonstrate an alternative high-order, element-based mapping approach used to implement a quasi-equal-area, finite volume physics grid in E3SM. Unlike similar methods, the new method in E3SM requires topology data purely local to each spectral element, which trivially allows for regional mesh refinement. Simulations with physics grids defined by 2 × 2, 3 × 3, and 4 × 4 divisions of each element are shown to verify that the alternative physics grid does not qualitatively alter the model solution. The model performance is substantially affected by the reduction of physics columns when using the 2 × 2 grid, which can increase the throughput of physics calculations by roughly 60%–120% depending on whether the computational resources are configured to maximize throughput or efficiency. A pair of regionally refined cases are also shown to highlight the refinement capability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On-the-fly autonomous control of neutron diffraction via physics-informed Bayesian active learning

We demonstrate the first live, autonomous control over neutron diffraction experiments by developing and deploying ANDiE: the autonomous neutron diffraction explorer. Neutron scattering is a unique and versatile characterization technique for probing the magnetic structure and behavior of materials. However, instruments at neutron scattering facilities in the world is limited, and instruments at such facilities are perennially oversubscribed. We demonstrate a significant reduction in experimental time required for neutron diffraction experiments by implementation of autonomous navigation of measurement parameter space through machine learning. Prior scientific knowledge and Bayesian active learning are used to dynamically steer the sequence of measurements. We show that ANDiE can experimentally determine the magnetic ordering transition of both MnO and Fe 1.09 Te all while providing a fivefold enhancement in measurement efficiency. Furthermore, in a hypothesis testing post-processing step, ANDiE can determine transition behavior from a set of possible physical models. ANDiE's active learning approach is broadly applicable to a variety of neutron-based experiments and can open the door for neutron scattering as a tool of accelerated materials discovery.

36 MATERIALS SCIENCE↗

MACHINE LEARNING-ENABLED PREDICTION OF TRANSIENT INJECTION MAP IN AUTOMOTIVE INJECTORS WITH UNCERTAINTY QUANTIFICATION

Accurate prediction of injection profiles is a critical aspect of linking injector operation with engine performance and emissions. However, highly resolved injector simulations can take one to two weeks of wall-clock time, which is incompatible with engine design cycles with desired turnaround times of less than a day. Hence, it is important to reduce the time-to-solution of the internal flow simulations by several orders of magnitude to make it compatible with engine simulations. This work demonstrates a data-driven approach for tackling the computational overhead of injector simulations, whereby the transient injection profiles are emulated for a side-oriented, single-hole diesel injector using a Bayesian machine-learning framework. First, an interpretable Bayesian learning strategy was employed to understand the effect of design parameters on the total void fraction field. Then, autoencoders are utilized for efficient dimensionality reduction of the flowfields. Gaussian process models are finally used to predict the spatiotemporal void fraction field at the injector exit for unknown operating conditions. The Gaussian process models produce principled uncertainty estimates associated with the emulated flowfields, which provide the engine designer with valuable information of where the data-driven predictions can be trusted in the design space. The Bayesian flowfield predictions are compared with the corresponding predictions from a deep neural network, which has been transfer-learned from static needle simulations from a previous work by the authors. The emulation framework can predict the void fraction field at the exit of the orifice within a few seconds, thus achieving a speed-up factor of up to 38 x 10(6) over the traditional simulation-based approach of generating transient injection maps.

machine learning↗

The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals

A two-control volume is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the through flow and a 'capacitance accumulator' model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals can not be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transfer functions are required to account for the reaction forces, and calculated here as a lead-lag term for the direct force function and a lag term for the cross-coupled function. These first order functions are simple compared to transfer functions for magnetic bearings or foundations, For synchronous response to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamic codes. Correct predictions for stability and transient response will require more general algorithms, pressumably using a state-space format.

Childs, Dara W.↗

Microchannel-based Membrane-less Extraction of Li from Unconventional Lithium Sources & the Separation of REE

This final report provides an overview of the Project's entire duration, covering July 1, 2021 to December 31, 2023. It primarily focuses on the achievements, technological developments, and unique challenges the team faced while working on separating and extracting Lithium from produced waters. The project's primary aim was to create an integrated, high-throughput, membrane-less, and modular microfluidic platform that could extract Lithium from unconventional sources. We have successfully met all goals and milestones envisioned in the SOPO document. The most critical primary milestones, including the Go-No-Go milestone (refer to the Gantt chart in the Appendices), were successfully accomplished. We demonstrated phase separation (>90%) and extraction (>85%) performance in the MPSE using synthetic, and representative produced water composition feed at 50 ml/min total flow through MPSE 36. We have also performed a parametric study of the MPSE operations, beyond the scope of SOPO, exploring operating conditions of current and broader interest. The extended investigation of operational parameters is concurrent with our efforts to seek further development of the MPSE technology beyond the scope of the Project. Along these lines of development, we have made efforts to be responsive to DOE calls for technological developments of other types of resources (beyond PW) for the recovery of Critical Materials and higher TRL development (beyond TRL 4). During the work on this Project, we developed and implemented three innovative technical approaches that emerged from our efforts to successfully meet the Project milestones. The innovative & original technical approaches developed and implemented in this Project are now the contributions to process engineering that could be clearly credited to the Project. First, Convergent Design Approach is a comprehensive feedforward & feedback loop of four design phases: i) design for functionality, ii) design for manufacturing, iii) design for sustainability, and iv) design for market. Next was Process Intensification. A major aim of this Project was to create an innovative phase separation & extraction microscale-based technology for Li separation – thus the words microchannel-based in the Project title. A microscale-based technology is intrinsically in the center of the Process Intensification domain as defined by its unique principles. Therefore, Process Intensification was implicitly envisioned in the Project’s SOPO. Lastly, Time Scale Analysis is a novel tool for discovering the needs and directions of Process Intensification implementations in any process technology. This Project is fully credited for developing and implementing the three novel technical approaches mentioned above. These are general contributions to process engineering that emerged from this Project. Beyond the original SOPO scope, the OSU-U.Pitt research group utilized a Convergent Design methodology, integrating first-principles mathematical modeling with experimental validation on the Minimum Development Vehicle. By creating these Digital Twins, the team rapidly assessed manufacturing iterations to support TEA analysis. This framework further enabled the development of advanced Surface Modification Techniques, where hydrophobic and oleophobic coating strategies were optimized via Digital Twin tools and validated through rigorous 100-hour longevity testing. TEA Analysis: The closing efforts of this Project were focused on the TEA analysis. TEA analysis had two primary functions: i) enabling critical assessments of design variations withing 10 the Concurrent Design Approach, thus enabling evolution of the MPSE design to reach faster- better-cheaper alternatives; and ii) to create a bridge between the accomplishments of this Project and future projects of higher TRL, beyond TRL 6 level. It is important to note that the TEA model created in the Project stirred the technological solutions for the recovery of critical materials toward a vision of a very profitable modular plant that has unique zero-waste water discharge signature. More importantly, thanks to our experimental performance data and conservative assumptions, the TEA model predicts minimal technological and investment risks. Low cost of a modular unit of a nominal capacity of [1000 tons of Li 2 CO 3 /year] positions the MPSE based technology within the reach of community investors, thus offering a paradigm shift in the development of critical technologies. The project successfully navigated two primary challenges: solvent selection and manufacturing adaptation. Restricted by the SOPO to existing literature for lithium recovery, the team identified a critical need for a "material excellence program" to develop next-generation solvents, eventually concluding with a preliminary investigation into promising Ionic Liquids (ILs). Simultaneously, COVID-19 supply chain disruptions forced a pivot from traditional manufacturing to advanced additive methods at ATAMI-OSU. By transitioning from stainless steel to 3D-printed polymer substrates, the team achieved a transformative three-order-of- magnitude reduction in manufacturing costs and compressed prototyping timelines from several months to just two days. The MPSE technology offers significant energy, environmental, and economic advantages by overcoming the traditional bottlenecks of phase-separation hardware and contactor size. Unlike conventional mixer-settlers or membrane-based systems, MPSE operates without moving parts or fouling-prone membranes, achieving robust performance even with challenging, viscous, or particulate-heavy feeds. Key performance metrics include an energy intensity reduction of 5–50x (3–40 kJ/m 3 ) compared to incumbent technologies and a dramatic reduction of processing time to under 60 seconds, which drastically reduces the physical plant footprint. These technical efficiencies translate into superior economic outcomes; for a 100 t/year Li 2 CO 3 facility, implementing MPSE is projected to nearly halve contactor CAPEX (from $\$$6.08M to $\$$3.01M) and significantly increase the project's Net Present Value (NPV), derisking new investment and enabling distributed critical-mineral processing configurations. The commercialization of MPSE technology is being spearheaded by Vigsur Dynamics Inc., which has adopted a structured, parallel approach to technical and business development since its formation in January 2026. Following extensive customer discovery and engagement with the Oregon State University accelerator, Vigsur Dynamics is working to establish a business model that transitions from pilot demonstrations to modular hardware sales, ultimately aiming for a "build-own-operate" service strategy. Current technical milestones—including 100 hours of continuous operation, superior energy efficiency, and successful 6-unit modular scale-up— provide a foundation for this transition. Backed by ongoing IP licensing and a growing network of industrial and venture advisors, the company is actively de-risking the platform to replace conventional mixer-settler systems in the critical minerals market.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

Harnessing Virtual Power Plants Reliably: Enabling tools for increased observability, controllability, operation, and aggregation of distributed energy resources

Harnessing virtual power plants enhances the integration of distributed energy resources into utility grids for a sustainable energy future. Virtual power plants (VPPs) aggregate DERs to enhance resource adequacy and reduce emissions. U.S. utilities are exploring various technologies to manage DERs effectively. FERC Order 2222 allows DERs to participate in both wholesale and retail markets. Enhancing observability and controllability of behind-the-meter (BTM) DERs is essential for reliable grid operations. A hierarchical control architecture can improve coordination among residential energy resources. Field tests showed nearly 20% energy savings and 30% peak power reduction during grid events. Effective management of DERs requires enhanced situational awareness to prevent grid congestion. Integrating DER management systems (DERMS) with existing planning tools can improve operational security. Near-real-time grid models can validate optimal resource set points against resource uncertainty. Traditional uninterruptible power supplies (UPS) can be upgraded to support grid services and become part of VPPs. Upgrading UPS systems can reduce costs by 75% and unlock significant battery capacity. New battery management systems and grid-aware controllers are essential for optimizing UPS performance. Continued research and development are necessary to address challenges in integrating DERs into utility grids. Encouraging customer participation in pilot programs is vital for the evolution of VPPs. Here, the shift towards price-responsive DERs and VPPs is expected to enhance energy distribution efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Electrode kinetics of oxygen reduction - A theoretical and experimental analysis of the rotating ring-disc electrode method

In order to calculate most of the rate constants for the intermediate formation of H2O2 in the electroreduction of O2 to H2O, the theoretical treatments of the rotating ring-disc electrode method by Damjanovic et al. (1966, 1967), Bagotskii et al. (1968, 1969), and Wroblowa et al. (1976) are modified. Rotating ring-disc electrode experimental data obtained for O2 reduction in Pt in 0.55 M H2SO4 are used to illustrate the calculations of rate constants according to the above theoretical treatments. A simple reaction model as proposed by the first author is consistent with the experimental data. The results indicate that O2 (97 percent) reduces to H2O in a direct four-electron transfer reaction. The adsorption of O2 is probably the rate-determining step in the potential region more negative than 0.5 V vs. reversible hydrogen electrode.

Hsueh, K.-L.↗

Reflected Sunlight Reduction and Characterization for a Deep-Space Optical Receiver Antenna (DSORA)

A baffle system for the elimination of first-order specular and diffuse reflection of sunlight from the sunshade of a deep-space optical receiver telescope is presented. This baffle system consists of rings of 0.5cm blades spaced 2.5 cm apart on the walls of GO hexagonal sunshade tubes that combine to form the telescope sunshade. The shadow cast by the blades, walls, and rims of the tubes prevent all first-order reflections of direct sunlight from reaching the primary mirror of the telescope. A reflection model of the sunshade without baffles is also presented for comparison. Since manufacturers of absorbing surfaces do not measure data near grazing incidence, the reflection properties at anticipated angles of incidence must be characterized. A description of reflection from matte surfaces in term of bidirectional reflection distribution function (BRDF) is presented along with a discussion of measuring BRDF near grazing incidence.

Clymer, B. D.↗

Diastereoselectivity Controlled by the Hydrogenation Mechanisms during the Electrochemical Reduction of a Carbonyl Group

Stereocontrol is of critical importance in organic synthesis. In this study, we demonstrate how heterogeneous electrochemical hydrogenation enables diastereocontrol simply by tuning electrochemical hydrogenation mechanisms without altering the adsorption conformation of a reactant on the electrode. We use 4-hydroxy-1-tetralone (4-OH-tetralone) as a model reactant, where diastereomers can be produced during the hydrogenation of the carbonyl group. In traditional thermocatalytic hydrogenation, H 2 first dissociates on the catalyst surface to form surface-adsorbed hydrogen (H*), and therefore, H* is always added to the organic reactant from the catalyst side via hydrogen atom transfer (HAT). Thus, in order to flip the diastereoselectivity, the adsorbed reactant itself must be physically flipped. In contrast, electrochemical hydrogenation can occur either via HAT, where H is added from the electrode surface, or via proton-coupled electron transfer (PCET), where H is added from the solution side of the adsorbed reactant. Thus, without changing the adsorption conformation of the reactant, opposite diastereomers can be obtained by switching the hydrogenation mechanism (HAT vs PCET). In this work, using a combination of experimental and computational studies, we demonstrate two examples of flipping diastereoselectivity by different electrochemical hydrogenation mechanisms. In the first case, we achieve opposite diastereoselectivities using metals that adopt different hydrogenation mechanisms (HAT vs PCET). In the second case, we flip the diastereoselectivity by varying the applied potential, which switches one hydrogenation mechanism to the other on the same metal electrode. In each case, our results offer an atomic-level understanding of the preferred hydrogenation mechanism that enables the corresponding diastereoselectivity.

adsorption↗

Renewable Activated Carbon Sorbent for the Desulfurization of Liquid Fuels

In recent years, significant efforts have been devoted to the reduction of sulfur levels in transportation fuels in order to reach regulatory limits and reduce the emission of harmful SO x into the atmosphere. In particular, adsorptive desulfurization (ADS) has the potential to produce zero-sulfur fuels without the need for a high energy intensity process, high H 2 pressure, and long process times as in the case of other technologies such as hydrodesulfurization. In this work, we have demonstrated the effectiveness of renewable activated carbons derived from food waste (FWAC) for the ADS of model jet and diesel fuels. The optimal FWAC materials were those fabricated to maximize the micropore volume, providing available sites for the adsorption of dibenzothiophene (DBT) and dimethyldibenzothiophene (DMDBT). The FWAC had a greater sulfur adsorption capacity than commercial AC, Y zeolite sorbents, and AC derived from other biomass sources including miscanthus, coconut shell, and walnut shell. Elemental analysis suggests that the inorganic impurities inherent in food waste, notably K, Ca, P, and Na, may contribute to its improved sulfur adsorption compared to other AC materials. Microscopy and X-ray diffraction studies further demonstrated the presence of inorganic species on FWAC that may provide active sites for the chemisorption of sulfur molecules.

Adsorption↗

Group-equivariant autoencoder for identifying spontaneously broken symmetries

We introduce the group-equivariant autoencoder (GE autoencoder), a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use group theory to deduce which symmetries of the system remain intact in all phases, and then use this information to constrain the parameters of the GE autoencoder such that the encoder learns an order parameter invariant to these “never-broken” symmetries. This procedure produces a dramatic reduction in the number of free parameters such that the GE-autoencoder size is independent of the system size. We include symmetry regularization terms in the loss function of the GE autoencoder so that the learned order parameter is also equivariant to the remaining symmetries of the system. By examining the group representation by which the learned order parameter transforms, we are then able to extract information about the associated spontaneous symmetry breaking. We test the GE autoencoder on the 2D classical ferromagnetic and antiferromagnetic Ising models, finding that the GE autoencoder (1) accurately determines which symmetries have spontaneously broken at each temperature; (2) estimates the critical temperature in the thermodynamic limit with greater accuracy, robustness, and time efficiency than a symmetry-agnostic baseline autoencoder; and (3) detects the presence of an external symmetry-breaking magnetic field with greater sensitivity than the baseline method. Lastly, we describe various key implementation details, including a quadratic-programming-based method for extracting the critical temperature estimate from trained autoencoders and calculations of the DNN initialization and learning rate settings required for fair model comparisons.

42 ENGINEERING↗

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Tiffany, Sherwood H.↗