Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “positive feedback”

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 253 records · Page 14

BraggNN : fast X-ray Bragg peak analysis using deep learning

X-ray diffraction based microscopy techniques such as high-energy diffraction microscopy (HEDM) rely on knowledge of the position of diffraction peaks with high precision. These positions are typically computed by fitting the observed intensities in detector data to a theoretical peak shape such as pseudo-Voigt. As experiments become more complex and detector technologies evolve, the computational cost of such peak-shape fitting becomes the biggest hurdle to the rapid analysis required for real-time feedback in experiments. To this end, we propose BraggNN, a deep-learning based method that can determine peak positions much more rapidly than conventional pseudo-Voigt peak fitting. When applied to a test dataset, peak center-of-mass positions obtained from BraggNN deviate less than 0.29 and 0.57 pixels for 75 and 95% of the peaks, respectively, from positions obtained using conventional pseudo-Voigt fitting (Euclidean distance). When applied to a real experimental dataset and using grain positions from near-field HEDM reconstruction as ground-truth, grain positions using BraggNN result in 15% smaller errors compared with those calculated using pseudo-Voigt. Recent advances in deep-learning method implementations and special-purpose model inference accelerators allow BraggNN to deliver enormous performance improvements relative to the conventional method, running, for example, more than 200 times faster on a consumer-class GPU card with out-of-the-box software.

36 MATERIALS SCIENCE↗

Atomic precision imaging with an on-chip scanning tunneling microscope integrated into a commercial ultrahigh vacuum STM system

In this article, we replace the Z axis of the piezotube of a conventional Ultrahigh-Vacuum (UHV) Scanning Tunneling Microscope (STM) with a one-degree-of-freedom Microelectromechanical-System (MEMS) nanopositioner. As a result, a hybrid system is realized in which motions in the XY plane are carried out by the piezotube, while the MEMS device performs the Z-axis positioning with a smaller footprint and higher sensitivity. With the proposed system and a feedback loop, STM imaging is conducted on an H-passivated Si (100)-2×1 sample in a UHV condition, demonstrating that this on-chip STM is conducive to atomic precision scanning tunneling microscopy.

Engineering↗

Constraining the properties of gaseous halos via cross-correlations of upcoming galaxy surveys and thermal Sunyaev-Zel’dovich maps

The thermal Sunyaev-Zel’dovich (tSZ) effect induces a Compton-$\mathit{y}$ distortion in cosmic microwave background (CMB) temperature maps that is sensitive to a line-of-sight integral of the ionized gas pressure. By correlating the positions of galaxies with maps of the Compton-$\mathit{y}$ distortion, one can probe baryonic feedback processes and study the thermodynamic properties of a significant fraction of the gas in the Universe. Using a model fitting approach, we forecast how well future galaxy and CMB surveys will be able to measure these correlations, and show that powerful constraints on halo pressure profiles can be obtained. In this work, our forecasts are focused on correlations between galaxies and halos identified by the upcoming Dark Energy Spectroscopic Instrument survey and tSZ maps from the Simons Observatory and CMB-S4 experiments, but have general applicability to other surveys, such as the Large Synoptic Survey Telescope. We include prescriptions for observational systematics, such as halo miscentering and halo mass bias, demonstrating several important degeneracies with pressure profile parameters. Assuming modest priors on these systematics, we find that measurements of halo-$\mathit{y}$ and galaxy-$\mathit{y}$ correlations with future surveys yield tight constraints on the pressure profiles of group-scale dark matter halos, and enable current feedback models to either be confirmed or ruled out.

79 ASTRONOMY AND ASTROPHYSICS↗

Ultrafast method for scanning tunneling spectroscopy

A scanning tunneling microscope (STM) combines unique capabilities in imaging and spectroscopy with atomic precision, and it can obtain energy-resolved spectroscopic data with atomic resolution. In this paper, we utilize a recently proposed modification to the STM feedback control loop to acquire high quality d 2 I/dV 2 images. We have developed a constant differential conductance imaging method by closing the STM feedback loop with a high precision dI/dV measurement. In this mode, the tip’s vertical position is adjusted so as to keep the differential conductance constant during raster scanning of the surface. Based on this imaging mode, we propose a new technique to acquire fast and reliable scanning tunneling spectroscopy (STS) data simultaneously with the imaging.

47 OTHER INSTRUMENTATION↗

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. Here, we present a spectral decomposition method that allows for corrections to line positions and bound–bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

47 OTHER INSTRUMENTATION↗

Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive

The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploring Sources of Surface Bias in HRRR Using New York State Mesonet

In recent years, there has been increasing demand for applications of short-term forecasting of renewable energy potential and assessments of the likelihood of extreme weather events using the High-Resolution Rapid Refresh (HRRR) model. Examining the biases in the newest version of HRRR is necessary to promote further model development. Using data from one of the most comprehensive and dense monitoring networks, New York State Mesonet (NYSM), we evaluate the HRRR version 3 meteorological fields for an entire year. In this work, the land-atmosphere-cloud coupling system is evaluated as an integrated whole. We investigate the physical processes influencing the soil hydrological balance and the thermodynamic interactions, from surface fluxes up to the level of boundary layer convection from both temporal (seasonal and diurnal) and spatial perspectives. Results show that the model 2 m temperature and humidity biases are seasonally dependent, with warm and dry bias present during the warm season, and an extreme nocturnal cold bias in winter. The summer warm bias includes both a land-surface-induced bias and a cloud-induced bias. Inaccurate representation of energy partition and soil hydrological process across different land use types as well as a hydrological bias in describing spring snowmelt are identified as the main source of the land-surface-induced bias. A feedback loop linking cloud presence, flux changes, and temperature contributes to the cloud-induced bias. The positive solar radiation bias increases from clear sky to overcast sky conditions. The most significant bias occurs during overcast and thick cloud conditions associated with frontal passage and thunderstorms.

54 ENVIRONMENTAL SCIENCES↗

Direct observation of tRNA-chaperoned folding of a dynamic mRNA ensemble

T-box riboswitches are multi-domain noncoding RNAs that surveil individual amino acid availabilities in most Gram-positive bacteria. T-boxes directly bind specific tRNAs, query their aminoacylation status to detect starvation, and feedback control the transcription or translation of downstream amino-acid metabolic genes. Most T-boxes rapidly recruit their cognate tRNA ligands through an intricate three-way stem I-stem II-tRNA interaction, whose establishment is not understood. Using single-molecule FRET, SAXS, and time-resolved fluorescence, we find that the free T-box RNA assumes a broad distribution of open, semi-open, and closed conformations that only slowly interconvert. tRNA directly binds all three conformers with distinct kinetics, triggers nearly instantaneous collapses of the open conformations, and returns the T-box RNA to their pre-binding conformations upon dissociation. This scissors-like dynamic behavior is enabled by a hinge-like pseudoknot domain which poises the T-box for rapid tRNA-induced domain closure. This study reveals tRNA-chaperoned folding of flexible, multi-domain mRNAs through a Venus flytrap-like mechanism.

59 BASIC BIOLOGICAL SCIENCES↗

CONTROLLED END GAS AUTO IGNITION WITH EXHAUST GAS RECIRCULATION ON A STOICHIOMETRIC, SPARK IGNITED, NATURAL GAS ENGINE

The goal of this study is to address fundamental limitations to achieving diesel-like efficiencies in heavy duty on-highway natural gas (NG) engines. Engine knock and misfire are barriers to pathways leading to higher efficiency engines. This study explores enabling technologies for development of high efficiency stoichiometric, spark ignited, natural gas engines. These include design strategies for fast and stable combustion and higher dilution tolerance. Additionally, advanced control methodologies are implemented to maintain stable operation between knock and misfire limits. To implement controlled end- gas autoignition (C-EGAI) strategies a Combustion Intensity Metric (CIM) is used for ignition control with the use of a Woodward large engine control module (LECM). Tests were conducted using a single cylinder, variable compression ratio, cooperative fuel research (CFR) engine with baseline conditions of 900 RPM, engine load of 800 kPa indicated mean effective pressure (IMEP), and stoichiometric air/fuel ratio. Exhaust gas recirculation (EGR) tests were performed using a custom EGR system that simulates a high pressure EGR loop and can provide a range of EGR rates from 0 to 40%. The experimental measurements included the variance of EGR rate, compression ratio, engine speed, IMEP, and CIM. These five variables were optimized through a Modified Box- Benken design Surface Response Method (RSM), with brake efficiency as the merit function. A positive linear correlation between CIM and f-EGAI was identified. Consequently, CIM was used as the feedback control parameter for C-EGAI. As such, implementation of C-EGAI effectively allowed for the utilization of high EGR rates and CRs, controlling combustion between a narrower gap between knock and lean limits. The change from fixed to parametric ignition timing with CIM targeted select values of f-EGAI with an average coefficient of variance (COV) of peak pressure of 5.4. The RSM efficiency optimization concluded with operational conditions of 1080 RPM, 1150 kPa IMEP, 10.55:1 compression ratio, and 17.8% EGR rate with a brake efficiency of 21.3%. At this optimized point of peak performance, a f-EGAI for C-EGAI was observed at 34.1% heat release due to auto ignition, a knock onset crank angle value of 10.3° aTDC and ignition timing of - 24.7° aTDC. This work has demonstrated that combustion at a fixed f-EGAI can be maintained through advanced ignition control of CIM without experiencing heavy knocking events.

Cooperative Fuel Research Engine, Auto Ignition, E↗

Numerical simulation of NSLS-II fast orbit feedback system

We discuss recent work on the construction of a numerical simulation of the fast orbit feedback system at NSLS-II. The simulation operates in the time domain and also includes the spatial domain, i.e. all beam position monitors (BPMs) and correctors. It can accept inputs of the real beam orbit and the measured orbit response matrix. It can also add errors to every stage of the calculation. We present methods to verify the simulation results by comparing the simulation results with experimental data collected at NSLS-II. The results are in very good agreement. The effects of errors from BPMs and correctors, as well as the amplitude of excitation, on the feedback performance, are also explored. This simulation can be used to predict the behavior and performance of the system for a future upgrade.

36 MATERIALS SCIENCE↗

Virtual Reality for Shoot/No-Shoot Decision Training in Law Enforcement: A Literature Review and Research Agenda

Virtual reality (VR) can materially improve “shoot / no-shoot” (SNS) training by giving officers realistic, repeatable practice making high-stakes decisions under pressure. Traditional tools—live-fire ranges and video simulators—build basics, but they cannot adapt to each officer in real time or fully mirror the complexity of the field. VR closes that gap by creating immersive scenarios that are safer, more flexible, easier to scale across units, and able to capture objective performance data. SNS decisions are not just about marksmanship; they rely on perception, judgment, memory, and the ability to hold fire when a threat is uncertain. Effective training therefore needs realism, decision complexity, and branching outcomes that reflect the true consequences of choices. These elements strengthen recognition of hostile intent while reducing false positives and building the self-control required in ambiguous situations. VR brings specific advantages: dynamic environments, full-body interaction, and the ability to measure performance with precision—enabling targeted feedback and better transfer of learning to the street. At the same time, responsible deployment must address scenario quality (credible environments and behaviors), lawful decision models, and user wellbeing (appropriate stress levels, comfort, and safety). Sandia’s VIPER Lab is positioned to lead this work. The team combines human-performance science, AI/ML, and VR/AR development with a deep equipment bench (e.g., omnidirectional treadmill, eye-tracking, haptics, multiple HMDs). This ecosystem supports building and validating next-generation SNS training that is immersive, measurable, and trustworthy. Bottom line: Investment in VR-enabled SNS training that blends evidence-based design with careful validation and legal safeguards is expected to pay off in safer, more consistent decision-making and improved community trust, delivered through training that is practical to deploy at scale.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

An optical-input Maximum Likelihood Estimation feedback system demonstrated on tokamak horizontal equilibrium control

A readily parallelized Maximum Likelihood Estimation (MLE) algorithm with linear computational complexity is demonstrated in real time using only measurements from an extreme ultraviolet (EUV) diagnostic to control the horizontal position of a tokamak plasma. A set of trial emissivity profiles are parameterized by the control quantity of interest (R m ), and the MLE is identified from the profile which minimizes the signal reconstruction residual. The algorithm depends on an empirically determined likelihood function with exponential form. EUV emission (λ ≈ 15eV-1keV) is captured in a poloidal plane by four 16-channel AXUV diodes mounted at different poloidal angles with radial and angular resolution sufficient to discern plasma equilibrium evolution in HBT-EP. Calculations of the plasma major radius by the system are consistent within diagnostic uncertainty for the majority of the discharge with those of: a weighted average of vertical soft X-ray or EUV chords, magnetic sensors, and an equilibrium reconstruction. The feedback system corrects for a horizontal displacement of the major radius equal to 20% of the plasma minor radius by adjusting the vertical field produced from 40 in-vessel control coils in real time. The MLE calculation is performed on a GPU in a 15 μs cycle, with similar performance in this application to a simple weighted average of vertical chords. Finally, results demonstrate horizontal position control using magnetic actuators and an optical observer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Aerosol Influences on Cloud Water: Insights From ARM EPCAPE Observations With Explainable Machine Learning

This study employs an explainable machine learning (ML) framework (XGBoost-SHapley Additive exPlanations analysis) to investigate controlling factors on cloud liquid water path (LWP) using EPCAPE observations near the California coast. Aerosols are found to be the dominant factor explaining LWP variability, surpassing meteorological factors (MFs). By isolating aerosol effects from meteorological influences, the ML reveals a negative linear relationship between LWP and cloud droplet number concentration (Nd) in log space, likely driven by entrainment drying via evaporation-entrainment feedback. This aligns with the negative regime of the inverted-V relationship reported in previous studies, while no positive LWP responses are found due to a limited number of precipitating cases in EPCAPE. Furthermore, the sensitivity of LWP to Nd shows a non-linear dependence on MFs like moisture contrast between surface and free troposphere and lower-tropospheric stability. This occurs due to the interplay between the MFs' direct effects on entrainment drying and indirect effects through LWP adjustments.

EPCAPE observations↗

Molecular dissection of the glutamine synthetase-GlnR nitrogen regulatory circuitry in Gram-positive bacteria

How bacteria sense and respond to nitrogen levels are central questions in microbial physiology. In Gram-positive bacteria, nitrogen homeostasis is controlled by an operon encoding glutamine synthetase (GS), a dodecameric machine that assimilates ammonium into glutamine, and the GlnR repressor. GlnR detects nitrogen excess indirectly by binding glutamine-feedback-inhibited-GS (FBI-GS), which activates its transcription-repression function. The molecular mechanisms behind this regulatory circuitry, however, are unknown. Here we describe biochemical and structural analyses of GS and FBI-GS-GlnR complexes from pathogenic and non-pathogenic Gram-positive bacteria. The structures show FBI-GS binds the GlnR C-terminal domain within its active-site cavity, juxtaposing two GlnR monomers to form a DNA-binding-competent GlnR dimer. The FBI-GS-GlnR interaction stabilizes the inactive GS conformation. Strikingly, this interaction also favors a remarkable dodecamer to tetradecamer transition in some GS, breaking the paradigm that all bacterial GS are dodecamers. These data thus unveil unique structural mechanisms of transcription and enzymatic regulation.

59 BASIC BIOLOGICAL SCIENCES↗

Combined TDLAS and chemiluminescence imaging in a flat flame burner operated with NH3/H2 blends

Ammonia is viewed as a viable hydrogen carrier due to favorable storage and transport characteristics. While it can be re-converted to hydrogen at point-of-use via thermal catalytic cracking, direct utilization in combustion systems can result in reduced costs and improved efficiency. A major barrier to this approach is the low flammability and potential for high nitrogen oxide emissions, driven by fuel-bound nitrogen and complex kinetic pathways. While a number of kinetic mechanisms currently exist for simulating ammonia combustion, a major need continues to be direct information about species profiles in easy-to-model systems capable of isolating chemical kinetics from multi-dimensional fluid dynamic effects. This paper reports on recent species measurements made in a flat flame burner using a combined tunable-diode-laser-absorption-spectroscopy (TDLAS) and chemiluminescence imaging approach. Three flame conditions were included representative of NH3/H2 blends, partially cracked NH3 (inc. N2), and 100% NH3 with enhanced air (30% oxygen). Two NIR distributed feedback (DFB) laser diodes were used to determine H2O concentration and temperature (via ratio thermometry) at various radial and axial positions, after which an inverse Abel transform was used to infer centerline values. Companion images were collected using a Princeton Instrument PI-MAX intensified camera equipped with a 105mm UV lens and multiple filter sets targeting OH*, NH*, and NH2* emission. Results were compared to companion Cantera burner-stabilized flame simulations using various kinetic mechanisms. A recent mechanism including excited species chemistry was also included, to investigate whether excited and ground state profiles exhibit significant differences.

ammonia combustion↗

Unstructured mesh-based multi-physics reactor transient simulation with iMC code

In this study, we present a time-dependent Monte Carlo simulation result about a complex fuel-loaded light water reactor system with thermal-hydraulic feedback using the KAIST iMC code. The intra-pin temperature distribution is calculated based on Monte Carlo-tallied detailed power distribution and the finite element heat transfer method. The temperature effect of fuel, absorber, and coolant are adequately reflected into the dynamic response by the on-the-fly Doppler broadened cross-section correction. For the time-dependent Monte Carlo transport simulation, the predictor-corrector quasi-static Monte Carlo method is used for this study. We tested the coupled analysis framework with a 17-by-17 fuel assembly loaded with the centrally-shielded burnable absorber (CSBA) fuel element. The temperature feedback effect on the material cross-section and the moderator density incurred negative reactivity in response to the external positive reactivity insertion, showing the inherent stability of the reactor system. The pin-wise power and temperature change during the system transient are presented and discussed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Analyzer-based X-ray phase contrast imaging using the forward-diffracted o-beam in a few-millimetre-thick Bragg-case asymmetrically cut crystal

An analyzer-based X-ray phase contrast imaging experiment employing the forward-diffracted o-beam in a few-millimetre-thick Bragg-case asymmetrically cut analyzer crystal has been implemented and tested in a geometry similar to that used in conventional radiography. The high angular stability requirements were overcome using specially designed crystals and a closed-loop feedback intensity system, monitoring the intensity of the diffracted h-beam. Analyzer-based images (ABis) taken at different angular positions on the forward-diffracted o-beam rocking curve show different contrasts, as expected. However, the ABis did not show sharp borders. This was closely investigated by X-ray topography and Δ d / d mapping and was attributed to the stresses caused by the analyzer crystal's own weight in the bulk. Further investigation of the crystal design using finite element analysis coupled with dynamical theory of X-ray diffraction is envisaged.

Honnicke, Marcelo Goncalves (ORCID:000000033276432↗

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗