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Results for “Parameter Dimensionality 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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Simulating bioclogging effects on dynamic riverbed permeability and infiltration

Bioclogging in rivers can detrimentally impact aquifer recharge. This is particularly so in dry regions, where losing rivers are common, and where disconnection between surface water and groundwater (leading to the development of an unsaturated zone) can occur. Reduction in riverbed permeability due to biomass growth is a time-variable parameter that is often neglected, yet permeability reduction from bioclogging can introduce order of magnitude changes in seepage fluxes from rivers over short (i.e., monthly) timescales. To address the combined effects of bioclogging and disconnection on infiltration, we developed in this paper numerical representations of bioclogging processes within a one-dimensional, variably saturated flow model representing losing-connected and losing-disconnected rivers. We tested these formulations using a synthetic case study informed with biological data obtained from the Russian River, California, USA. Our findings show that modeled biomass growth reduced seepage for losing-connected and losing-disconnected rivers. However, for rivers undergoing disconnection, infiltration declines occurred only after the system was fully disconnected. Before full disconnection, biologically induced permeability declines were not significant enough to offset the infiltration gains introduced by disconnection. The two effects combine to lead to a characteristic infiltration curve where peak infiltration magnitude and timing is controlled by permeability declines relative to hydraulic gradient gains. Biomass growth was found to hasten the onset of full disconnection; a condition we term ‘effective disconnection’. Finally, our results show that river infiltration can respond dynamically to bioclogging and subsequent permeability declines that are highly dependent on river connection status.

58 GEOSCIENCES↗
DOE OSTI2016

Enhancements to the RAVEN code in FY16

The RAVEN code has been under development at the Idaho National Laboratory since 2012. Its main goal is to create a multi-purpose platform for the deploying of all the capabilities needed for Probabilistic Risk Assessment, uncertainty quantification, data mining analysis and optimization studies. RAVEN has currently reached a good level of maturity in terms of deployed state-of-art and advanced capabilities. The main subject of this report is to show the activities that have been recently accomplished: • Implementation of ensemble modeling for time-series, and • initial implementation of model validation for surrogate models, and • advanced visualization capability for topology based data analysis The development of ensemble modeling for time-series has been performed in order to begin tackling the needs of those RISMC applications that need to communicate 1-Dimensional information (e.g. power histories, etc.) among different models. In this document the implementation details and an application example is reported. The second subject of this report is about the initial development of methods, within the RAVEN framework, to assess the validity of the predictive capabilities of surrogate models. Indeed, after the construction of a surrogate tight to a certain physical model, it is crucial to assess the goodness of its representation, in order to be confident with its prediction. In this initial activity, a cross-validation technique has been employed. This report will highlight the implementation details and proof its correct implementation by an application example. The final subject of this report is about the implementation of advanced visualization capability in RAVEN, for interactive data analysis. Indeed, RAVEN offers several post-processing capabilities that can structurally decompose data extracted from experimental results offering both data clustering/partitioning and dimensionality reduction techniques. A disadvantage of the workflow available in RAVEN is that it treats these as black box operations and the user is expected to know specific information about their data including the number of partitions to expect in some cases or the “correct” parameter settings for a particular algorithm. In order to overcome this limitation, it has been added an interactive user interface that can be run in RAVEN to explore different parameter settings on the fly specifically for the topological post-processor and allows the user to explore the data interactively. The design of this user interface is generalizable to other algorithms and can be used as a model to generate more dynamic and user-friendly visualization capabilities within RAVEN.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Self-action of a wave field in one-dimensional system of weakly coupled active optical waveguides

The dynamics of self-action of a wave field in an array of weakly coupled active optical waveguides is studied analytically and numerically. It is shown that the introduction of weak gain in each of the waveguides allows significant reduction of radiation losses and efficient capture of all radiation in a single optical waveguide. The possibility of controlling the radiation localisation in the desired waveguide at the expense of varying the injection angle of the wave field into the considered system is demonstrated. The dependences of the characteristic parameters of the wave field are determined. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.

42 ENGINEERING↗
DOE OSTI2016

Analysis of dpa rates in the HFIR reactor vessel using a hybrid Monte Carlo/deterministic method

The Oak Ridge High Flux Isotope Reactor (HFIR), which began full-power operation in 1966, provides one of the highest steady-state neutron flux levels of any research reactor in the world. An ongoing vessel integrity analysis program to assess radiation-induced embrittlement of the HFIR reactor vessel requires the calculation of neutron and gamma displacements per atom (dpa), particularly at locations near the beam tube nozzles, where radiation streaming effects are most pronounced. In this study we apply the Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) technique in the ADVANTG code to develop variance reduction parameters for use in the MCNP radiation transport code. We initially evaluated dpa rates for dosimetry capsule locations, regions in the vicinity of the HB-2 beamline, and the vessel beltline region. We then extended the study to provide dpa rate maps using three-dimensional cylindrical mesh tallies that extend from approximately 12 below to approximately 12 above the axial extent of the core. The mesh tally structures contain over 15,000 mesh cells, providing a detailed spatial map of neutron and photon dpa rates at all locations of interest. Relative errors in the mesh tally cells are typically less than 1%.

Blakeman, Edward↗
NASA NTRS2013

Validating an Air Traffic Management Concept of Operation Using Statistical Modeling

Validating a concept of operation for a complex, safety-critical system (like the National Airspace System) is challenging because of the high dimensionality of the controllable parameters and the infinite number of states of the system. In this paper, we use statistical modeling techniques to explore the behavior of a conflict detection and resolution algorithm designed for the terminal airspace. These techniques predict the robustness of the system simulation to both nominal and off-nominal behaviors within the overall airspace. They also can be used to evaluate the output of the simulation against recorded airspace data. Additionally, the techniques carry with them a mathematical value of the worth of each prediction-a statistical uncertainty for any robustness estimate. Uncertainty Quantification (UQ) is the process of quantitative characterization and ultimately a reduction of uncertainties in complex systems. UQ is important for understanding the influence of uncertainties on the behavior of a system and therefore is valuable for design, analysis, and verification and validation. In this paper, we apply advanced statistical modeling methodologies and techniques on an advanced air traffic management system, namely the Terminal Tactical Separation Assured Flight Environment (T-TSAFE). We show initial results for a parameter analysis and safety boundary (envelope) detection in the high-dimensional parameter space. For our boundary analysis, we developed a new sequential approach based upon the design of computer experiments, allowing us to incorporate knowledge from domain experts into our modeling and to determine the most likely boundary shapes and its parameters. We carried out the analysis on system parameters and describe an initial approach that will allow us to include time-series inputs, such as the radar track data, into the analysis

Statistical emulation↗
DOE OSTI2020

Controlled plasma–droplet interactions: a quantitative study of OH transfer in plasma–liquid interaction

Plasmas in contact with liquids are a rich source of OH radicals and have been extensively studied in the last decade to leverage the ability to generate chemically reactive species in gas phase plasmas to decompose organics. Multiphase transfer of OH radicals is highly transport limited and to overcome transport limits, the plasma activation of aerosols, small liquid droplets, interspersed in the plasma has been proposed. In this work, we report a combined experimental and modeling study of a controlled plasma–droplet interaction experiment using a diffuse RF glow discharge in He + 0.2% H 2 O with detailed plasma diagnostics, ex situ analysis of the plasma-induced chemistry in the droplet containing formate, droplet trajectory and size measurements. This enables a quantitative study of the reactivity transfer of OH from the gas phase plasma to the liquid phase and how its diffusion limitations impact formate decomposition in the water droplet. For a droplet with a diameter of 36 μm, we observed 50% reduction in formate concentration in the droplets after plasma treatment for droplet residence times in the plasma of ~10 ms. These short droplet residence times in the plasma allow in some cases for droplet size reductions of ~5% in spite gas temperatures of 360 K. A one-dimensional reaction–diffusion model was used to calculate the OH transport and formate oxidation inside the droplet and was able to predict the conversion of formate by plasma in a droplet without any fitting parameters. The model further shows that formate conversion is dominated by near-interfacial reactions with OH radicals and is limited by diffusion of formate in the droplet. Here, the results show that a controlled plasma–micro-droplet reactor as reported in this study might be an excellent tool for detailed quantitative plasma–liquid interaction studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Uncertainty quantification and optimization of precipitating hydrometeor parameters for winter precipitation in a cloud microphysics scheme

The precipitating hydrometeor parameters used in cloud microphysics schemes carry inherent uncertainties. The quantification of these uncertainties, together with parameter optimization, can significantly improve precipitation forecasts. This study investigates the effects of 13 parameters in the Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) microphysics scheme, which define the hydrometeor characteristics such as fall velocity–diameter and mass–diameter relationships, as well as the shape parameter of the drop size distribution for precipitating particles such as rain, snow, and graupel on simulated winter precipitation. A comparison between the model's pre-defined parameters and observations from the International Collaborative Experiments for the PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign reveals that the fall velocity–diameter relationship for rain, the mass–diameter relationships for snow and graupel, and the shape parameters for all precipitating particles in the WDM6 scheme deviate from the median values observed by the two-dimensional video disdrometer (2DVD). To quantify parameter sensitivities, a perturbed parameter ensemble (PPE) of 256 simulations was conducted within parameter ranges constrained by 2DVD observations for three winter precipitation cases. Bayesian optimization was then applied to identify parameter sets that minimized the root mean square error (RMSE) for each case, achieving reductions of up to 30.2 %. These results demonstrate that ensemble-based uncertainty quantification and parameter optimization can help identify key parameters and provide a pathway to improving precipitation simulation performance. In addition, measurement sites can be strategically selected based on regions that show high sensitivity to variations in hydrometeor characteristic parameters.

Bayesian optimization↗
DOE OSTI2020

Predictive Inverse Model for Advective Heat Transfer in a Short–Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

Identifying fluid flow maldistribution in planar geometries is a well–established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two–dimensional Hele–Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C–Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir–scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding–plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. Here, the results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.

42 ENGINEERING↗
NASA NTRS1996

Recent Developments in Gun Operating Techniques at the NASA Ames Ballistic Ranges

This paper describes recent developments in gun operating techniques at the Ames ballistic range complex. This range complex has been in operation since the early 1960s. Behavior of sabots during separation and projectile-target impact phenomena have long been observed by means of short-duration flash X-rays: new versions allow operation in the lower-energy ("soft") X-ray range and have been found to be more effective than the earlier designs. The dynamics of sabot separation is investigated in some depth from X-ray photographs of sabots launched in the Ames 1.0 in and 1.5 in guns; the sabot separation dynamics appears to be in reasonably good agreement with standard aerodynamic theory. Certain sabot packages appear to suffer no erosion or plastic deformation on traversing the gun barrel, contrary to what would be expected. Gun erosion data from the Ames 0.5 in, 1.0 in, and 1.5 in guns is examined in detail and can be correlated with a particular non- dimensionalized powder mass parameter. The gun erosion increases very rapidly as this parameter is increased. Representative shapes of eroded gun barrels are given. Guided by a computational fluid dynamics (CFD) code, the operating conditions of the Ames 0.5 in and 1.5 in guns were modified. These changes involved: (1) reduction in the piston mass, powder mass and hydrogen fill pressure and (2) reduction in pump tube volume, while maintaining hydrogen mass. These changes resulted in muzzle velocity increases of 0.5-0.8 km/sec, achieved simultaneously with 30-50 percent reductions in gun erosion.

Bogdanoff, D. W.↗
NASA NTRS1992

The evolution of the FIGARO data reduction system

The Figaro data reduction system originated at Caltech around 1983. It was based on concepts being developed in the U.K. by the Starlink organization, particularly the use of hierarchical self-defining data structures and the abstraction of most user-interaction into a set of 'parameter system' routines. Since 1984 it has continued to be developed at AAO, in collaboration with Starlink and Caltech. It was adopted as Starlink's main spectroscopic data reduction package, although it is by no means limited to spectra; it has operations for images and data cubes and even a few (very specialized) for four-dimensional data hypercubes. It continued to be used at Caltech and will be used at the Keck. It is also in use at a variety of other organizations around the world. Figaro was originally a system for VMS Vaxes. Recently it was ported (at Caltech) to run on SUN's, and work is underway at the University of New South Wales on a DecStation version. It is hoped to coordinate all this work into a unified release, but coordination of the development of a system by organizations covering three continents poses a number of interesting administrative problems. The hierarchical data structures used by Figaro allow it to handle a variety of types of data, and to add new items to data structures. Error and data quality information was added to the basic file format used, error information being particularly useful for infrared data. Cooperating sets of programs can add specific sub-structures to data files to carry information that they understand (polarimetry data containing multiple data arrays, for example), without this affecting the way other programs handle the files. Complex instrument-specific ancillary information can be added to data files written at a telescope and can be used by programs that understand the instrumental details in order to produce properly calibrated data files. Once this preliminary data processing was done the resulting files contain 'ordinary' spectra or images that can be processed by programs that are not instrument-specific. The structures holding the instrumental information can then be discarded from the files. Much effort has gone into trying to make it easy to write Figaro programs; data access subroutines are now available to handle access to all the conventional items found in Figaro files (main data arrays, error information, quality information etc), and programs that only need to access such items can be very simple indeed. A large number of Figaro users do indeed write their own Figaro applications using these routines. The fact that Figaro programs are written as callable subroutines getting information from the user through a small set of parameter routines means that they can be invoked in numerous ways; they are normally linked and run as individual programs (called by a small main routine that is generated automatically), but are also available linked to run under the ADAM data acquisition system and there is an interface that lets them be called as part of a user-written Fortran program. The long-term future of Figaro probably depends to a large extent on how successfully it manages the transition from being a VMS-only system to being a multi-platform system.

Shortridge, K.↗
DOE OSTI2015

Parameter estimation by implicit sampling

© 2015 Mathematical Sciences Publishers. Implicit sampling is a weighted sampling method that is used in data assimilation to sequentially update state estimates of a stochastic model based on noisy and incomplete data. Here we apply implicit sampling to sample the posterior probability density of parameter estimation problems. The posterior probability combines prior information about the parameter with information from a numerical model, e.g., a partial differential equation (PDE), and noisy data. The result of our computations are parameters that lead to simulations that are compatible with the data. We demonstrate the usefulness of our implicit sampling algorithm with an example from subsurface flow. For an efficient implementation, we make use of multiple grids, BFGS optimization coupled to adjoint equations, and Karhunen-Loève expansions for dimensional reduction. Several difficulties of Markov chain Monte Carlo methods, e.g., estimation of burn-in times or correlations among the samples, are avoided because the implicit samples are independent.

Morzfeld, Matthias↗
DOE OSTI2022

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Abstract The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra, which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep-learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot-Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Parametric model-order-reduction development for unsteady convection

A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parameter space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.

leray regularization↗
DOE OSTI2020

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.

42 ENGINEERING↗
DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗