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NASA NTRS2017

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗
NASA NTRS2021

Machine Learning the COSMO Model for Predicting Thermodynamics of Electrolyte Mixtures

Bottom-up design of electrolyte mixtures for battery systems requires predicting macro thermodynamic properties from molecular constituents. For instance, molten salt electrolyte batteries require conditions far above room temperature to operate. Therefore, discovering mixtures with increasingly lower eutectic melting points is desirable. A model that can approximate chemical activity is a valuable tool to search through the vast compositional design space. Machine learning can predict properties of materials such as vibrational free energies, electronic energy gaps, and thermal conductivities. Moreover, they can learn physical models such as interatomic potentials. The COSMO-SAC model uses theory and empirical parameterization to predict liquid-vapor and liquid-solid properties using first-principles calculations. However, obtaining activity coefficients required for parameterizing the COSMO-SAC model is costly and limited to a select chemical space. In this work, we explored if machine learning methods could improve the COSMO-SAC model and bridge density functional theory calculations to liquid phase thermodynamic properties. Our data-driven approach uses existing databases for sigma-profiles of organic solvents and reconciles their methodological differences via ensemble averaging. First, an optimal machine learning model is constructed for each dataset. Our machine learning algorithms use the sigma-profile as an input feature to predict binary mixtures' activity coefficients using multi-output regression. Each dataset uses different choices of functionals, methods, and basis sets. Therefore, our ensemble model attempts to predict corrected activity coefficients given the combination of all the model outputs. The activity coefficients used for training are generated using the COSMO-SAC model. This approach enables the extraction of meaningful information from the existing datasets to improve the COSMO-SAC model for obtaining thermodynamic properties of electrolyte mixtures. With the liquid phase activities, we can identify electrolyte mixtures that meet desired phase equilibria conditions.

Thermodynamics↗
NASA NTRS2012

A Comparison of Perturbed Initial Conditions and Multiphysics Ensembles in a Severe Weather Episode in Spain

Ensembles of numerical model forecasts are of interest to operational early warning forecasters as the spread of the ensemble provides an indication of the uncertainty of the alerts, and the mean value is deemed to outperform the forecasts of the individual models. This paper explores two ensembles on a severe weather episode in Spain, aiming to ascertain the relative usefulness of each one. One ensemble uses sensible choices of physical parameterizations (precipitation microphysics, land surface physics, and cumulus physics) while the other follows a perturbed initial conditions approach. The results show that, depending on the parameterizations, large differences can be expected in terms of storm location, spatial structure of the precipitation field, and rain intensity. It is also found that the spread of the perturbed initial conditions ensemble is smaller than the dispersion due to physical parameterizations. This confirms that in severe weather situations operational forecasts should address moist physics deficiencies to realize the full benefits of the ensemble approach, in addition to optimizing initial conditions. The results also provide insights into differences in simulations arising from ensembles of weather models using several combinations of different physical parameterizations.

severe weather↗
NASA NTRS2002

A 12-year (1987-1998) Ensemble Simulation of the US Climate with a Variable Resolution Stretched Grid GCM

The variable-resolution stretched-grid (SG) GEOS (Goddard Earth Observing System) GCM has been used for limited ensemble integrations with a relatively coarse, 60 to 100 km, regional resolution over the U.S. The experiments have been run for the 12-year period, 1987-1998, that includes the recent ENSO cycles. Initial conditions 1-2 days apart are used for ensemble members. The goal of the experiments is analyzing the long-term SG-GCM ensemble integrations in terms of their potential in reducing the uncertainties of regional climate simulation while producing realistic mesoscales. The ensemble integration results are analyzed for both prognostic and diagnostic fields. A special attention is devoted to analyzing the variability of precipitation over the U.S. The internal variability of the SG-GCM has been assessed. The ensemble means appear to be closer to the verifying analyses than the individual ensemble members. The ensemble means capture realistic mesoscale patterns, especially those of induced by orography. Two ENSO cycles have been analyzed in terms their impact on the U.S. climate, especially on precipitation. The ability of the SG-GCM simulations to produce regional climate anomalies has been confirmed. However, the optimal size of the ensembles depending on fine regional resolution used, is still to be determined. The SG-GCM ensemble simulations are performed as a preparation or a preliminary stage for the international SGMIP (Stretched-Grid Model Intercomparison Project) that is under way with participation of the major centers and groups employing the SG-approach for regional climate modeling.

Fox-Rabinovitz, Michael S.↗
NASA NTRS2019

Soil Moisture Data Assimilation

Accurate knowledge of soil moisture at the continental scale is important for improving predictions of weather, agricultural productivity and natural hazards, but observations of soil moisture at such scales are limited to indirect measurements, either obtained through satellite remote sensing or from meteorological networks. Land surface models simulate soil moisture processes, using observation-based meteorological forcing data, and auxiliary information about soil, terrain and vegetation characteristics. Enhanced estimates of soil moisture and other land surface variables, along with their uncertainty, can be obtained by assimilating observations of soil moisture into land surface models. These assimilation results are of direct relevance for the initialization of hydro-meteorological ensemble forecasting systems. The success of the assimilation depends on the choice of the assimilation technique, the nature of the model and the assimilated observations, and, most importantly, the characterization of model and observation error. Systematic differences between satellite-based microwave observations or satellite-retrieved soil moisture and their simulated counterparts require special attention. Other challenges include inferring root-zone soil moisture information from observations that pertain to a shallow surface soil layer, propagating information to unobserved areas and downscaling of coarse information to finer-scale soil moisture estimates. This chapter summarizes state-of-the-art solutions to these issues with conceptual data assimilation examples, using techniques ranging from simplified optimal interpolation to spatial ensemble Kalman filtering. In addition, operational soil moisture assimilation systems are discussed that support numerical weather prediction at ECMWF and provide value-added soil moisture products for the NASA Soil Moisture Active Passive mission.

radar backscatter↗
NASA NTRS2012

A review of reduced Kalman filters for clock ensembles

This paper reviews the author’s previous work on free-running timescales based on Kalman filters that act upon clock comparisons. The natural Kalman clock ensemble algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each postmeasurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability. A new result on covariance matrix reduction is also stated.

Greenhall, Charles A.↗
NASA NTRS2005

Optimized program completeness

Overall program completeness is optimized by selecting the ordered set of observations and targets that maximizes the efficiency for the ensemble of stars. We describe the optimization approach and report on completeness sensitivity to instrument throughput, inner working angle, instrument sensitivity, observational overhead, exo-zodiacal brightness, and target revisit constraints.

optimization↗
NASA NTRS2017

Assimilation of MODIS Dark Target and Deep Blue Observations in the Dust Aerosol Component of NMMB-MONARCH version 1.0

A data assimilation capability has been built for the NMMB-MONARCH chemical weather prediction system, with a focus on mineral dust, a prominent type of aerosol. An ensemble-based Kalman filter technique (namely the local ensemble transform Kalman filter - LETKF) has been utilized to optimally combine model background and satellite retrievals. Our implementation of the ensemble is based on known uncertainties in the physical parametrizations of the dust emission scheme. Experiments showed that MODIS AOD retrievals using the Dark Target algorithm can help NMMB-MONARCH to better characterize atmospheric dust. This is particularly true for the analysis of the dust outflow in the Sahel region and over the African Atlantic coast. The assimilation of MODIS AOD retrievals based on the Deep Blue algorithm has a further positive impact in the analysis downwind from the strongest dust sources of the Sahara and in the Arabian Peninsula. An analysis-initialized forecast performs better (lower forecast error and higher correlation with observations) than a standard forecast, with the exception of underestimating dust in the long-range Atlantic transport and degradation of the temporal evolution of dust in some regions after day 1. Particularly relevant is the improved forecast over the Sahara throughout the forecast range thanks to the assimilation of Deep Blue retrievals over areas not easily covered by other observational datasets.The present study on mineral dust is a first step towards data assimilation with a complete aerosol prediction system that includes multiple aerosol species.

atmospheric dust↗
NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in A Mach 4.5 Boundary Layer

We use deep learning, an ensemble variationaltechnique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (Deep-ONets), which have the known ability to learn com-plex nonlinear operators within dynamical systems,are used for machine learning. For the baseline config-uration of a smooth flat plate, the second-mode wavesat the DNS inflow cause a quick nonlinear breakdownof the high-speed boundary layer within the computa-tional domain. Results reported in the present studyvalidate the ability of DeepONets to model the tran-sition delay via a given topography of the roughnesselement. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substan-tially lowered by the DeepONets-based reduced-ordermodel. In comparison to the baseline method of EnVaroptimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition pastthe outflow boundary of the computational domainwhile utilizing almost 5–6 times fewer DNS.

Machine Learning↗
NASA NTRS1994

In Vitro Selection of Optimal DNA Substrates for Ligation by a Water-Soluble Carbodiimide

We have used in vitro selection to investigate the sequence requirements for efficient template-directed ligation of oligonucleotides at 0 deg C using a water-soluble carbodiimide as condensing agent. We find that only 2 bp at each side of the ligation junction are needed. We also studied chemical ligation of substrate ensembles that we have previously selected as optimal by RNA ligase or by DNA ligase. As anticipated, we find that substrates selected with DNA ligase ligate efficiently with a chemical ligating agent, and vice versa. Substrates selected using RNA ligase are not ligated by the chemical condensing agent and vice versa. The implications of these results for prebiotic chemistry are discussed.

Harada, Kazuo↗
NASA NTRS2016

Application of Aviation Turbulence Information to Air-Traffic Management (ATM): Chapter - 24

Unexpected turbulence especially in the upper troposphere and lower stratosphere where cabin crews and passengers in cruising aircraft are likely to unbuckle causes in-flight injuries, structural damage, and flight delay. Therefore, turbulence information can be used to improve safety while pursuing efficiency in Air-Traffic Management (ATM). In this chapter, simple modeling of aircraft trajectories combined with wind and turbulence predictions can suggest the optimal solution of flight plans that minimizes both total flight time (e.g., fuel consumption) and potential encounters of turbulence from departure to arrival airports. Also, probabilistic ensemble turbulence forecasts are applied to suggest an optimal strategic and tactical ATM route planning in a given weather and turbulence condition in the United States which are evaluated against in situ Eddy Dissipation Rate observations from commercial aircraft. Finally, variations of long-haul trans-Oceanic flight routes and their turbulence potentials are investigated using a global reanalysis data to understand how the upper-level large-scale flow patterns can affect the long-term ATM planning through the changes of winds and turbulence conditions.

Wind Optimal↗
NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in a Mach 4.5 Boundary Layer

We use deep learning, an ensemble variational technique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (DeepONets), which have the known ability to learn complex nonlinear operators within dynamical systems, are used for machine learning. For the baseline configuration of a smooth flat plate, the second-mode waves at the DNS inflow cause a quick nonlinear breakdown of the high-speed boundary layer within the computational domain. Results reported in the present study validate the ability of DeepONets to model the transition delay via a given topography of the roughness element. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substantially lowered by the DeepONets-based reduced-order model. In comparison to the baseline method of EnVar optimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition past the outflow boundary of the computational domain while utilizing almost 5–6 times fewer DNS.

Machine Learning↗
NASA NTRS2020

An Examination of the Impact of Grid Spacing on WRF Simulations of Wintertime Precipitation in the Mid-Atlantic United States

A large set of deterministic and ensemble forecasts was produced to identify the optimal spacing for forecasting U.S. East Coast snowstorms. WRF forecasts were produced on cloud-allowing (~1-km grid spacing) and convection-allowing (3–4 km) grids, and compared against forecasts with parameterized convection (>~10 km). Performance diagrams were used to evaluate 19 deterministic forecasts from the winter of 2013–14. Ensemble forecasts of five disruptive snowstorms spanning the years 2015–18 were evaluated using various methods to evaluate probabilistic forecasts. While deterministic forecasts using cloud-allowing grids were not better than convection-allowing forecasts, both had lower bias and higher success ratios than forecasts with parameterized convection. All forecasts were underdispersive. Nevertheless, forecasts on the higher-resolution grids were more reliable than those with parameterized convection. Forecasts on the cloud-allowing grid were best able to discriminate areas that received heavy snow and those that did not, while the forecasts with parameterized convection were least able to do so. It is recommended to use convection-resolving and (if computationally possible) to use cloud-allowing forecast grids when predicting East Coast winter storms.

Snowstorms↗
NASA NTRSDate not supplied

A Framework for Evaluating Climate Model Performance Metrics

The CMIP5 archive contains future climate projections from over 50 models provided by dozens of modeling centers from around the world. Individual model projections, however, are subject to biases created by structural model uncertainties. As a result, ensemble averaging of multiple models is often used to add value to model projections: consensus projections have been shown to consistently outperform individual models. Previous reports for the IPCC establish climate change projections based on an equal-weighted average of all model projections. However, certain models reproduce climate processes better than other models. Should models be weighted based on performance? Unequal ensemble averages have previously been constructed using a variety of mean state metrics. What metrics are most relevant for constraining future climate projections? This project develops a framework for systematically testing metrics in models to identify optimal metrics for unequal weighting multi-model ensembles. A unique aspect of this project is the construction and testing of climate process-based model evaluation metrics. A climate process-based metric is defined as a metric based on the relationship between two physically related climate variables?e.g., outgoing longwave radiation and surface temperature. Metrics are constructed using high-quality Earth radiation budget data from NASA's Clouds and Earth's Radiant Energy System (CERES) instrument and surface temperature data sets. It is found that regional values of tested quantities can vary significantly when comparing weighted and unweighted model ensembles. For example, one tested metric weights the ensemble by how well models reproduce the time-series probability distribution of the cloud forcing component of reflected shortwave radiation. The weighted ensemble for this metric indicates lower simulated precipitation (up to .7 mm/day) in tropical regions than the unweighted ensemble: since CMIP5 models have been shown to overproduce precipitation, this result could indicate that the metric is effective in identifying models which simulate more realistic precipitation. Ultimately, the goal of the framework is to identify performance metrics for advising better methods for ensemble averaging models and create better climate predictions.

Noel C Baker↗
NASA NTRS2010

Forecasting Lightning Threat Using WRF Proxy Fields

Objectives: Given that high-resolution WRF forecasts can capture the character of convective outbreaks, we seek to: 1. Create WRF forecasts of LTG threat (1-24 h), based on 2 proxy fields from explicitly simulated convection: - graupel flux near -15 C (captures LTG time variability) - vertically integrated ice (captures LTG threat area). 2. Calibrate each threat to yield accurate quantitative peak flash rate densities. 3. Also evaluate threats for areal coverage, time variability. 4. Blend threats to optimize results. 5. Examine sensitivity to model mesh, microphysics. Methods: 1. Use high-resolution 2-km WRF simulations to prognose convection for a diverse series of selected case studies. 2. Evaluate graupel fluxes; vertically integrated ice (VII). 3. Calibrate WRF LTG proxies using peak total LTG flash rate densities from NALMA; relationships look linear, with regression line passing through origin. 4. Truncate low threat values to make threat areal coverage match NALMA flash extent density obs. 5. Blend proxies to achieve optimal performance 6. Study CAPS 4-km ensembles to evaluate sensitivities.

McCaul, E. W., Jr.↗
NASA NTRS2014

Reply to Comment by Laprise on 'the Added Value to Global Model Projections of Climate Change by Dynamical Downscaling: a Case Study over the Continental U.S. Using the GISS-ModelE2 and WRF Models'

In his comment, Laprise raises several points that we agree merit consideration. His primary critique is that our study [Racherla et al., 2012] tested the ability of the WRF regional climate model to reproduce historical temperature and precipitation change relative to the driving global climate model (GCM) using only a single simulation rather than an ensemble. He asserts that the observed changes are smaller than the internal variability in the climate system (i.e., not statistically significant) and that thus a single simulation should not necessarily be able to capture the observations. Laprise points out that the statistical signal is reduced for a multi-decadal trend such as the one we analyzed in comparison with mean climatology and cites two studies showing that for particular climate parameters it can take any years for a signal to be discerned over internal variability. He states that The results of theexperiment as designed were strongly influenced by the presence of internal variability and sampling errors,which masked the rather small climate changes that may have occurred as a consequence of changes inforcing during the period considered. While Laprise discusses statistics in general terms at some length, for the actual climate trends examined in our study, he offers no evidence that the forced signal was smallcompared with internal variability. The two studies he cites [de Ela et al., 2013; Maraun, 2013] do not provide convincing evidence as they concern climate variables averaged over different times and areas. One in fact examines extreme precipitation events, which by definition are rare and thus have a lower significance level. We accept the general point that it is important to consider internal variability, and as noted in our paper we agree that an ensemble of simulations is in principle an optimal, though computationally expensive, approach. While we did not present the statistical significance of the observations in our original paper, we have now evaluated those for the regional temperature trends used in our study to evaluate the added value of WRF and thus can analyze data as to the magnitude of the trends with respect to internal variability.

climate↗