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Results for “ensemble optimization”

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NASA NTRSDate not supplied

Model Calibration for Cancer Risk Projections According to Uncertain Data

This paper presents forward and inverse formulations for the calibration of computational models according to uncertain data. Uncertainty in the data might be caused by a poor metrology system, measurement noise, missing or uncontrollable input variables, or by the inability to directly measure the inputs and/or outputs of interest. The forward approach performs the calibration in the space of the model’s output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model’s parameters. As such, the computational demands of the inverse approach are considerably lower. These strategies are applied to the calibration of a radiation model that in-forms cancer risk projections for future deep space missions.

uncertainty quantification↗

NASA NTRS2022

Artificial Neural Network Modeling for Airline Disruption Management

Since the 1970s, most airlines have incorporated computerized support for managing disruptions during flight schedule execution. However, existing platforms for airline disruption management (ADM) employ monolithic system design methods that rely on the creation of specific rules and requirements through explicit optimization routines, before a system that meets the specifications is designed. Thus, current platforms for ADM are unable to readily accommodate additional system complexities resulting from the introduction of new capabilities, such as the introduction of unmanned aerial systems (UAS), operations and infrastructure, to the system. To this end, we use historical data on airline scheduling and operations recovery to develop a system of artificial neural networks (ANNs), which describe a predictive transfer function model (PTFM) for promptly estimating the recovery impact of disruption resolutions at separate phases of flight schedule execution during ADM. Furthermore, we provide a modular approach for assessing and executing the PTFM by employing a parallel ensemble method to develop generative routines that amalgamate the system of ANNs. Our modular approach ensures that current industry standards for tardiness in flight schedule execution during ADM are satisfied, while accurately estimating appropriate time-based performance metrics for the separate phases of flight schedule execution.

Kolawole Ogunsina↗

NASA NTRS2016

Basin-Scale Assessment of the Land Surface Water Budget in the National Centers for Environmental Prediction Operational and Research NLDAS-2 Systems

The purpose of this study is to evaluate the components of the land surface water budget in the four land surface models (Noah, SAC-Sacramento Soil Moisture Accounting Model, (VIC) Variable Infiltration Capacity Model, and Mosaic) applied in the newly implemented National Centers for Environmental Prediction (NCEP) operational and research versions of the North American Land Data Assimilation System version 2 (NLDAS-2). This work focuses on monthly and annual components of the water budget over 12 National Weather Service (NWS) River Forecast Centers (RFCs). Monthly gridded FLUX Network (FLUXNET) evapotranspiration (ET) from the Max-Planck Institute (MPI) of Germany, U.S. Geological Survey (USGS) total runoff (Q), changes in total water storage (dS/dt, derived as a residual by utilizing MPI ET and USGS Q in the water balance equation), and Gravity Recovery and Climate Experiment (GRACE) observed total water storage anomaly (TWSA) and change (TWSC) are used as reference data sets. Compared to these ET and Q benchmarks, Mosaic and SAC (Noah and VIC) in the operational NLDAS-2 overestimate (underestimate) mean annual reference ET and underestimate (overestimate) mean annual reference Q. The multimodel ensemble mean (MME) is closer to the mean annual reference ET and Q. An anomaly correlation (AC) analysis shows good AC values for simulated monthly mean Q and dS/dt but significantly smaller AC values for simulated ET. Upgraded versions of the models utilized in the research side of NLDAS-2 yield largely improved performance in the simulation of these mean annual and monthly water component diagnostics. These results demonstrate that the three intertwined efforts of improving (1) the scientific understanding of parameterization of land surface processes, (2) the spatial and temporal extent of systematic validation of land surface processes, and (3) the engineering-oriented aspects such as parameter calibration and optimization are key to substantially improving product quality in various land data assimilation systems.

NLDAS-2↗

NASA NTRS1992

Optimization of armored spherical tanks for storage on the lunar surface

A redundancy strategy for reducing micrometeroid armoring mass is investigated, with application to cryogenic reactant storage for a regenerative fuel cell (RFC) on the lunar surface. In that micrometeoroid environment, the cryogenic fuel must be protected from loss due to tank puncture. The tankage must have a sufficiently high probability of survival over the length of the mission so that the probability of system failure due to tank puncture is low compared to the other mission risk factors. Assuming that a single meteoroid penetration can cause a storage tank to lose its contents, two means are available to raise the probability of surviving micrometeoroid attack to the desired level. One can armor the tanks to a thickness sufficient to reduce probability of penetration of any tank to the desired level or add extra capacity in the form of spare tanks that results in survival of a given number out of the ensemble at the desired level. A combination of these strategies (armoring and redundancy) is investigated. The objective is to find the optimum combination which yields the lowest shielding mass per cubic meter of surviving fuel out of the original ensemble. The investigation found that, for the volumes of fuel associated with multikilowatt class cryo storage RFC's, and the armoring methodology and meteoroid models used, storage should be fragmented into small individual tanks. Larger installations (more fuel) pay less of a shielding penalty than small installations. For the same survival probability over the same time period, larger volumes will require less armoring mass per unit volume protected.

Bents, D. J.↗

NASA NTRS1992

Optimization of armored spherical tanks for storage on the lunar surface

Bents, D. J.↗

NASA NTRS2017

Uncertainty Assessment of Space-Borne Passive Soil Moisture Retrievals

The uncertainty associated with passive soil moisture retrieval is hard to quantify, and known to be underlain by various, diverse, and complex causes. Factors affecting space-borne retrieved soil moisture estimation include: (i) the optimization or inversion method applied to the radiative transfer model (RTM), such as e.g. the Single Channel Algorithm (SCA), or the Land Parameter Retrieval Model (LPRM), (ii) the selection of the observed brightness temperatures (Tbs), e.g. polarization and incidence angle, (iii) the definition of the cost function and the impact of prior information in it, and (iv) the RTM parameterization (e.g. parameterizations officially used by the SMOS L2 and SMAP L2 retrieval products, ECMWF-based SMOS assimilation product, SMAP L4 assimilation product, and perturbations from those configurations). This study aims at disentangling the relative importance of the above-mentioned sources of uncertainty, by carrying out soil moisture retrieval experiments, using SMOS Tb observations in different settings, of which some are mentioned above. The ensemble uncertainties are evaluated at 11 reference CalVal sites, over a time period of more than 5 years. These experimental retrievals were inter-compared, and further confronted with in situ soil moisture measurements and operational SMOS L2 retrievals, using commonly used skill metrics to quantify the temporal uncertainty in the retrievals.

Quets, Jan↗

NASA NTRS2015

An Assessment of Actual and Potential Building Climate Zone Change and Variability From the Last 30 Years Through 2100 Using NASA's MERRA and CMIP5 Simulations

Background: In the US, residential and commercial building infrastructure combined consumes about 40% of total energy usage and emits about 39% of total CO2 emission (DOE/EIA "Annual Energy Outlook 2013"). Building codes, as used by local and state enforcement entities are typically tied to the dominant climate within an enforcement jurisdiction classified according to various climate zones. These climate zones are based upon a 30-year average of local surface observations and are developed by DOE and ASHRAE. Establishing the current variability and potential changes to future building climate zones is very important for increasing the energy efficiency of buildings and reducing energy costs and emissions in the future. Objectives: This paper demonstrates the usefulness of using NASA's Modern Era Retrospective-analysis for Research and Applications (MERRA) atmospheric data assimilation to derive the DOE/ASHRAE building climate zone maps and then using MERRA to define the last 30 years of variability in climate zones for the Continental US. An atmospheric assimilation is a global atmospheric model optimized to satellite, atmospheric and surface in situ measurements. Using MERRA as a baseline, we then evaluate the latest Climate Model Inter-comparison Project (CMIP) climate model Version 5 runs to assess potential variability in future climate zones under various assumptions. Methods: We derive DOE/ASHRAE building climate zones using surface and temperature data products from MERRA. We assess these zones using the uncertainties derived by comparison to surface measurements. Using statistical tests, we evaluate variability of the climate zones in time and assess areas in the continental US for statistically significant trends by region. CMIP 5 produced a data base of over two dozen detailed climate model runs under various greenhouse gas forcing assumptions. We evaluate the variation in building climate zones for 3 different decades using an ensemble and quartile statistics to provide an assessment of potential building climate zone changes relative to the uncertainties demonstrated using MERRA. Findings and Conclusions: These results show that there is a statistically significant increase in the area covered by warmer climate zones and a tendency for a reduction of area in colder climate zones in some limited regions. The CMIP analysis shows that models vary from relatively little building climate zone change for the least sensitive and conservation assumptions to a warming of at most 3 zones for certain areas, particularly the north central US by the end of the 21st century.

Stackhouse, Paul W., Jr.↗

NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗

NASA NTRS2004

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗

NASA NTRS2011

Quantifying the Aerosol Semi-Direct Effect in the NASA GEOS-5 AGCM

Aerosols such as black carbon, dust, and some organic carbon species both scatter and absorb incoming solar radiation. This direct aerosol radiative forcing (DARF) redistributes solar energy both by cooling the surface and warming the atmosphere. As a result, these aerosols affect atmospheric stability and cloud cover (the semi-direct effect, or SDE). Furthermore, in regions with persistent high loadings of absorbing aerosols (e.g. Asia), regional circulation patterns may be altered, potentially resulting in changes in precipitation patterns. Here we investigate aerosol-climate coupling using the NASA Goddard Earth Observing System model version 5 (GEOS-5) atmospheric general circulation model (AGCM), in which we have implemented an online version of the Goddard Chemistry, Aerosol, Radiation and Transport (GOCART) model. GOCART includes representations of the sources, sinks, and chemical transformation of externally mixed dust, sea salt, sulfate, and carbonaceous aerosols. We examine a series of free-running ensemble climate simulations of the present-day period (2000-2009) forced by observed sea surface temperatures to determine the impact of aerosols on the model climate. The SDE and response of each simulation is determined by differencing with respect to the control simulation (no aerosol forcing). In a free-running model, any estimate of the SDE includes changes in clouds due both to atmospheric heating from aerosols and changes in circulation. To try and quantify the SDE without these circulation changes we then examine the DARF and SDE in GEOS-5 with prescribed meteorological analyses introduced by the MERRA analysis. By doing so, we are able to examine changes in model clouds that occur on shorter scales (six hours). In the GEOS-5 data assimilation system (DAS), the analysis is defined as the best estimate of the atmospheric state at any given time, and it is determined by optimally combining a first-guess short-term GCM forecast with all available observations. The Incremental Analysis Update (IAU) is added to the model forecast tendencies to align them with the analysis every six hours, thus preventing longer timescale feedbacks due to the aerosol forcing. We calculate the SDE by comparing model runs with and without aerosols, and the difference in the IAU between these runs is a useful metric with which to evaluate the impact of the SDE on the model atmosphere and clouds. Decreasing the IAU indicates that the aerosol direct and semi-direct effects act to reduce the bias between the model and observations and vice versa.

Randles, Cynthia A.↗

NASA NTRS2000

Improving Global Analysis and Short-Range Forecast Using Rainfall and Moisture Observations Derived from TRMM and SSM/I Passive Microwave Instruments

The Global Precipitation Mission, a satellite project under consideration as a follow-on to the Tropical Rainfall Measuring Mission (TRMM) by the National Aeronautics and Space Agency (NASA) in the United States, the National Space Development Agency (NASDA) in Japan, and other international partners, comprises an improved TRMM-like satellite and a constellation of 8 satellites carrying passive microwave radiometers to provide global rainfall measurements at 3-hour intervals. The success of this concept relies on the merits of rainfall estimates derived from passive microwave radiometers. This article offers a proof-of-concept demonstration of the benefits of using, rainfall and total precipitable water (TPW) information derived from such instruments in global data assimilation with observations from the TRMM Microwave Imager (TMI) and 2 Special Sensor Microwave/Imager (SSM/I) instruments. Global analyses that optimally combine observations from diverse sources with physical models of atmospheric and land processes can provide a comprehensive description of the climate systems. Currently, such data analyses contain significant errors in primary hydrological fields such as precipitation and evaporation, especially in the tropics. We show that assimilating the 6-h averaged TMI and SSM/I surface rainrate and TPW retrievals improves not only the hydrological cycle but also key climate parameters such as clouds, radiation, and the upper tropospheric moisture in the analysis produced by the Goddard Earth Observing System (GEOS) Data Assimilation System, as verified against radiation measurements by the Clouds and the Earth's Radiant Energy System (CERES) instrument and brightness temperature observations by the TIROS Operational Vertical Sounder (TOVS) instruments. Typically, rainfall assimilation improves clouds and radiation in areas of active convection, as well as the latent heating and large-scale motions in the tropics, while TPW assimilation leads to reduced moisture biases and improved radiative fluxes in clear-sky regions. Ensemble forecasts initialized with analyses that incorporate TMI and SSM/I rainfall and TPW data also yield better short-range predictions of geopotential heights, winds, and precipitation in the tropics. This study offers a compelling illustration of the potential of using rainfall and TPW information derived from passive microwave instruments to significantly improve the quality of 4-dimensional global datasets for climate analysis and weather forecasting applications.

Hou, Arthur Y.↗

NASA NTRS2014

Benchmarking a Soil Moisture Data Assimilation System for Agricultural Drought Monitoring

Despite considerable interest in the application of land surface data assimilation systems (LDAS) for agricultural drought applications, relatively little is known about the large-scale performance of such systems and, thus, the optimal methodological approach for implementing them. To address this need, this paper evaluates an LDAS for agricultural drought monitoring by benchmarking individual components of the system (i.e., a satellite soil moisture retrieval algorithm, a soil water balance model and a sequential data assimilation filter) against a series of linear models which perform the same function (i.e., have the same basic inputoutput structure) as the full system component. Benchmarking is based on the calculation of the lagged rank cross-correlation between the normalized difference vegetation index (NDVI) and soil moisture estimates acquired for various components of the system. Lagged soil moistureNDVI correlations obtained using individual LDAS components versus their linear analogs reveal the degree to which non-linearities andor complexities contained within each component actually contribute to the performance of the LDAS system as a whole. Here, a particular system based on surface soil moisture retrievals from the Land Parameter Retrieval Model (LPRM), a two-layer Palmer soil water balance model and an Ensemble Kalman filter (EnKF) is benchmarked. Results suggest significant room for improvement in each component of the system.

soil moisture↗

NASA NTRS1999

Improving Assimilated Global Data Sets using TMI Rainfall and Columnar Moisture Observations

A global analysis that optimally combine observations from diverse sources with physical models of atmospheric and land processes can provide a comprehensive description of the climate systems. Currently, such data products contain significant errors in primary hydrological fields such as precipitation and evaporation, especially in the tropics. In this study, we show that assimilating precipitation and total precipitable water (TPW) retrievals derived from the TRMM Microwave Imager (TMI) improves not only the hydrological cycle but also key climate parameters such as clouds, radiation, and the large-scale circulation produced by the Goddard Earth Observing System (GEOS) data assimilation system (DAS). In particular, assimilating TMI rain improves clouds and radiation in areas of active convection, as well as the latent heating distribution and the large-scale motion field in the tropics, while assimilating TMI TPW heating distribution and the large-scale motion field in the tropics, while assimilating TMI TPW retrievals leads to reduced moisture biases and improved radiative fluxes in clear-sky regions. The improved analysis also improves short-range forecasts in the tropics. Ensemble forecasts initialized with the GEOS analysis incorporating TMI rain rates and TPW yield smaller biases in tropical precipitation forecasts beyond 1 day and better 500 hPa geopotential height forecasts up to 5 days. Results of this study demonstrate the potential of using high-quality space-borne rainfall and moisture observations to improve the quality of assimilated global data for climate analysis and weather forecasting applications

Hou, Arthur Y.↗

NASA NTRS2016

Assimilation of SMOS Brightness Temperatures or Soil Moisture Retrievals into a Land Surface Model

Three different data products from the Soil Moisture Ocean Salinity (SMOS) mission are assimilated separately into the Goddard Earth Observing System Model, version 5 (GEOS-5) to improve estimates of surface and root-zone soil moisture. The first product consists of multi-angle, dual-polarization brightness temperature (Tb) observations at the bottom of the atmosphere extracted from Level 1 data. The second product is a derived SMOS Tb product that mimics the data at a 40 degree incidence angle from the Soil Moisture Active Passive (SMAP) mission. The third product is the operational SMOS Level 2 surface soil moisture (SM) retrieval product. The assimilation system uses a spatially distributed ensemble Kalman filter (EnKF) with seasonally varying climatological bias mitigation for Tb assimilation, whereas a time-invariant cumulative density function matching is used for SM retrieval assimilation. All assimilation experiments improve the soil moisture estimates compared to model-only simulations in terms of unbiased root-mean-square differences and anomaly correlations during the period from 1 July 2010 to 1 May 2015 and for 187 sites across the US. Especially in areas where the satellite data are most sensitive to surface soil moisture, large skill improvements (e.g., an increase in the anomaly correlation by 0.1) are found in the surface soil moisture. The domain-average surface and root-zone skill metrics are similar among the various assimilation experiments, but large differences in skill are found locally. The observation-minus-forecast residuals and analysis increments reveal large differences in how the observations add value in the Tb and SM retrieval assimilation systems. The distinct patterns of these diagnostics in the two systems reflect observation and model errors patterns that are not well captured in the assigned EnKF error parameters. Consequently, a localized optimization of the EnKF error parameters is needed to further improve Tb or SM retrieval assimilation.

SMOS↗

NASA NTRS2021

Optimizing GRACE/GRACE-FO Data and A priori Hydrological Knowledge for Improved Global Terrestial Water Storage Component Estimates

The comprehensive information of global terrestrial water storage (TWS) components (soil moisture, groundwater, snow, surface water) is essential for effective assessment of water resource availability, climate variation, and disaster mitigation measures. Observational data provided by the Gravity Recovery And Climate Experiment (GRACE) and GRACE Follow-On satellite missions offer global TWS variation (ΔTWS) in terms of an integrated water column. However, GRACE spatial resolution is relatively coarse (i.e., 3°), and the vertically integrated value cannot be separated into ΔTWS components directly. This study demonstrates the feasibility to estimate ΔTWS components at any desired spatial-vertical resolution by effectively maintaining the native resolution of the employed hydrological knowledge. It utilizes a least-squares with constraints (LSC) approach to rigorously incorporate GRACE and GRACE-FO data and a priori hydrological knowledge, with the aim to improve global ΔTWS components’ accuracy and spatial resolution. The 3°×3° GRACE mascon derived ΔTWS data is disaggregated into the 0.5°×0.5° anomalous soil moisture storage (ΔSMS), groundwater storage (ΔGWS), snow water equivalent (ΔSWE), and surface water storage (ΔSWS) based on the covariance information obtained from the Community Atmosphere Biosphere Land Exchange (CABLE) and the PCRaster Global Water Balance (PCR-GLOBWB) models. Evaluation with different ground measurements and satellite products between 2002 and 2019 exhibits significantly improved accuracy in all individual ΔTWS components. This improvement is of particular note in ΔGWS and ΔSWS, where the LSC approach increases the globally averaged correlation values by approximately 0.13 and 0.05, respectively. Reliable prior knowledge leads to a more accurate ΔTWS component estimate, and the use of ensemble-mean knowledge yields the best result.

GRACE↗

NASA NTRS2021

Passive Microwave Brightness Temperature Assimilation to Improve Snow Mass Estimation across Complex Terrain in Pakistan, Afghanistan, and Tajikistan

An ensemble Kalman filter is used to assimilate Advanced Microwave Scanning Radiometer-2 (AMSR2) observations of passive microwave (PMW) brightness temperatures (spectral differences, ΔT b ) into land surface model estimates of snow mass over northwestern high mountain Asia (HMA). Trained support vector machines serve as the observation operator and map the geophysical modeled variables into ΔT b space within the assimilation framework. Evaluation of the assimilation routine is carried out through comparison of assimilated snow mass estimates with an in situ dataset. The assimilation framework helps improve the land surface model estimates through PMW ΔT b assimilation, particularly in terms of decreasing the domain-wide bias. The assimilation framework proved more effective during the (dry) snow accumulation season and decreased the bias and root-mean-square error (RMSE) in snow mass estimates at 76% and 58% of the comparative pixels, respectively. During the snow ablation season, the PMW brightness temperature signal contained less information related to snow mass due to the presence of other concurrent geophysical features that effectively serve as noise during the snow mass update. The utilization of PMW ΔT b for accurate snow mass estimation in complex terrain such as HMA is dependent on a multitude of factors for optimal results; however, it does add utility to the land surface model if the relevant pitfalls are taken into consideration prior to the state variable update.

Jawairia Ahmad↗

NASA NTRS1993

Advances in time-scale algorithms

The term clock is usually used to refer to a device that counts a nearly periodic signal. A group of clocks, called an ensemble, is often used for time keeping in mission critical applications that cannot tolerate loss of time due to the failure of a single clock. The time generated by the ensemble of clocks is called a time scale. The question arises how to combine the times of the individual clocks to form the time scale. One might naively be tempted to suggest the expedient of averaging the times of the individual clocks, but a simple thought experiment demonstrates the inadequacy of this approach. Suppose a time scale is composed of two noiseless clocks having equal and opposite frequencies. The mean time scale has zero frequency. However if either clock fails, the time-scale frequency immediately changes to the frequency of the remaining clock. This performance is generally unacceptable and simple mean time scales are not used. First, previous time-scale developments are reviewed and then some new methods that result in enhanced performance are presented. The historical perspective is based upon several time scales: the AT1 and TA time scales of the National Institute of Standards and Technology (NIST), the A.1(MEAN) time scale of the US Naval observatory (USNO), the TAI time scale of the Bureau International des Poids et Measures (BIPM), and the KAS-1 time scale of the Naval Research laboratory (NRL). The new method was incorporated in the KAS-2 time scale recently developed by Timing Solutions Corporation. The goal is to present time-scale concepts in a nonmathematical form with as few equations as possible. Many other papers and texts discuss the details of the optimal estimation techniques that may be used to implement these concepts.

Stein, S. R.↗

NASA NTRSDate not supplied

Adding GPU Support to the Markov Chain Monte Carlo Code Catmip

In geophysics, we are confronted with many under-determined inverse problems. For example, all of our observations of earthquakes are made at the Earth’s surface. So, when we try to infer how slip during an earthquake evolves in space and time, we find that there are many potential slip histories that are consistent with our limited observations and our understanding of earthquake physics. One way to approach these problems is with Bayesian analysis which allows us to infer the ensemble of all potential slip models that satisfy the observations and our prior knowledge of earthquake physics. In Bayesian analysis, our prior knowledge is known as the prior probability density function or prior PDF, the fit to the data is known as the data likelihood, and the target PDF that satisfies both the prior PDF and data likelihood is known as the posterior PDF. However, simulating the posterior PDF typically requires using Markov Chain Monte Carlo (MCMC) to draw tens of billions of random realizations of earthquake slip models, which may not be computationally feasible. To make this and similar geophysical inversions computationally tractable, we developed the Cascading Adaptive Transitional Metropolis In Parallel (CATMIP) algorithm. CATMIP is an efficient parallel Markov Chain Monte Carlo (MCMC) sampler that is used for model fitting and uncertainty quantification in geophysics. Example use cases are earthquake rupture modeling, determining mineral composition on Mars, reconstructing the history of ocean salinity, and historical earthquake relocation. CATMIP employs many parallel instances of the Metropolis algorithm for sampling in a transitioning framework. Transitioning is a process in which a set of random samples at equilibrium with a known probability density function (PDF) are used as seeds for the Markov chains to sample successive target PDFs that incrementally move the distribution from the starting seeds to the final desired PDF that describes the relative plausibility of potential values for the model parameters. The algorithm is implemented as a Master-Worker model employing MPI for communication. The worker processes are loosely coupled with global parameters periodically optimized by the master process. This provides a very high amount of parallelism with little communication between updates. During the presentation we will discuss the history of the algorithm and elaborate the earthquake rupture modeling use case for the CATMIP package. Our first step toward GPU optimization was to optimize the code for the CPU. CPU profiling revealed that most of the compute time is spent in calls to level 2 BLAS routines and calls to GSL random number generators. We revised the algorithm to employ level 3 BLAS routines instead. In our presentation we will describe how this was accomplished. Adding GPU support to CATMIP consisted mostly of replacing the calls to GSL with calls to GPU vendor-provided library routines. A small number of loops were directly implemented in CUDA. In the presentation will provide implementation details. Finally, we will discuss methods for profiling and opportunities for further optimizing GPU execution. By creating a code with the flexibility to run on either a CPU or GPU architecture, CATMIP can be used on systems ranging from large CPU-based HPC environments to single servers with GPU acceleration and everything in between.

HECC↗