Results for “Probability Distribution Function” — Page 21

DOE OSTI2014

Parameter Tuning and Calibration of RegCM3 with MIT-Emanuel Cumulus Parameterization Scheme over CORDEX East Asian Domain

In this study, we calibrated the performance of regional climate model RegCM3 with Massachusetts Institute of Technology (MIT)-Emanuel cumulus parameterization scheme over CORDEX East Asia domain by tuning the selected seven parameters through multiple very fast simulated annealing (MVFSA) sampling method. The seven parameters were selected based on previous studies, which customized the RegCM3 with MIT-Emanuel scheme through three different ways by using the sensitivity experiments. The responses of model results to the seven parameters were investigated. Since the monthly total rainfall is constrained, the simulated spatial pattern of rainfall and the probability density function (PDF) distribution of daily rainfall rates are significantly improved in the optimal simulation. Sensitivity analysis suggest that the parameter “relative humidity criteria” (RH), which has not been considered in the default simulation, has the largest effect on the model results. The responses of total rainfall over different regions to RH were examined. Positive responses of total rainfall to RH are found over northern equatorial western Pacific, which are contributed by the positive responses of explicit rainfall. Followed by an increase of RH, the increases of the low-level convergence and the associated increases in cloud water favor the increase of the explicit rainfall. The identified optimal parameters constrained by the total rainfall have positive effects on the low-level circulation and the surface air temperature. Furthermore, the optimized parameters based on the extreme case are suitable for a normal case and the model’s new version with mixed convection scheme.

emanual cumulus parameterization↗

DOE OSTI2019

Thermodynamic versus Dynamic Controls on Extreme Precipitation in a Warming Climate from the Community Earth System Model Large Ensemble

The moisture budget is evaluated as a function of the probability distribution of precipitation for the end of the twentieth century and projected end of the twenty-first century in the Community Earth System Model Large Ensemble. For a given precipitation percentile, a conditional moisture budget equation relates precipitation minus evaporation ( P − E) to vertical moisture transport, horizontal moisture advection, and moisture storage. At high percentiles, moisture advection and moisture storage cancel and evaporation is negligible, so that precipitation is approximately equal to vertical moisture transport, and likewise for projected changes. Therefore, projected changes to extreme precipitation are approximately equal to the sum of thermodynamic and dynamic tendencies, representing changes to the vertical profiles of moisture content and mass convergence, respectively. The thermodynamic tendency is uniform across percentiles and regions as an intensification of the hydrological cycle, but the dynamic tendency is more complex. For extreme events, per degree of warming, in the mid-to-high latitudes the dynamic tendency is small, so that precipitation approximately scales by the Clausius–Clapeyron 7% K −1 increase. In the subtropics, a drying tendency originating from dynamics offsets the thermodynamic wetting tendency, with the net effect on precipitation varying among regions. The effect of this dynamic drying decreases with increasing percentile. In the deep tropics, a positive dynamic tendency occurs with magnitude similar to or greater than the positive thermodynamic tendency, resulting in generally a 10%–15% K −1 precipitation increase, and with a >25% K −1 increase over the tropical east Pacific. This reinforcing dynamical tendency increases rapidly for high percentiles.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2011

Gravity dual for a model of perception

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based on a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Statistical estimates of the binary properties of rotational variables

ABSTRACT We present a model to estimate the average primary masses, companion mass ranges, the inclination limit for recognizing a rotational variable, and the primary mass spreads for populations of binary stars. The model fits a population’s binary mass function distribution and allows for a probability that some mass functions are incorrectly estimated. Using tests with synthetic data, we assess the model’s sensitivity to each parameter, finding that we are most sensitive to the average primary mass and the minimum companion mass, with less sensitivity to the inclination limit and little to no sensitivity to the primary mass spread. We apply the model to five populations of binary spotted rotational variables identified in ASAS-SN, computing their binary mass functions using RV data from APOGEE. Their average primary mass estimates are consistent with our expectations based on their CMD locations ($\sim 0.75 \, {\rm M}_{\odot }$ for lower main sequence primaries and $\sim 0.9$–$1.2 \, {\rm M}_{\odot }$ for RS CVn and sub-subgiants). Their companion mass range estimates allow companion masses down to $M_2/M_1\simeq 0.1$, although the main sequence population may have a higher minimum mass fraction ($\sim 0.4$). We see weak evidence of an inclination limit $\gtrsim 50^{\circ }$ for the main sequence and sub-subgiant groups and no evidence of an inclination limit in the other groups. No groups show strong evidence for a preferred primary mass spread. We conclude by demonstrating that the approach will provide significantly better estimates of the primary mass and the minimum mass ratio and reasonable sensitivity to the inclination limit with 10 times as many systems.

Phillips, Anya (ORCID:000900051914974X)↗

DOE OSTI2015

TU-AB-BRB-00: New Methods to Ensure Target Coverage

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-AB-BRB-01: Coverage Evaluation and Probabilistic Treatment Planning as a Margin Alternative

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-AB-BRB-02: Stochastic Programming Methods for Handling Uncertainty and Motion in IMRT Planning

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-AB-BRB-03: Coverage-Based Treatment Planning to Accommodate Organ Deformable Motions and Contouring Uncertainties for Prostate Treatment

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2010

Wind and Load Forecast Error Model for Multiple Geographically Distributed Forecasts

The impact of wind and load forecast errors on power grid operations is frequently evaluated by conducting multi-variant studies, where these errors are simulated repeatedly as random processes based on their known statistical characteristics. To generate these errors correctly, we need to reflect their distributions (which do not necessarily follow a known distribution law), standard deviations, auto- and cross-correlations. For instance, load and wind forecast errors can be closely correlated in different zones of the system. This paper introduces a new methodology for generating multiple cross-correlated random processes to simulate forecast error curves based on a transition probability matrix computed from an empirical error distribution function. The matrix will be used to generate new error time series with statistical features similar to observed errors. We present the derivation of the method and present some experimental results by generating new error forecasts together with their statistics.

17 WIND ENERGY↗

DOE OSTI2026

Improved energies and local energies with weighted variational Monte Carlo

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Prediction of dislocation - grain boundary interactions in FCC aluminum bicrystals using a modified continuum criterion and machine learning methods

Mechanical properties of metals such as strength and toughness are strongly correlated to complex interactions between various defects in the crystalline structure. While elementary interactions between these defects have been investigated using recent micro- and nano-characterization techniques, understanding of the detailed interaction mechanisms has hardly been obtained. To understand defect-driven plasticity at various time and length scales, it is necessary to formulate a general guideline to predict both the interaction type (transmission or reflection) and the dislocation's subsequent slip system after the interaction. Many criteria based on the geometric alignment of the defects have been developed to predict this phenomenon, but these have yet to be found to be accurate when applied to general data sets of grain boundaries (GBs). With this motivation, we conduct a systematic study using molecular dynamics (MD) models of bicrystals to analyze defect interaction process between a prismatic dislocation loop and eleven different grain boundaries of the following character: three tilt, three twist, and five mixed. Based on the MD observations, two new prediction methods are developed: the first is a new data-driven parametric score function based on the classical geometric criteria, and the second is by applying Gaussian process machine learning methods to find the probability distribution of a hidden function. In conclusion, the proposed data-driven prediction methods could pave a new way to predict the unit interaction of dislocations with various GBs, which could show much higher accuracy compared to pre-existing geometric criteria.

36 MATERIALS SCIENCE↗

DOE OSTI2014

ForQint

ForQint is a Fortran software library to adaptively integrate multivariable functions versus well known probability distributions (e.g. normal, lognormal, etc.) using quadrature rules. Such integration is known to be more efficient and accurate especially when the function evaluation is expensive. The library also FQint enables the creation of both full and sparse anisotropic multi-dimensional quadrature rules. These latter encompass different such as Gauss-Hermite, Gauss-Legendre, etc. The functions Maher Salloum, Bert Debusschere, Kenny Chowdhary and subroutines rely on the C++ Stokhos package of Trilinos (trilinos.sandia.gov) where the appropriate classes were wrapped into Fortran.

Chowdhary, Kamalijit↗

DOE OSTI2014

ForQint

ForQint is a Fortran software library to adaptively integrate multivariable functions versus well known probability distributions (e.g. normal, lognormal, etc.) using quadrature rules. Such integration is known to be more efficient and accurate especially when the function evaluation is expensive. The library also FQint enables the creation of both full and sparse anisotropic multi-dimensional quadrature rules. These latter encompass different such as Gauss-Hermite, Gauss-Legendre, etc. The functions Maher Salloum, Bert Debusschere, Kenny Chowdhary and subroutines rely on the C++ Stokhos package of Trilinos (trilinos.sandia.gov) where the appropriate classes were wrapped into Fortran.

Source record↗

DOE OSTI2011

TURBULENT CLUSTERING OF PROTOPLANETARY DUST AND PLANETESIMAL FORMATION

We study the clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, St, defined as the ratio of the particle friction timescale, {tau}{sub p}, to the Kolmogorov timescale in the flow. In agreement with previous studies, we find that, in the dissipation range, the clustering intensity strongly peaks at St {approx_equal} 1, and the RDF for St {approx} 1 shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these large scales, the strongest clustering is from particles with {tau}{sub p} in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is {approx}{tau}{sub p}. We find that particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in two recent models for planetesimal formation. We argue that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

On bias of kinetic temperature measurements in complex plasmas

The kinetic temperature in complex plasmas is often measured using particle tracking velocimetry. Here, we introduce a criterion which minimizes the probability of faulty tracking of particles with normally distributed random displacements in consecutive frames. Faulty particle tracking results in a measurement bias of the deduced velocity distribution function and hence the deduced kinetic temperature. For particles with a normal velocity distribution function, mistracking biases the obtained velocity distribution function towards small velocities at the expense of large velocities, i.e., the inferred velocity distribution is more peaked and its tail is less pronounced. The kinetic temperature is therefore systematically underestimated in measurements. We give a prescription to mitigate this type of error.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

A temperature-dependent coarse-grained model for the thermoresponsive polymer poly(N-isopropylacrylamide)

A coarse-grained (CG) model is developed for the thermoresponsive polymer poly(N-isopropylacrylamide) (PNIPAM), using a hybrid top-down and bottom-up approach. Nonbonded parameters are fit to experimental thermodynamic data following the procedures of the SDK (Shinoda, DeVane, and Klein) CG force field, with minor adjustments to provide better agreement with radial distribution functions from atomistic simulations. Bonded parameters are fit to probability distributions from atomistic simulations using multi-centered Gaussian-based potentials. The temperature-dependent potentials derived for the PNIPAM CG model in this work properly capture the coil–globule transition of PNIPAM single chains and yield a chain-length dependence consistent with atomistic simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Uncertainty quantification for nuclear density functional theory and information content of new measurements

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. In addition, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Advanced methods for uncertainty quantification in tail regions of climate model predictions.

Conventional methods for uncertainty quantification are generally challenged in the 'tails' of probability distributions. This is specifically an issue for many climate observables since extensive sampling to obtain a reasonable accuracy in tail regions is especially costly in climate models. Moreover, the accuracy of spectral representations of uncertainty is weighted in favor of more probable ranges of the underlying basis variable, which, in conventional bases does not particularly target tail regions. Therefore, what is ideally desired is a methodology that requires only a limited number of full computational model evaluations while remaining accurate enough in the tail region. To develop such a methodology, we explore the use of surrogate models based on non-intrusive Polynomial Chaos expansions and Galerkin projection. We consider non-conventional and custom basis functions, orthogonal with respect to probability distributions that exhibit fat-tailed regions. We illustrate how the use of non-conventional basis functions, and surrogate model analysis, improves the accuracy of the spectral expansions in the tail regions. Finally, we also demonstrate these methodologies using precipitation data from CCSM simulations.

54 ENVIRONMENTAL SCIENCES↗