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At least 1,243 records · Page 69

Physics-based statistical learning approach to mesoscopic model selection

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. Here, we apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD “training” data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD “test” data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

36 MATERIALS SCIENCE↗

An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty faced in the process is the excessive computational cost. In this paper, we present an efficient, partitioned ensemble algorithm to determine multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which models MHD flows at low magnetic Reynolds number. The algorithm decouples the fully coupled problem into two smaller subphysics problems, which reduces the size of the linear systems that to be solved and allows the use of optimized codes for each subphysics problem. Moreover, the resulting coefficient matrices are the same for all realizations at each time step, which allows faster computation of all realizations and significant savings in computational cost. We prove this algorithm is first order accurate and long time stable under a time step condition. Numerical examples are provided to verify the theoretical results and demonstrate the efficiency of the algorithm.

Jiang, Nan↗

Predictive drug dosage control through a Fokker–Planck observer

During the years, various techniques have been presented for optimal control of tumor growth for which its stochastic behavior has rarely been considered. This article uses the well-known Gompertz stochastic model, for describing tumor growth, and by receding horizon model predictive control (RH-MPC) scheme computes the drug dosage for minimizing the tumor-cell population. To do this, a predictive control problem is defined based on the difference between the probability density function of tumor-cell population and the desired probability density function. In the model, both the drug dosage limitation and the Fokker–Planck equation have been considered as constraints. By solving this problem, the drug dosage which is considered as an external input to tumor model, is computed. In this article, the Fokker–Planck equation is used (1) as a nonlinear observer of probability density function of tumor-cell population and (2) a mapping vehicle from stochastic to deterministic domain. The Fokker–Planck equation is written for the Gompertz stochastic model of tumor growth. The equation is then solved through the path integral method. In this way, the probability density function of tumor-cell population, which contains the entire stochastic characteristics of the tumor growth, is obtained for any instance of time. The simulation results have also been presented for the evaluation of the suggested approach. The results show that the tumor-cell population can be controlled within a number of time windows (15 time windows in our case study) if an appropriate desired PDF is selected.

97 MATHEMATICS AND COMPUTING↗

Application of stochastic Galerkin FEM to the complete electrode model of electrical impedance tomography

The aim of electrical impedance tomography is to determine the internal conductivity distribution of some physical body from boundary measurements of current and voltage. The most accurate forward model for impedance tomography is the complete electrode model, which consists of the conductivity equation coupled with boundary conditions that take into account the electrode shapes and the contact resistances at the corresponding interfaces. If the reconstruction task of impedance tomography is recast as a Bayesian inference problem, it is essential to be able to solve the complete electrode model forward problem with the conductivity and the contact resistances treated as a random field and random variables, respectively. In this work, we apply a stochastic Galerkin finite element method to the ensuing elliptic stochastic boundary value problem and compare the results with Monte Carlo simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Demand Response Under Stochastic, Price-Dependent User Behavior

This letter focuses on price-based demand response (DR) implemented through dynamic adjustments of electricity prices. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. We propose a stochastic, feedback-based pricing strategy to compensate for estimation errors and uncertainty in customer response, establish theoretical results demonstrating the stability and near-optimality of the proposed approach, and validate its effectiveness through numerical simulations.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Stochastic Dynamic Analysis for Power Systems Under Uncertain Variability

This paper proposes a novel method to analyze impacts of uncertain variability on power system dynamics. There is considerable interest in integrating intermittent renewable energy and plug-in electric vehicles into power systems. Therefore, power systems are in an environment with increasing uncertain variability. In this paper, the uncertain variability is described as a continuous-time stochastic process, and thus, the power system under uncertain variability is modeled by stochastic differential equations. To quantify impacts of uncertain variability on power system dynamics, an intra-region probability index is presented. Based on the stochastic averaging method, an analytical method is proposed to calculate the intra-region probability. Compared to Monte Carlo simulation, the proposed method is many orders of magnitude faster without sacrificing the result accuracy. As a result, several insights are given to improve the power system dynamics under uncertain variability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Statistics of particle time-temperature histories

Particles in non-isothermal turbulent flow are subject to a stochastic environment that produces a distribution of particle time-temperature histories. This distribution is a function of the dispersion of the non-isothermal (continuous) gas phase and the distribution of particles relative to that gas phase. In this work we extend the one-dimensional turbulence (ODT) model to predict the joint dispersion of a dispersed particle phase and a continuous phase. The ODT model predicts the turbulent evolution of continuous scalar fields with a model for the cascade of fluctuations to smaller scales (the ‘triplet map’) at a rate that is a function of the fully resolved one-dimensional velocity field. Stochastic triplet maps also drive Lagrangian particle dispersion with finite Stokes numbers including inertial and eddy trajectory-crossing effects included. Two distinct approaches to this coupling between triplet maps and particle dispersion are developed and implemented along with a hybrid approach. An ‘instantaneous’ particle displacement model matches the tracer particle limit and provides an accurate description of particle dispersion. A ‘continuous’ particle displacement model translates triplet maps into a continuous velocity field to which particles respond. Particles can alter the turbulence, and modifications to the stochastic rate expression are developed for two-way coupling between particles and the continuous phase. Each aspect of model development is evaluated in canonical flows (homogeneous turbulence, free-shear flows and wall-bounded flows) for which quality measurements are available. ODT simulations of non-isothermal flows provide statistics for particle heating. These simulations show the significance of accurately predicting the joint statistics of particle and fluid dispersion. Inhomogeneous turbulence coupled with the influence of the mean flow fields on particles of varying properties alters particle dispersion. The joint particle-temperature dispersion leads to a distribution of temperature histories predicted by the ODT. Predictions are shown for the lower moments and the full distributions of the particle positions, particle-observed gas temperatures and particle temperatures. An analysis of the time scales affecting particle-temperature interactions covers Lagrangian integral time scales based on temperature autocorrelations, rates of temperature change associated with particle motion relative to the temperature field and rates of diffusional change of temperatures. These latter two time scales have not been investigated previously; they are shown to be strongly intermittent having peaked distributions with long tails. The logarithm of the absolute value of these time scales exhibits a distribution closer to normal.

Hewson, John C.↗

Non-Genomic Origins of Proteins and Metabolism

It is proposed that evolution of inanimate matter to cells endowed with a nucleic acid- based coding of genetic information was preceded by an evolutionary phase, in which peptides not coded by nucleic acids were able to self-organize into networks capable of evolution towards increasing metabolic complexity. Recent findings that truly different, simple peptides (Keefe and Szostak, 2001) can perform the same function (such as ATP binding) provide experimental support for this mechanism of early protobiological evolution. The central concept underlying this mechanism is that the reproduction of cellular functions alone was sufficient for self-maintenance of protocells, and that self- replication of macromolecules was not required at this stage of evolution. The precise transfer of information between successive generations of the earliest protocells was unnecessary and, possibly, undesirable. The key requirement in the initial stage of protocellular evolution was an ability to rapidly explore a large number of protein sequences in order to discover a set of molecules capable of supporting self- maintenance and growth of protocells. Undoubtedly, the essential protocellular functions were carried out by molecules not nearly as efficient or as specific as contemporary proteins. Many, potentially unrelated sequences could have performed each of these functions at an evolutionarily acceptable level. As evolution progressed, however proteins must have performed their functions with increasing efficiency and specificity. This, in turn, put additional constraints on protein sequences and the fraction of proteins capable of performing their functions at the required level decreased. At some point, the likelihood of generating a sufficiently efficient set of proteins through a non-coded synthesis was so small that further evolution was not possible without storing information about the sequences of these proteins. Beyond this point, further evolution required coupling between proteins and informational polymers that is characteristic to all known forms of life. The emergence of such coupling must be postulated in any scenario of the origin of life, no matter whether it starts with RNA or proteins. To examine the evolutionary potential of non-genomic systems, a simple, computationally tractable model, which is still capable of capturing the essential features of the real system, has been studied computationally. Both constructive and destructive processes have been introduced into the model in a stochastic manner. Instead of assuming random reaction sets, only a suite of protobiologically plausible reactions has been considered. Peptides have been explicitly considered as protoenzymes and their catalytic efficiencies have been assigned on the basis of biochemical principles and experimental estimates. Simulations have been carried out using a novel approach (The Next Reaction Method) that is appropriate even for very low concentrations of reactants. Studies have focused on global autocatalytic processes and their diversity.

Pohorille, Andrew↗

A stochastic differential equation model of diurnal cortisol patterns

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

NASA Discipline Space Human Factors↗

Conditional Tree Reduction in the ADAPT Framework

Probabilistic Risk Assessment (PRA) uses fault tree/event tree analysis to evaluate the environmental impacts of nuclear power plants due to internal or external initiating events. In a fault tree, basic failure events are assembled using primarily And/Or logic to determine the combinations of failures that lead to failure of the system as a whole. An event tree is forward-facing, and begins with a single initiating event. From there the analysis considers what event may occur next, and branches out among the possible configurations of occurrence and non-occurrence of that event. This branching continues until end states are reached. End states may include a safe and stable configuration of the plant, or any number of differing failure states. Both fault and event trees require basic event probabilities as inputs to provide insight on the likelihood of different outcomes. PRA has been applied to nuclear power plants as an analysis tool since the 1975 Reactor Safety Study. In a traditional PRA, the order of events is prescribed by the analyst and each event is typically a binary aleatory uncertainty: occurrence or non-occurrence. Discrete dynamic event tree (DDET) analysis eliminates this subjectivity in ordering of events by using the output of a dynamic system model (simulator) to inform the branching. Branching conditions are triggered by the existence of a relevant plant state in the code, and therefore only occur as physically appropriate. The DDET approach also allows consideration of both epistemic and aleatory uncertainties on a phenomenologically and stochastically consistent platform. A DDET may be orders of magnitude larger than a traditional event tree for the same initiating event, as more of the uncertainty space is likely to be explored and the tree does not require manual assembly. Because of the size, manual inspection of the entire DDET is often infeasible. This problem may be approached from the front by reducing the number of sampled branching values or by online pruning of the tree, thus reducing the total number of branches. Utilizing post-processing techniques to draw actionable insights via clustering has also been proposed. One post-processing tool to reduce the DDET according to user-defined rules has been recently implemented in the Analysis of Dynamic Accident Progression Trees (ADAPT) DDET driver code. The tool creates a 'slice' of the DDET comprised of the set of branches that meet a set of user-input rules, for immediate visualization or for further calculations conditional on the rules being met. This extension is expected to ease analysis of the results of large and complex DDETs, leading to greater applicability of DDETs in PRA. It should be emphasized that this tool is a visualization aide and does not impact the theoretical basis of the DDET approach. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Dynamic Importance Measures in the ADAPT Framework

Probabilistic Risk Assessment (PRA) uses fault tree/event tree analysis to evaluate the environmental impacts of nuclear power plants due to internal or external initiating events. In a fault tree, basic failure events are assembled using primarily And/Or logic to determine the combinations of failures that lead to failure of the system as a whole. An event tree is forward-facing, and begins with a single initiating event. From there the analysis considers what event may occur next, and branches out among the possible configurations of occurrence and non-occurrence of that event. This branching continues until user-defined end states are reached. End states may include a safe and stable configuration of the plant, or any number of differing failure states. Both fault and event trees require basic event probabilities as inputs to provide insight on the likelihood of different outcomes. PRA has been applied to nuclear power plants as an analysis tool since the 1975 Reactor Safety Study. In a traditional PRA, the order of events is prescribed by the analyst and each event is typically a binary aleatory uncertainty: occurrence or non-occurrence. Discrete dynamic event tree (DDET) analysis eliminates this subjectivity in ordering of events by using the output of a dynamic system model (simulator) to inform the branching. Branching conditions are triggered by the existence of a relevant plant state in the code, and therefore only occur as physically appropriate. The DDET approach also allows consideration of both epistemic and aleatory uncertainties on a phenomenologically and stochastically consistent platform. One current limitation of DDETs is the assessment of results, which is not as well developed as in traditional PRA. A concept that is used in PRA to assess the significance of a basic event is the concept of importance measures (IMs). In traditional PRA, IMs only consider the likelihood of occurrence of non-occurrence of a basic event. The application of importance measures to DDETs must take into consideration not only the occurrence and non-occurrence of an event, but also uncertain timing or severity. This work describes three general dynamic importance measures (DIMs) as implemented in the Analysis of Dynamic Accident Progression Trees (ADAPT) DDET driver code. The measures account for the change in progression of the DDET resulting from the different values of each uncertain variable under investigation. The DIMs are applied to a sample DDET to demonstrate the type of insights that may be gained from each one. These measures will facilitate comparison of the impact of dynamic branching events on a consequence of interest, which also allow DDETs to be used in prioritizing plant investments. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Stochastic simulation of electron avalanches on supercomputers

In the paper, we present a three-dimensional parallel Monte Carlo algorithm named ELSHOW which is developed for simulation of electron avalanches in gases. Parallel implementation of the ELSHOW was made on supercomputers with different architectures (massive parallel and hybrid ones). Using the ELSHOW, calculations of such integral characteristics as the number of particles in an avalanche, the coefficient of impact ionization, the drift velocity, and the others were made. Also, special precise computations were made to select an appropriate size of the time step using the technique of dependent statistical tests. Particularly, the algorithm consists of special methods of distribution modeling, a lexicographic implementation scheme for “branching” of trajectories, justified estimation of functionals. A comparison of the obtained results for nitrogen with previously published theoretical and experimental data was made.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Model for Ice Accretion Roughness Evolution and Spatial Variations

Over the past decade, multiple investigations of ice accretion roughness and spatial variations have been performed in the Icing Research Tunnel (IRT) at the NASA Glenn Research Center. The early investigations used models of NACA 0012 airfoils with different chord sizes and focused on temporal scaling and primary cloud scaling parameters such as stagnation point collection efficiency. Subsequent investigations included the effects of model sweep, airfoil shape, airfoil lifting condition, and freestream static temperature. To develop a predictive model for roughness evolution in generalized icing situations, the maximum roughness values for the airfoils and conditions used in the angle of attack and freestream temperature investigations were scaled to eliminate the temporal variations. LEWICE simulations were employed to identify the local collection efficiency at the locations of maximum roughness, and a two-dimensional panel-method code was used to identify the local static pressure at the location of the maximum roughness. Because of the stochastic nature of ice accretion roughness, a physics-directed approach was employed to develop a multi-dimensional correlation based on the local pressure coefficient, the local total temperature, the cloud properties, and the cloud exposure time. The resulting correlation predictions are compared to ice shapes measured in the IRT for both a 21-in. NACA 0012 airfoil model and a 60-in. HAARP-II model. The resulting predictions indicate that the local freezing fraction must be included in the roughness predictive model. Implications regarding icing heat transfer predictions using the resulting roughness model are also discussed.

Icing↗

Hierarchy of forward-backward stochastic Schrödinger equation

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

In silico prediction of toxicity of non-congeneric industrial chemicals using ensemble learning based modeling approaches

Ensemble learning approach based decision treeboost (DTB) and decision tree forest (DTF) models are introduced in order to establish quantitative structure–toxicity relationship (QSTR) for the prediction of toxicity of 1450 diverse chemicals. Eight non-quantum mechanical molecular descriptors were derived. Structural diversity of the chemicals was evaluated using Tanimoto similarity index. Stochastic gradient boosting and bagging algorithms supplemented DTB and DTF models were constructed for classification and function optimization problems using the toxicity end-point in T. pyriformis. Special attention was drawn to prediction ability and robustness of the models, investigated both in external and 10-fold cross validation processes. In complete data, optimal DTB and DTF models rendered accuracies of 98.90%, 98.83% in two-category and 98.14%, 98.14% in four-category toxicity classifications. Both the models further yielded classification accuracies of 100% in external toxicity data of T. pyriformis. The constructed regression models (DTB and DTF) using five descriptors yielded correlation coefficients (R{sup 2}) of 0.945, 0.944 between the measured and predicted toxicities with mean squared errors (MSEs) of 0.059, and 0.064 in complete T. pyriformis data. The T. pyriformis regression models (DTB and DTF) applied to the external toxicity data sets yielded R{sup 2} and MSE values of 0.637, 0.655; 0.534, 0.507 (marine bacteria) and 0.741, 0.691; 0.155, 0.173 (algae). The results suggest for wide applicability of the inter-species models in predicting toxicity of new chemicals for regulatory purposes. These approaches provide useful strategy and robust tools in the screening of ecotoxicological risk or environmental hazard potential of chemicals. - Graphical abstract: Importance of input variables in DTB and DTF classification models for (a) two-category, and (b) four-category toxicity intervals in T. pyriformis data. Generalization and predictive abilities of the constructed (c) DTB and (d) DTF regression models to predict the T. pyriformis toxicity of diverse chemicals. - Highlights: • Ensemble learning (EL) based models constructed for toxicity prediction of chemicals • Predictive models used a few simple non-quantum mechanical molecular descriptors. • EL-based DTB/DTF models successfully discriminated toxic and non-toxic chemicals. • DTB/DTF regression models precisely predicted toxicity of chemicals in multi-species. • Proposed EL based models can be used as tool to predict toxicity of new chemicals.

60 APPLIED LIFE SCIENCES↗

A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging

Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope of a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Scalable Solution Framework for Stochastic Transmission and Generation Planning Problems. Draft

Current commercial software tools for transmission and generation investment planning have limited stochastic modeling capabilities. Because of this limitation, electric power utilities generally rely on scenario planning heuristics to identify potentially robust and cost effective investment plans for a broad range of system, economic, and policy conditions. Several research studies have shown that stochastic models perform significantly better than deterministic or heuristic approaches, in terms of overall costs. However, there is a lack of practical solution approaches to solve such models. In this paper we propose a scalable decomposition algorithm to solve stochastic transmission and generation planning problems, respectively considering discrete and continuous decision variables for transmission and generation investments. Given stochasticity restricted to loads and wind, solar, and hydro power output, we develop a simple scenario reduction framework based on a clustering algorithm, to yield a more tractable model. The resulting stochastic optimization model is decomposed on a scenario basis and solved using a variant of the Progressive Hedging (PH) algorithm. We perform numerical experiments using a 240-bus network representation of the Western Electricity Coordinating Council in the US. Although convergence of PH to an optimal solution is not guaranteed for mixed-integer linear optimization models, we find that it is possible to obtain solutions with acceptable optimality gaps for practical applications. Our numerical simulations are performed both on a commodity workstation and on a high-performance cluster. The results indicate that large-scale problems can be solved to a high degree of accuracy in at most two hours of wall clock time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Impact of confined geometries on hopping and trapping of motile bacteria in porous media

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Lastly, our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

54 ENVIRONMENTAL SCIENCES↗