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DOE OSTI2015

Multivariate moment closure techniques for stochastic kinetic models

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

TU-H-CAMPUS-JeP3-05: Adaptive Determination of Needle Sequence HDR Prostate Brachytherapy with Divergent Needle-By-Needle Delivery

Purpose: To develop a new method which adaptively determines the optimal needle insertion sequence for HDR prostate brachytherapy involving divergent needle-by-needle dose delivery by e.g. a robotic device. A needle insertion sequence is calculated at the beginning of the intervention and updated after each needle insertion with feedback on needle positioning errors. Methods: Needle positioning errors and anatomy changes may occur during HDR brachytherapy which can lead to errors in the delivered dose. A novel strategy was developed to calculate and update the needle sequence and the dose plan after each needle insertion with feedback on needle positioning errors. The dose plan optimization was performed by numerical simulations. The proposed needle sequence determination optimizes the final dose distribution based on the dose coverage impact of each needle. This impact is predicted stochastically by needle insertion simulations. HDR procedures were simulated with varying number of needle insertions (4 to 12) using 11 patient MR data-sets with PTV, prostate, urethra, bladder and rectum delineated. Needle positioning errors were modeled by random normally distributed angulation errors (standard deviation of 3 mm at the needle’s tip). The final dose parameters were compared in the situations where the needle with the largest vs. the smallest dose coverage impact was selected at each insertion. Results: Over all scenarios, the percentage of clinically acceptable final dose distribution improved when the needle selected had the largest dose coverage impact (91%) compared to the smallest (88%). The differences were larger for few (4 to 6) needle insertions (maximum difference scenario: 79% vs. 60%). The computation time of the needle sequence optimization was below 60s. Conclusion: A new adaptive needle sequence determination for HDR prostate brachytherapy was developed. Coupled to adaptive planning, the selection of the needle with the largest dose coverage impact increases chances of reaching the clinical constraints. M. Borot de Battisti is funded by Philips Medical Systems Nederland B.V.; M. Moerland is principal investigator on a contract funded by Philips Medical Systems Nederland B.V.; G. Hautvast and D. Binnekamp are fulltime employees of Philips Medical Systems Nederland B.V.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Breakups are complicated: an efficient representation of collisional breakup in the superdroplet method

Abstract. A key constraint of particle-based methods for modeling cloud microphysics is the conservation of total particle number, which is required for computational tractability. The process of collisional breakup poses a particular challenge to this framework, as breakup events often produce many droplet fragments of varying sizes, which would require creating new particles in the system. This work introduces a representation of collisional breakup in the so-called “superdroplet” method which conserves the total number of superdroplets in the system. This representation extends an existing stochastic collisional-coalescence scheme and samples from a fragment size distribution in an additional Monte Carlo step. This method is demonstrated in a set of idealized box model and single-column warm-rain simulations. We further discuss the effects of the breakup dynamic and fragment size distribution on the particle size distribution, hydrometeor population, and microphysical process rates. Box model experiments serve to characterize the impacts of properties such as coalescence efficiency and fragmentation function on the relative roles of collisional breakup and coalescence. The results demonstrate that this representation of collisional breakup can produce a stationary particle size distribution, in which breakup and coalescence rates are approximately equal, and that it recovers expected behavior such as a reduction in precipitate-sized particles in the column model. The breakup algorithm presented here contributes to an open-source pythonic implementation of the superdroplet method, PySDM, which will facilitate future research using particle-based microphysics.

de Jong, Emily (ORCID:0000000253104554)↗

NASA NTRS1979

Optimization and simulation of flight control laws under parameter uncertainty and external disturbances

Several tasks pertinent to flight control in parameter uncertainty and wind-gust loading were successfully completed. Identification algorithms for extracting stability and control derivatives from flight data taking gust loading into account were developed. They were verified by simulation and evaluated throughly on actual flight data taken on a Lockheed Jet Star flying in turbulence. In particular the need for automatically generated dither-like inputs was studied. Criteria for performance evaluation using stochastic models were developed for gust alleviation as well as handling quantities. Algorithms for assessing degradation in performance due to parameter uncertainty were developed and evaluated using flight test data.

Source record↗

DOE OSTI2022

Distribution Function Instead of Steady-State Assumption in Time-Series Simulation

The quasi-steady-state assumption in time-series simulation is inadequate to model phenomena of interest to energy system integration such as inverter clipping, sell-back of excess electricity to a utility and utility hosting capacity, and battery throughput. Researchers are working on stochastic modeling, higher-resolution time series data, and machine learning approaches to address this need. This poster describes a distribution function that allows a maximum value, minimum value, and shape to the curve that can vary within each time-step based only on data inputs at the resolution of that time step (eg. Hourly). The distribution function is not used to synthesize high-resolution data, rather scalar integrals are used to calculate the quantities of interest within each time step. The form of the distribution function shows significant reduction in error when compared to 1 minute data and commercial software employing the distribution function (HOMER Pro version 14.3 and higher) shows a much improved estimate of inverter clipping in an example.

battery↗

DOE OSTI2016

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

58 GEOSCIENCES↗

DOE OSTI2014

Model reduction for slow–fast stochastic systems with metastable behaviour

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediated chemical switch coupled to a slower varying species), and one from ecology (a predator–prey system). Numerical simulations of each model reduction are compared with those of the full system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Asynchronous Reciprocal Coupling of Martini 2.2 Coarse-Grained and CHARMM36 All-Atom Simulations in an Automated Multiscale Framework

The appeal of multiscale modeling approaches is predicated on the promise of combinatorial synergy. However, this promise can only be realized when distinct scales are combined with reciprocal consistency. Here, we consider multiscale molecular dynamics (MD) simulations that combine the accuracy and macromolecular flexibility accessible to fixed-charge all-atom (AA) representations with the sampling speed accessible to reductive, coarse-grained (CG) representations. AA-to-CG conversions are relatively straightforward because deterministic routines with unique outcomes are achievable. Conversely, CG-to-AA conversions have many solutions due to a surge in the number of degrees of freedom. While automated tools for biomolecular CG-to-AA transformation exist, we find that one popular option, called Backward, is prone to stochastic failure and the AA models that it does generate frequently have compromised protein structure and incorrect stereochemistry. Although these shortcomings can likely be circumvented by human intervention in isolated instances, automated multiscale coupling requires reliable and robust scale conversion. In this work, we detail an extension to Multiscale Machine-learned Modeling Infrastructure (MuMMI), including an improved CG-to-AA conversion tool called sinceCG. This tool is reliable (~98% weakly correlated repeat success rate), automatable (no unrecoverable hangs), and yields AA models that generally preserve protein secondary structure and maintain correct stereochemistry. We describe how the MuMMI framework identifies CG system configurations of interest, converts them to AA representations, and simulates them at the AA scale while on-the-fly analyses provide feedback to update CG parameters. Application to systems containing the peripheral membrane protein RAS and proximal components of RAF kinase on complex eight-component lipid bilayers with ~1.5 million atoms is discussed in the context of MuMMI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1971

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Parrish, R. V.↗

DOE OSTI2012

Robust volume calculations for Constructive Solid Geometry (CSG) components in Monte Carlo transport calculations

In this paper we consider a new generalized algorithm for the efficient calculation of component object volumes given their equivalent constructive solid geometry (CSG) definition. The new method relies on domain decomposition to recursively subdivide the original component into smaller pieces with volumes that can be computed analytically or stochastically, if needed. Unlike simpler brute-force approaches, the proposed decomposition scheme is guaranteed to be robust and accurate to within a user-defined tolerance. The new algorithm is also fully general and can handle any valid CSG component definition, without the need for additional input from the user. The new technique has been specifically optimized to calculate volumes of component definitions commonly found in models used for Monte Carlo particle transport simulations for criticality safety and reactor analysis applications. However, the algorithm can be easily extended to any application which uses CSG representations for component objects. The paper provides a complete description of the novel volume calculation algorithm, along with a discussion of the conjectured error bounds on volumes calculated within the method. In addition, numerical results comparing the new algorithm with a standard stochastic volume calculation algorithm are presented for a series of problems spanning a range of representative component sizes and complexities. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Post-hoc reweighting of hadron production in the Lund string model

We present a method for reweighting flavor selection in the Lund string fragmentation model. This is the process of calculating and applying event weights enabling fast and exact variation of hadronization parameters on pre-generated event samples. The procedure is post hoc, requiring only a small amount of additional information stored per event, and allowing for efficient estimation of hadronization uncertainties without repeated simulation. Weight expressions are derived from the hadronization algorithm itself, and validated against direct simulation for a wide range of observables and parameter shifts. The hadronization algorithm can be viewed as a hierarchical Markov process with stochastic rejections, a structure common to many complex simulations outside of high-energy physics. This perspective makes the method modular, extensible, and potentially transferable to other domains. We demonstrate the approach in Pythia, including both coverage considerations and timing benefits. For the purpose of this paper, our goal is to develop and demonstrate the the formalism, and we therefore exclude several model variations for baryon production (popcorn model, junction production) needed for proton collisions. These will be the topic of a future paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2011

The Analysis of the Patterns of Radiation-Induced DNA Damage Foci by a Stochastic Monte Carlo Model of DNA Double Strand Breaks Induction by Heavy Ions and Image Segmentation Software

To create a generalized mechanistic model of DNA damage in human cells that will generate analytical and image data corresponding to experimentally observed DNA damage foci and will help to improve the experimental foci yields by simulating spatial foci patterns and resolving problems with quantitative image analysis. Material and Methods: The analysis of patterns of RIFs (radiation-induced foci) produced by low- and high-LET (linear energy transfer) radiation was conducted by using a Monte Carlo model that combines the heavy ion track structure with characteristics of the human genome on the level of chromosomes. The foci patterns were also simulated in the maximum projection plane for flat nuclei. Some data analysis was done with the help of image segmentation software that identifies individual classes of RIFs and colocolized RIFs, which is of importance to some experimental assays that assign DNA damage a dual phosphorescent signal. Results: The model predicts the spatial and genomic distributions of DNA DSBs (double strand breaks) and associated RIFs in a human cell nucleus for a particular dose of either low- or high-LET radiation. We used the model to do analyses for different irradiation scenarios. In the beam-parallel-to-the-disk-of-a-flattened-nucleus scenario we found that the foci appeared to be merged due to their high density, while, in the perpendicular-beam scenario, the foci appeared as one bright spot per hit. The statistics and spatial distribution of regions of densely arranged foci, termed DNA foci chains, were predicted numerically using this model. Another analysis was done to evaluate the number of ion hits per nucleus, which were visible from streaks of closely located foci. In another analysis, our image segmentaiton software determined foci yields directly from images with single-class or colocolized foci. Conclusions: We showed that DSB clustering needs to be taken into account to determine the true DNA damage foci yield, which helps to determine the DSB yield. Using the model analysis, a researcher can refine the DSB yield per nucleus per particle. We showed that purely geometric artifacts, present in the experimental images, can be analytically resolved with the model, and that the quantization of track hits and DSB yields can be provided to the experimentalists who use enumeration of radiation-induced foci in immunofluorescence experiments using proteins that detect DNA damage. An automated image segmentaiton software can prove useful in a faster and more precise object counting for colocolized foci images.

Ponomarev, Artem↗

DOE OSTI2017

Methods of Reverberation Mapping. I. Time-lag Determination by Measures of Randomness

A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical estimators are considered that do not rely on polynomial interpolations of the light curves nor on their stochastic modeling, and do not require binning in correlation space. Methods based on von Neumann’s mean-square successive-difference estimator are found to be superior to those using other estimators. An optimized von Neumann scheme is formulated, which better handles sparsely sampled data and outperforms current implementations of discrete correlation function methods. This scheme is applied to existing reverberation data of varying quality, and consistency with previously reported time delays is found. In particular, the size–luminosity relation of the broad-line region in quasars is recovered with a scatter comparable to that obtained by other works, yet with fewer assumptions made concerning the process underlying the variability. The proposed method for time-lag determination is particularly relevant for irregularly sampled time series, and in cases where the process underlying the variability cannot be adequately modeled.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

A NUMERICAL SIMULATION OF COSMIC RAY MODULATION NEAR THE HELIOPAUSE. II. SOME PHYSICAL INSIGHTS

Cosmic ray (CR) transport near the heliopause (HP) is studied using a hybrid transport model, with the parameters constrained by observations from the Voyager 1 spacecraft. We simulate the CR radial flux along different directions in the heliosphere. There is no well-defined thin layer between the solar wind region and the interstellar region along the tail and polar directions of the heliosphere. By analyzing the radial flux curve along the direction of Voyager 2 , together with its trajectory information, the crossing time of the HP by Voyager 2 is predicted to be in 2017.14. We simulate the CR radial flux for different energy values along the direction of Voyager 1 . We find that there is only a modest modulation region of about 10 au wide beyond the HP, so that Voyager 1 observing the Local Interstellar Spectra is justified in numerical modeling. We analyze the heliospheric exit information of pseudo-particles in our stochastic numerical (time-backward) method, conjecturing that they represent the behavior of CR particles, and we find that pseudo-particles that have been traced from the nose region exit in the tail region. This implies that many CR particles diffuse directly from the heliospheric tail region to the nose region near the HP. In addition, when pseudo-particles were traced from the Local Interstellar Medium (LISM), it is found that their exit location (entrance for real particles) from the simulation domain is along the prescribed Interstellar Magnetic Field direction. This indicates that parallel diffusion dominates CR particle transport in the LISM.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Centralized Stochastic Optimal Control of Complex Systems

In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain using the long-run expected average cost per unit time criterion, and we show that the control policy yielding the Pareto optimal solution minimizes the average cost criterion online. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.

complex systems↗

DOE OSTI2016

Synchronous parallel spatially resolved stochastic cluster dynamics

In this work, a spatially resolved stochastic cluster dynamics (SRSCD) model for radiation damage accumulation in metals is implemented using a synchronous parallel kinetic Monte Carlo algorithm. The parallel algorithm is shown to significantly increase the size of representative volumes achievable in SRSCD simulations of radiation damage accumulation. Additionally, weak scaling performance of the method is tested in two cases: (1) an idealized case of Frenkel pair diffusion and annihilation, and (2) a characteristic example problem including defect cluster formation and growth in α-Fe. For the latter case, weak scaling is tested using both Frenkel pair and displacement cascade damage. To improve scaling of simulations with cascade damage, an explicit cascade implantation scheme is developed for cases in which fast-moving defects are created in displacement cascades. For the first time, simulation of radiation damage accumulation in nanopolycrystals can be achieved with a three dimensional rendition of the microstructure, allowing demonstration of the effect of grain size on defect accumulation in Frenkel pair-irradiated α-Fe.

36 MATERIALS SCIENCE↗