scholarly journals Hierarchical Stochastic Model in Bayesian Inference for Engineering Applications: Theoretical Implications and Efficient Approximation

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Stephen Wu ◽  
Panagiotis Angelikopoulos ◽  
James L. Beck ◽  
Petros Koumoutsakos
Keyword(s):  
Stochastic Model ◽  
Interpolation Method ◽  
Computational Cost ◽  
Dynamics Simulation ◽  
Cancer Drug ◽  
Engineering Applications ◽  
Pkpd Model ◽  
Selection Framework ◽  
Model Class Selection ◽  
Efficient Approximation

Hierarchical Bayesian models (HBMs) have been increasingly used for various engineering applications. We classify two types of HBM found in the literature as hierarchical prior model (HPM) and hierarchical stochastic model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on importance sampling (IS) and empirical interpolation method (EIM). We illustrate our method using two engineering examples—a molecular dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamics (PKPD) model for cancer drug.

Bayesian active learning of interatomic force field for molecular dynamics simulation of Pt/Ag(111)

2021 ◽  
Author(s):  
Kai Xu ◽  
Lei Yan ◽  
Bingran You
Keyword(s):  
Molecular Dynamics ◽  
Active Learning ◽  
Force Field ◽  
Density Functional ◽  
Process Model ◽  
Large Scale ◽  
Computational Cost ◽  
Dynamics Simulation ◽  
Potential Energy Landscape ◽  
Three Body

Force field is a central requirement in molecular dynamics (MD) simulation for accurate description of the potential energy landscape and the time evolution of individual atomic motions. Most energy models are limited by a fundamental tradeoff between accuracy and speed. Although ab initio MD based on density functional theory (DFT) has high accuracy, its high computational cost prevents its use for large-scale and long-timescale simulations. Here, we use Bayesian active learning to construct a Gaussian process model of interatomic forces to describe Pt deposited on Ag(111). An accurate model is obtained within one day of wall time after selecting only 126 atomic environments based on two- and three-body interactions, providing mean absolute errors of 52 and 142 meV/Å for Ag and Pt, respectively. Our work highlights automated and minimalistic training of machine-learning force fields with high fidelity to DFT, which would enable large-scale and long-timescale simulations of alloy surfaces at first-principles accuracy.

Simulating swing dynamics of a power system model using nonlinear model order reduction

2019 ◽  
Vol 38 (6) ◽  
pp. 1918-1930
Author(s):  
Satyavir Singh ◽  
Mohammad Abid Bazaz ◽  
Shahkar Ahmad Nahvi
Keyword(s):  
Power System ◽  
System Dynamics ◽  
Interpolation Method ◽  
Computational Cost ◽  
Nonlinear Function ◽  
Computational Time ◽  
Reduced Basis ◽  
Power System Dynamics ◽  
Content Type ◽  
On Line

Purpose The purpose of this paper is to demonstrate the applicability of the Discrete Empirical Interpolation method (DEIM) for simulating the swing dynamics of benchmark power system problems. The authors demonstrate that considerable savings in computational time and resources are obtained using this methodology. Another purpose is to apply a recently developed modified DEIM strategy with a reduced on-line computational burden on this problem. Design/methodology/approach On-line computational cost of the power system dynamics problem is reduced by using DEIM, which reduces the complexity of the evaluation of the nonlinear function in the reduced model to a cost proportional to the number of reduced modes. The on-line computational cost is reduced by using an approximate snap-shot ensemble to construct the reduced basis. Findings Considerable savings in computational resources and time are obtained when DEIM is used for simulating swing dynamics. The on-line cost implications of DEIM are also reduced considerably by using approximate snapshots to construct the reduced basis. Originality/value Applicability of DEIM (with and without approximate ensemble) to a large-scale power system dynamics problem is demonstrated for the first time.

A Jupyter Notebook Environment for Multibody Dynamics

2020 ◽  
Author(s):  
Aaron Gaut ◽  
Jonathan Cameron ◽  
Abhinandan Jain
Keyword(s):  
Modeling And Simulation ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Training Needs ◽  
Simulation Software ◽  
Dynamics Simulation ◽  
Engineering Applications ◽  
Topic Area ◽  
Significant Extension ◽  
On Line

Abstract DARTS is a rigid/flexible multibody dynamics toolkit for the modeling and simulation of aerospace and robotic vehicles for engineering applications. In this paper we describe an on-line, browser-based environment using Jupyter notebooks to support training needs for the DARTS software. The suite of curated tutorial notebooks is organized into different topic areas, and into multiple themes within each topic area. The notebooks within a theme use a progression of examples for users to expand their understanding of the software. The topic areas include one on the DARTS multibody dynamics software and another one on the theory underlying the multibody dynamics formulation. We also describe a number of Jupyter extensions that were used — and some developed in house — to enhance the notebook interface for use with the dynamics simulation software. One significant extension we implemented allows the embedding of live 3D visualizations within simulation notebooks.

Calculation of Stall Margin Enhancement With Micro-Tip Injection in an Axial Compressor

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Xiaohua Liu ◽  
Jinfang Teng ◽  
Jun Yang ◽  
Xiaofeng Sun ◽  
Dakun Sun ◽  
...  
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Radial Profile ◽  
Computational Cost ◽  
Tip Clearance ◽  
Dynamics Simulation ◽  
Qualitative Assessment ◽  
Force Model ◽  
Tip Leakage Flow ◽  
Stall Margin

Although steady micro-injection is experimentally validated as an attractive method in improving the stall margin of axial compressors, up to now a fast prediction of stall boundary remains some way off. This investigation is to propose such a prediction model. A flow stability model is developed to further consider the effect of high-speed micro-injection. After the base flow field is calculated by steady computational fluid dynamics simulation, a body force model is applied to reproduce the effect of blade on the flow turning and loss. A group of homogeneous equations are obtained based on linearized Navier–Stokes equations and harmonic decomposition of small flow disturbance. The stall onset point can be judged by the imaginary part of the resultant eigenvalue. After the existing experimental results are summarized, an unsteady numerical simulation reveals that the computed characteristics and radial profile of pressure rise coefficient are almost unchanged. The unsteady response of compressor to the micro-injection is preliminarily verified based on the observation of the disturbed spillage of tip leakage flow. It is verified that this approach can provide a qualitative assessment of stall point with acceptable computational cost. Both high injection velocity and short axial gap between injector and rotor leading edge are beneficial for the stall margin extension. These theoretical findings agree well with experimental measurements. It is inferred that the spillage of tip clearance flow, which is inward pushed by higher speed injection with shortened distance away from rotor, could lead to further stable flow field.

The Research of High-Precision Interpolation for Complex Trajectory of SCARA Robot Based on NURBS

2011 ◽  
Vol 130-134 ◽  
pp. 147-153 ◽  
Author(s):  
Liang Zhao ◽  
Kai Qiang Chen ◽  
Zhi Zheng Zhang
Keyword(s):  
High Precision ◽  
Interpolation Method ◽  
Industrial Robot ◽  
Computational Cost ◽  
Nurbs Curve ◽  
Scara Robot ◽  
Curve Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Point To Point

The traditional interpolation methods can’t get high-precision result for the path planning of industrial robot, to solve this problem, this paper presented a new interpolation method based on NURBS curve. The paper established the kinematics transformation matrix of SCARA robot, put forward the principle of NURBS curve interpolation, and described the details of trajectory planning for industrial robot in the rectangular space. Finally, the method mentioned in the paper was tested and compared with point to point interpolation method by Matlab simulations, the result showed that the method mentioned in the paper can reduce the interpolation error and the computational cost markedly.

scholarly journals A Spatiotemporal Stochastic Model for Tropical Precipitation and Water Vapor Dynamics

2015 ◽  
Vol 72 (12) ◽  
pp. 4721-4738 ◽  
Author(s):  
Scott Hottovy ◽  
Samuel N. Stechmann
Keyword(s):  
Water Vapor ◽  
Stochastic Model ◽  
Climate Models ◽  
Free Field ◽  
Computational Cost ◽  
Tropical Convection ◽  
Gaussian Free Field ◽  
Time Step ◽  
Background Spectrum ◽  
Cloud Cluster

Abstract A linear stochastic model is presented for the dynamics of water vapor and tropical convection. Despite its linear formulation, the model reproduces a wide variety of observational statistics from disparate perspectives, including (i) a cloud cluster area distribution with an approximate power law; (ii) a power spectrum of spatiotemporal red noise, as in the “background spectrum” of tropical convection; and (iii) a suite of statistics that resemble the statistical physics concepts of critical phenomena and phase transitions. The physical processes of the model are precipitation, evaporation, and turbulent advection–diffusion of water vapor, and they are represented in idealized form as eddy diffusion, damping, and stochastic forcing. Consequently, the form of the model is a damped version of the two-dimensional stochastic heat equation. Exact analytical solutions are available for many statistics, and numerical realizations can be generated for minimal computational cost and for any desired time step. Given the simple form of the model, the results suggest that tropical convection may behave in a relatively simple, random way. Finally, relationships are also drawn with the Ising model, the Edwards–Wilkinson model, the Gaussian free field, and the Schramm–Loewner evolution and its possible connection with cloud cluster statistics. Potential applications of the model include several situations where realistic cloud fields must be generated for minimal cost, such as cloud parameterizations for climate models or radiative transfer models.

INTRODUCING AN INTERPOLATION METHOD TO EFFICIENTLY IMPLEMENT AN APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATOR FOR THE HURST EXPONENT

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550045 ◽  
Author(s):  
YEN-CHING CHANG
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Hurst Exponent ◽  
Interpolation Method ◽  
Computational Cost ◽  
Likelihood Estimator ◽  
Unknown Variance ◽  
Power Spectral ◽  
Levinson Algorithm ◽  
Approximate Maximum Likelihood Estimator

The efficiency and accuracy of estimating the Hurst exponent have been two inevitable considerations. Recently, an efficient implementation of the maximum likelihood estimator (MLE) (simply called the fast MLE) for the Hurst exponent was proposed based on a combination of the Levinson algorithm and Cholesky decomposition, and furthermore the fast MLE has also considered all four possible cases, including known mean, unknown mean, known variance, and unknown variance. In this paper, four cases of an approximate MLE (AMLE) were obtained based on two approximations of the logarithmic determinant and the inverse of a covariance matrix. The computational cost of the AMLE is much lower than that of the MLE, but a little higher than that of the fast MLE. To raise the computational efficiency of the proposed AMLE, a required power spectral density (PSD) was indirectly calculated by interpolating two suitable PSDs chosen from a set of established PSDs. Experimental results show that the AMLE through interpolation (simply called the interpolating AMLE) can speed up computation. The computational speed of the interpolating AMLE is on average over 24 times quicker than that of the fast MLE while remaining the accuracy very close to that of the MLE or the fast MLE.

scholarly journals A NEW MODEL APPROXIMATING M/PH/1 QUEUING SYSTEMS DURING THE TRANSIENT PERIOD

2001 ◽  
Vol 6 (2) ◽  
pp. 199-209
Author(s):  
H. Gao ◽  
M. A. M. Lynch
Keyword(s):  
Diffusion Approximation ◽  
Computational Cost ◽  
Queuing Systems ◽  
Diffusion Approximations ◽  
New Model ◽  
Transient Period ◽  
Efficient Approximation ◽  
Vector Valued ◽  
Low Traffic

This paper presents an efficient approximation for M/PH/1 queuing systems based on the replacement of the majority of the vector valued state probabilities by a diffusion approximation. The strength of the new approximation is that it gives more accurate results than the current diffusion approximations at both high and low traffic intensities and at little extra computational cost. The accuracy of the new approximation during the transient is shown by comparing it numerically with solutions to the M/PH/1 system and current approaches based on the diffusion approximation.

scholarly journals Simulating Protein-Ligand Binding with Neural Network Potentials

2019 ◽  
Author(s):  
Shae-Lynn Lahey ◽  
Christopher Rowley
Keyword(s):  
Neural Network ◽  
Ligand Binding ◽  
Computational Cost ◽  
Bound State ◽  
Drug Binding ◽  
Cancer Drug ◽  
Molecular Conformations ◽  
Drug Molecules ◽  
The Stability ◽  
Dynamics Simulations

Drug molecules adopt a range of conformations both in solution and in their protein-bound state. The strain and reduced flexibility of bound drugs can partially counter the intermolecular interactions that drive protein–ligand binding. To make accurate computational predictions of drug binding affinities, computational chemists have attempted to develop efficient empirical models of these interactions, although these methods are not always reliable. Machine learning has allowed the development of highly-accurate neural-network potentials (NNPs), which are capable of predicting the stability of molecular conformations with accuracy comparable to state-of-the-art quantum chemical calculations but at a billionth of the computational cost. Here, we demonstrate that these methods can be used to represent the intramolecular forces of protein-bound drugs within molecular dynamics simulations. These simulations are shown to be capable of predicting the protein–ligand binding pose and conformational component of the absolute Gibbs energy of binding for a set of drug molecules. Notably, the conformational energy for anti-cancer drug erlotinib binding to its target was found to considerably overestimated by a molecular mechanical model, while the NNP predicts a more moderate value. Although the ANI-1ccX NNP was not trained to describe ionic molecules, reasonable binding poses are predicted for charged ligands, although this method is not suitable for modeling the ligands in solution.

scholarly journals Statistical properties of a stochastic model of eddy hopping

2021 ◽  
Author(s):  
Izumi Saito ◽  
Takeshi Watanabe ◽  
Toshiyuki Gotoh
Keyword(s):  
Stochastic Model ◽  
Reference Data ◽  
Cloud Model ◽  
Computational Cost ◽  
Statistical Properties ◽  
Large Eddy Simulations ◽  
Cloud Droplets ◽  
Large Eddy ◽  
Typical Parameter ◽  
Proper Scaling

Abstract. Statistical properties are investigated for the stochastic model of eddy hopping, which is a novel cloud microphysical model that accounts for the effect of the supersaturation fluctuation at unresolved scales on the growth of cloud droplets and on spectral broadening. It is shown that the model fails to reproduce a proper scaling for a certain range of parameters, resulting in a deviation of the model prediction from the reference data taken from direct numerical simulations and large-eddy simulations (LESs). Corrections to the model are introduced so that the corrected model can accurately reproduce the reference data with the proper scaling. In addition, a possible simplification of the model is discussed, which may contribute to a reduction in computational cost while keeping the statistical properties almost unchanged in the typical parameter range for the model implementation in the LES Lagrangian cloud model.

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