SPUX - a Scalable Package for Bayesian Uncertainty Quantification

2020 ◽  
Author(s):  
Jonas Sukys ◽  
Marco Bacci
Keyword(s):  
Bayesian Inference ◽  
Uncertainty Quantification ◽  
High Performance ◽  
Performance Metrics ◽  
Expert Knowledge ◽  
Simple Random Walk ◽  
Scientific Workflow ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Computational Performance

<div> <div>SPUX (Scalable Package for Uncertainty Quantification in "X") is a modular framework for Bayesian inference and uncertainty quantification. The SPUX framework aims at harnessing high performance scientific computing to tackle complex aquatic dynamical systems rich in intrinsic uncertainties,</div> <div>such as ecological ecosystems, hydrological catchments, lake dynamics, subsurface flows, urban floods, etc. The challenging task of quantifying input, output and/or parameter uncertainties in such stochastic models is tackled using Bayesian inference techniques, where numerical sampling and filtering algorithms assimilate prior expert knowledge and available experimental data. The SPUX framework greatly simplifies uncertainty quantification for realistic computationally costly models and provides an accessible, modular, portable, scalable, interpretable and reproducible scientific workflow. To achieve this, SPUX can be coupled to any serial or parallel model written in any programming language (e.g. Python, R, C/C++, Fortran, Java), can be installed either on a laptop or on a parallel cluster, and has built-in support for automatic reports, including algorithmic and computational performance metrics. I will present key SPUX concepts using a simple random walk example, and showcase recent realistic applications for catchment and lake models. In particular, uncertainties in model parameters, meteorological inputs, and data observation processes are inferred by assimilating available in-situ and remotely sensed datasets.</div> </div>

Efficient parallelization of SPH algorithm on modern multi-core CPUs and massively parallel GPUs

2021 ◽  
pp. 2150054
Author(s):  
Pravin Jagtap ◽  
Rupesh Nasre ◽  
V. S. Sanapala ◽  
B. S. V. Patnaik
Keyword(s):  
High Performance ◽  
Performance Metrics ◽  
Computational Simulation ◽  
Massively Parallel ◽  
Benchmark Problems ◽  
Processing Unit ◽  
Central Processing ◽  
Neighbor Search ◽  
Computational Performance ◽  
Sph Algorithm

Smoothed Particle Hydrodynamics (SPH) is fast emerging as a practically useful computational simulation tool for a wide variety of engineering problems. SPH is also gaining popularity as the back bone for fast and realistic animations in graphics and video games. The Lagrangian and mesh-free nature of the method facilitates fast and accurate simulation of material deformation, interface capture, etc. Typically, particle-based methods would necessitate particle search and locate algorithms to be implemented efficiently, as continuous creation of neighbor particle lists is a computationally expensive step. Hence, it is advantageous to implement SPH, on modern multi-core platforms with the help of High-Performance Computing (HPC) tools. In this work, the computational performance of an SPH algorithm is assessed on multi-core Central Processing Unit (CPU) as well as massively parallel General Purpose Graphical Processing Units (GP-GPU). Parallelizing SPH faces several challenges such as, scalability of the neighbor search process, force calculations, minimizing thread divergence, achieving coalesced memory access patterns, balancing workload, ensuring optimum use of computational resources, etc. While addressing some of these challenges, detailed analysis of performance metrics such as speedup, global load efficiency, global store efficiency, warp execution efficiency, occupancy, etc. is evaluated. The OpenMP and Compute Unified Device Architecture[Formula: see text] parallel programming models have been used for parallel computing on Intel Xeon[Formula: see text] E5-[Formula: see text] multi-core CPU and NVIDIA Quadro M[Formula: see text] and NVIDIA Tesla p[Formula: see text] massively parallel GPU architectures. Standard benchmark problems from the Computational Fluid Dynamics (CFD) literature are chosen for the validation. The key concern of how to identify a suitable architecture for mesh-less methods which essentially require heavy workload of neighbor search and evaluation of local force fields from neighbor interactions is addressed.

scholarly journals Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Model Parameters ◽  
Geometrical Parameters ◽  
Parameter Uncertainties ◽  
Flame Response ◽  
Mode Stability

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain-based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible flow computations. They result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters, etc. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the problem is using adjoint perturbation theory. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo (MC) simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz, it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental data are available.

scholarly journals Uncertainty quantification in subject-specific estimation of local vessel mechanical properties

2021 ◽  
Author(s):  
Bruno V Rego ◽  
Dar Weiss ◽  
Matthew R Bersi ◽  
Jay D Humphrey
Keyword(s):  
Mechanical Properties ◽  
Uncertainty Quantification ◽  
Inverse Modeling ◽  
Quantitative Estimation ◽  
Small Animal ◽  
Image Correlation ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Local Point ◽  
Subject Specific

Quantitative estimation of local mechanical properties remains critically important in the ongoing effort to elucidate how blood vessels establish, maintain, or lose mechanical homeostasis. Recent advances based on panoramic digital image correlation (pDIC) have made high-fidelity 3D reconstructions of small-animal (e.g., murine) vessels possible when imaged in a variety of quasi-statically loaded configurations. While we have previously developed and validated inverse modeling approaches to translate pDIC-measured surface deformations into biomechanical metrics of interest, our workflow did not heretofore include a methodology to quantify uncertainties associated with local point estimates of mechanical properties. This limitation has compromised our ability to infer biomechanical properties on a subject-specific basis, such as whether stiffness differs significantly between multiple material locations on the same vessel or whether stiffness differs significantly between multiple vessels at a corresponding material location. In the present study, we have integrated a novel uncertainty quantification and propagation pipeline within our inverse modeling approach, relying on empirical and analytic Bayesian techniques. To demonstrate the approach, we present illustrative results for the ascending thoracic aorta from three mouse models, quantifying uncertainties in constitutive model parameters as well as circumferential and axial tangent stiffness. Our extended workflow not only allows parameter uncertainties to be systematically reported, but also facilitates both subject-specific and group-level statistical analyses of the mechanics of the vessel wall.

scholarly journals TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

2021 ◽  
Vol 247 ◽  
pp. 20005
Author(s):  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Predictive Modeling ◽  
Curse Of Dimensionality ◽  
Current Data ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Response Distribution ◽  
Parameter Uncertainties ◽  
Adjoint Sensitivity

This invited presentation summarizes new methodologies developed by the author for performing high-order sensitivity analysis, uncertainty quantification and predictive modeling. The presentation commences by summarizing the newly developed 3rd-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for linear systems, which overcomes the “curse of dimensionality” for sensitivity analysis and uncertainty quantification of a large variety of model responses of interest in reactor physics systems. The use of the exact expressions of the 2nd-, and 3rd-order sensitivities computed using the 3rd-ASAM is subsequently illustrated by presenting 3rd-order formulas for the first three cumulants of the response distribution, for quantifying response uncertainties (covariance, skewness) stemming from model parameter uncertainties. The use of the 1st-, 2nd-, and 3rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2nd/3rd-BERRU-PM (“Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”), which aims at overcoming the curse of dimensionality in predictive modeling. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing a subjective user-defined “cost functional quantifying the discrepancies between measurements and computations.” By utilizing the 1st-, 2nd- and 3rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2nd/3rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2nd- and 3rd-order are comprised in the mathematical framework of the 2nd/3rd-BERRU-PM formalism, the computations underlying the 2nd/3rd-BERRU-PM require the inversion of a single matrix of dimensions equal to the number of considered responses, thus overcoming the curse of dimensionality which would affect the inversion of hessian and higher-order matrices in the parameter space.

scholarly journals Surrogate-assisted Bayesian inversion for landscape and basin evolution models

2019 ◽  
Author(s):  
Rohitash Chandra ◽  
Danial Azam ◽  
Arpit Kapoor ◽  
R. Dietmar Mulller
Keyword(s):  
Parallel Computing ◽  
Uncertainty Quantification ◽  
High Performance ◽  
Large Scale ◽  
Likelihood Function ◽  
Computational Cost ◽  
Optimization Methods ◽  
Parallel Tempering ◽  
Model Parameters ◽  
Basin Evolution

Abstract. The complex and computationally expensive features of the forward landscape and sedimentary basin evolution models pose a major challenge in the development of efficient inference and optimization methods. Bayesian inference provides a methodology for estimation and uncertainty quantification of free model parameters. In our previous work, parallel tempering Bayeslands was developed as a framework for parameter estimation and uncertainty quantification for the landscape and basin evolution modelling software Badlands. Parallel tempering Bayeslands features high-performance computing with dozens of processing cores running in parallel to enhance computational efficiency. Although parallel computing is used, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape and basin evolution problems, a single model evaluation can take from several minutes to hours, and in certain cases, even days. Surrogate-assisted optimization has been with successfully applied to a number of engineering problems This motivates its use in optimisation and inference methods suited for complex models in geology and geophysics. Surrogates can speed up parallel tempering Bayeslands by developing computationally inexpensive surrogates to mimic expensive models. In this paper, we present an application of surrogate-assisted parallel tempering where that surrogate mimics a landscape evolution model including erosion, sediment transport and deposition, by estimating the likelihood function that is given by the model. We employ a machine learning model as a surrogate that learns from the samples generated by the parallel tempering algorithm and the likelihood from the model. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelization. The results show that the proposed methodology is effective in lowering the overall computational cost significantly while retaining the quality of solutions.

scholarly journals Towards Uncertainty Quantification of LES and URANS for the Buoyancy-Driven Mixing Process between Two Miscible Fluids—Differentially Heated Cavity of Aspect Ratio 4

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 161
Author(s):  
Philipp J. Wenig ◽  
Ruiyun Ji ◽  
Stephan Kelm ◽  
Markus Klein
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Uncertainty Quantification ◽  
Large Scale ◽  
Method Development ◽  
Model Parameters ◽  
Mixing Process ◽  
Reactor Accident ◽  
Hydrogen Distribution ◽  
Parameter Uncertainties

Numerical simulations are subject to uncertainties due to the imprecise knowledge of physical properties, model parameters, as well as initial and boundary conditions. The assessment of these uncertainties is required for some applications. In the field of Computational Fluid Dynamics (CFD), the reliable prediction of hydrogen distribution and pressure build-up in nuclear reactor containment after a severe reactor accident is a representative application where the assessment of these uncertainties is of essential importance. The inital and boundary conditions that significantly influence the present buoyancy-driven flow are subject to uncertainties. Therefore, the aim is to investigate the propagation of uncertainties in input parameters to the results variables. As a basis for the examination of a representative reactor test containment, the investigations are initially carried out using the Differentially Heated Cavity (DHC) of aspect ratio 4 with Ra=2×109 as a test case from the literature. This allows for gradual method development for guidelines to quantify the uncertainty of natural convection flows in large-scale industrial applications. A dual approach is applied, in which Large Eddy Simulation (LES) is used as reference for the Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations. A methodology for the uncertainty quantification in engineering applications with a preceding mesh convergence study and sensitivity analysis is presented. By taking the LES as a reference, the results indicate that URANS is able to predict the underlying mixing process at Ra=2×109 and the variability of the result variables due to parameter uncertainties.

scholarly journals Surrogate-assisted Bayesian inversion for landscape and basin evolution models

2020 ◽  
Vol 13 (7) ◽  
pp. 2959-2979
Author(s):  
Rohitash Chandra ◽  
Danial Azam ◽  
Arpit Kapoor ◽  
R. Dietmar Müller
Keyword(s):  
Uncertainty Quantification ◽  
High Performance ◽  
Large Scale ◽  
Likelihood Function ◽  
Landscape Evolution ◽  
Computational Cost ◽  
Evolution Model ◽  
Parallel Tempering ◽  
Model Parameters ◽  
Computationally Expensive

Abstract. The complex and computationally expensive nature of landscape evolution models poses significant challenges to the inference and optimization of unknown model parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed parallel tempering Bayeslands as a framework for parameter estimation and uncertainty quantification for the Badlands landscape evolution model. Parallel tempering Bayeslands features high-performance computing that can feature dozens of processing cores running in parallel to enhance computational efficiency. Nevertheless, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape evolution problems, a single model evaluation can take from several minutes to hours and in some instances, even days or weeks. Surrogate-assisted optimization has been used for several computationally expensive engineering problems which motivate its use in optimization and inference of complex geoscientific models. The use of surrogate models can speed up parallel tempering Bayeslands by developing computationally inexpensive models to mimic expensive ones. In this paper, we apply surrogate-assisted parallel tempering where the surrogate mimics a landscape evolution model by estimating the likelihood function from the model. We employ a neural-network-based surrogate model that learns from the history of samples generated. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelism. The results show that the proposed methodology is effective in lowering the computational cost significantly while retaining the quality of model predictions.

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