Stochastic simulations of ocean waves: An uncertainty quantification study

Yildirim, Battalgazi; Karniadakis, George Em

doi:10.1016/j.ocemod.2014.12.001

Cited by 19 publications

(15 citation statements)

References 70 publications

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“…Given that most neuroscience models contain a variety of uncertain parameters, the need for systematic approaches to quantify what confidence we can have in the model output is pressing. The importance of uncertainty quantification and sensitivity analysis of computational models is well known in a wide variety of fields (Leamer, 1985;Beck, 1987;Turanyi and Turányi, 1990;Oberkampf et al, 2002;Wood-Schultz, 2011;Marino et al, 2008;Najm, 2009;Rossa et al, 2011;Yildirim and Karniadakis, 2015;Wang and Sheen, 2015). Due the prevalence of inherent variability in the parameters of biological systems, uncertainty quantification and sensitivity analysis is at least as important in neuroscience.…”

Section: Introductionmentioning

confidence: 99%

Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience

Tennøe

Halnes

Einevoll

2018

Preprint

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Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience.Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it easy and quick to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches.Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-topoint comparison of the "raw" model output (e.g. membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, mean interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy.The aim of the current paper is to present Uncertainpy for the neuroscience community in a useroriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis on three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator. . 5, 2018; Keywords: uncertainty quantification, sensitivity analysis, features, polynomial chaos, quasi-Monte Carlo methods, stochastic modeling, computational modeling, PythonBY 4.0 International license not peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/274779 doi: bioRxiv preprint first posted online Mar SIGNIFICANCE STATEMENTA major challenge in computational neuroscience is to specify the often large number of parameters that define the neuron and neural network models. Many of these parameters have an inherent variability, and some may even be actively regulated and change with time. It is important to know how the uncertainty in model parameters affects the model predictions. To address this need we here present Uncertainpy, an open-source Python toolbox tailored to perform uncertainty quantification and sensiti...

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Section: Introductionmentioning

confidence: 99%

Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience

Tennøe

Halnes

Einevoll

2018

Preprint

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“…A core topic in the field of uncertainty quantification (UQ) is the question how to characterize the distribution of model outputs, given the distribution of the model inputs (or a sample thereof). Questions such as these are encountered in many fields of science and engineering [1,2,3,4,5], and have given rise to modern UQ methods including stochastic collocation, polynomial chaos expansion and stochastic Galerkin methods [6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Clustering-Based Collocation for Uncertainty Propagation With Multivariate Dependent Inputs

Eggels

Crommelin

Witteveen

2018

Int. J. UncertaintyQuantification

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In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend the use of collocation methods to uncertainty propagation with multivariate, dependent input, in which the output approximation is piecewise constant on the clusters. The approach is particularly useful in situations where the probability distribution of the input is unknown, and only a sample from the input distribution is available. We examine several clustering methods and assess the convergence of collocation based on these methods both theoretically and numerically. We demonstrate good performance of * a.w.eggels@cwi.nl the proposed methods, most notably for the challenging case of nonlinearly dependent inputs in higher dimensions. Numerical tests with input dimension up to 16 are included, using as benchmarks the Genz test functions and a test case from computational fluid dynamics (liddriven cavity flow).

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“…In [8] a combination of non-intrusive (collocation) PC and ANOVA decomposition was used for the propagation and sensitivity analysis of the uncertain parameters entering the SWE modeling the runup of waves. Unlike the preceding works, [9] studies the influence of uncertainties on the phase-averaged equation, which is suitable for slowly varying wave fields, e.g. ocean waves in deep water.…”

Section: Introductionmentioning

confidence: 99%

Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

Bigoni¹,

Engsig-Karup²,

Eskilsson³

2016

J Eng Math

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A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and non-intrusive methods based on generalized Polynomial Chaos (PC). These methods allow to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution in different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. We finally present a synthetic experiment studying the variance based sensitivity of the wave load on an offshore structure to a number of input uncertainties. In the numerical examples presented the PC methods have exhibited fast convergence, suggesting that the problem is amenable to being analyzed with such methods.

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Stochastic simulations of ocean waves: An uncertainty quantification study

Cited by 19 publications

References 70 publications

Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience

Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience

Clustering-Based Collocation for Uncertainty Propagation With Multivariate Dependent Inputs

Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

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