Hierarchical approximations for data reduction and learning at multiple scales

Shekhar, Prashant; Patra, Abani

doi:10.3934/fods.2020008

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…Depending on the available data, objective and the complexity of the problem, available computational expenditure and desired level of accuracy, various machine learning models, like the simplistic multiple linear regression, to the more complex artificial neural networks are available to choose from. Moreover, even for a machine learning model of choice, one would need to tune its hyperparameters that in turn affect their accuracy and efficiency drastically [21,22]. For example, for a neural network, the number of layers and neurons in each layer can be adjusted to affect its accuracy and efficiency [23].…”

Section: Selection Of Suitable Machine Learning Modelmentioning

confidence: 99%

Machine learning based surrogate modeling with SVD enabled training for nonlinear civil structures subject to dynamic loading

Parida¹,

Bose²,

Butcher³

et al. 2022

Preprint

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The computationally expensive estimation of engineering demand parameters (EDPs) via finite element (FE) models, while considering earthquake and parameter uncertainty limits the use of the Performance Based Earthquake Engineering framework. Attempts have been made to substitute FE models with surrogate models, however, most of these models are a function of building parameters only. This necessitates re-training for earthquakes not previously seen by the surrogate. In this paper, the authors propose a machine learning based surrogate model framework, which considers both these uncertainties in order to predict for unseen earthquakes. Accordingly,

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Section: Selection Of Suitable Machine Learning Modelmentioning

confidence: 99%

Machine learning based surrogate modeling with SVD enabled training for nonlinear civil structures subject to dynamic loading

Parida¹,

Bose²,

Butcher³

et al. 2022

Preprint

Self Cite

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“…Remark 1 From [44,2], we know that the numerical rank of the Gaussian Kernel increases monotonically with s (mainly due to the narrower support at higher scales), hence after sufficiently high s(≥ ω), || n i=1 α i ψ s i || 2 2 > 0 (= 0 only with α = 0), making the Gramian matrix K(x i , x j ) n i,j=1 numerically positive definite.…”

Section: Multiscale Kernelmentioning

confidence: 99%

“…Here, we have chosen to put a tolerance on the inner product as a termination criterion because it ensures that our basis remains well conditioned for ordinary least square computation, and also the reduction of MSE with the addition on b j s is lower bounded. This is crucial for our algorithm as kernel functions which constitute our basis are highly redundant and ill-conditioned (specially at the initial scales [44]). This is fundamentally different than the traditional forward greedy methods like in [12], which keeps on choosing function from a dictionary that is most correlated with the current residual (without any additional checks), and puts a tolerance on the residual as a termination criterion.…”

Section: Multiscale Algorithmmentioning

confidence: 99%

A Forward Backward Greedy approach for Sparse Multiscale Learning

Shekhar¹,

Patra²

2021

Preprint

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Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated kernel has a weighted multiscale structure. For generating approximations in this space, we provide a practical forward-backward algorithm that is shown to greedily construct a set of basis functions having a multiscale structure, while also creating sparse representations from the given data set, making representations and predictions very efficient. We provide a detailed analysis of the algorithm including recommendations for selecting algorithmic hyper-parameters and estimating probabilistic rates of convergence at individual scales. Then we extend this analysis to multiscale setting, studying the effects of finite scale truncation and quality of solution in the inherent RKHS. In the last section, we analyze the performance of the approach on a variety of simulation and real data sets, thereby justifying the efficiency claims in terms of model quality and data reduction.

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“…Finally, elevation change time series will be combined with models enabling estimation of mass change time series. 70,71 By deriving time series of elevation and mass changes with error estimates to decadal changes of an entire ice sheet, the resulting tool will provide much-needed flexibility for intercomparisons, both between observations and between models and observations.…”

Section: Surface Elevation Reconstruction and Change Detectionmentioning

confidence: 99%

“…Tools to interpolate the irregularly distributed observations into user‐defined meshes or grids, to estimate ice elevation and thickness change, and to perform spatial interpolation will be incorporated into the workflow. Finally, elevation change time series will be combined with models enabling estimation of mass change time series 70,71 . By deriving time series of elevation and mass changes with error estimates to decadal changes of an entire ice sheet, the resulting tool will provide much‐needed flexibility for intercomparisons, both between observations and between models and observations.…”

Section: Community Codesmentioning

confidence: 99%

GHub: Building a glaciology gateway to unify a community

Sperhac

Poinar

Jones-Ivey

et al. 2020

Concurrency and Computation

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There is no consensus on how quickly the earth's ice sheets are melting due to global warming, nor on the ramifications to sea level rise. Due to its potential effects on coastal populations and global economies, sea level rise is a grave concern, making ice melt rates an important area of study. The ice-sheet science community consists of two groups that perform related but distinct kinds of research: a data community, and a model building community. The data community characterizes past and current states of the ice sheets by assembling data from field and satellite observations. The modeling community forecasts the rate of ice-sheet decline with computational models validated against observations. Although observational data and models depend on one another, these two groups are not well integrated. Better coordination between data collection efforts and modeling efforts is imperative if we are to improve our understanding of ice sheet loss rates. We present a new science gateway, GHub, a collaboration space for ice sheet scientists. This web-accessible gateway will host datasets and modeling workflows, and provide access to codes that enable tool building by the ice sheet science community. Using GHub, we will collect and centralize existing datasets, creating data products that more completely catalog the ice sheets of Greenland and Antarctica. We will build workflows for model validation and uncertainty quantification, extending existing ice sheet models. Finally, we will host existing community codes, enabling scientists to build new tools utilizing them. With this new cyberinfrastructure, ice sheet scientists will gain integrated tools to quantify the rate and extent of sea level rise, benefitting human societies around the globe.

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Hierarchical approximations for data reduction and learning at multiple scales

Cited by 9 publications

References 15 publications

Machine learning based surrogate modeling with SVD enabled training for nonlinear civil structures subject to dynamic loading

Machine learning based surrogate modeling with SVD enabled training for nonlinear civil structures subject to dynamic loading

A Forward Backward Greedy approach for Sparse Multiscale Learning

GHub: Building a glaciology gateway to unify a community

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