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A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.

ABSTRACT: The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show limitations for such problems, especially when the size of the training data is limited. To address these difficulties, we have developed a general framework of constructing surrogate models on spaces of stochastic input with arbitrary probability measure irrespective of the mutual dependencies between individual components of the random inputs and the analytical form. The present Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework includes a data-driven construction of multivariate polynomial basis for arbitrary mutually dependent probability measures and a sparsity enhancement rotation procedure. This sparsity-enhancing rotation method was initially proposed in our previous work [1] for Gaussian density distributions, which may not be feasible for non-Gaussian distributions due to the loss of orthogonality after the rotation. To remedy such difficulties, we developed a new data-driven approach to construct orthonormal polynomials for arbitrary mutually dependent randomness, ensuring the constructed basis maintains the orthogonality/near-orthogonality with respect to the density of the rotated random vector, where directly applying the regular polynomial chaos including arbitrary polynomial chaos (aPC) [2] shows limitations due to the assumption of the mutual independence between the components of the random inputs. The developed DSRAR framework leads to accurate recovery, with only limited training data, of a sparse representation of the target functions. The effectiveness of our method is demonstrated in challenging problems such as partial differential equations and realistic molecular systems within high-dimensional (O(10)) conformational spaces where the underlying density is implicitly represented by a large collection of sample data, as well as systems with explicitly given non-Gaussian probabilistic measures.

SUBMITTER: Lei H

PROVIDER: S-EPMC7007047 | biostudies-literature | 2019 Jun

REPOSITORIES: biostudies-literature

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A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.

Lei Huan H Li Jing J Gao Peiyuan P Stinis Panagiotis P Baker Nathan A NA

Computer methods in applied mechanics and engineering 20190314

The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show limitations for such problems, especially when the size of the training data is limited. To address these difficulties, we have developed a general framework of constructing surrogate models on spaces of stochastic input with arbitrary probability measure irr ...[more]

PMID: 32038051

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Project description:BackgroundScientists striving to unlock mysteries within complex biological systems face myriad barriers in effectively integrating available information to enhance their understanding. While experimental techniques and available data sources are rapidly evolving, useful information is dispersed across a variety of sources, and sources of the same information often do not use the same format or nomenclature. To harness these expanding resources, scientists need tools that bridge nomenclature differences and allow them to integrate, organize, and evaluate the quality of information without extensive computation.ResultsSidekick, a genomic data driven analysis and decision making framework, is a web-based tool that provides a user-friendly intuitive solution to the problem of information inaccessibility. Sidekick enables scientists without training in computation and data management to pursue answers to research questions like "What are the mechanisms for disease X" or "Does the set of genes associated with disease X also influence other diseases." Sidekick enables the process of combining heterogeneous data, finding and maintaining the most up-to-date data, evaluating data sources, quantifying confidence in results based on evidence, and managing the multi-step research tasks needed to answer these questions. We demonstrate Sidekick's effectiveness by showing how to accomplish a complex published analysis in a fraction of the original time with no computational effort using Sidekick.ConclusionsSidekick is an easy-to-use web-based tool that organizes and facilitates complex genomic research, allowing scientists to explore genomic relationships and formulate hypotheses without computational effort. Possible analysis steps include gene list discovery, gene-pair list discovery, various enrichments for both types of lists, and convenient list manipulation. Further, Sidekick's ability to characterize pairs of genes offers new ways to approach genomic analysis that traditional single gene lists do not, particularly in areas such as interaction discovery.

Dataset Information

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.

Publications

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.

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