Mutual information analysis to approach nonlinearity in groundwater stochastic fields

Butera, Ilaria; Vallivero, Luca; Ridolfi, Luca

doi:10.1007/s00477-018-1591-4

Cited by 7 publications

(5 citation statements)

References 35 publications

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“…Mutual Information turns out to be null in case of independent random variables, while the equality H(X) = H(Z) = I(X; Z) holds in case that the knowledge of one variable is sufficient to predicted the other one exactly. Mutual Information is again measured in nats as in (4). It is important to recall here that mutual information is a nonlinear dependence metric, i.e., it is capable of detecting dependence between random variables which are not induced by a linear relationship.…”

Section: Information Theorymentioning

confidence: 99%

“…For example several studies have relied on the concept of entropy as an indicator of uncertainty within risk assessment procedures [23,1] or to set up optimal experimental design for model discrimination [17]. IT mutual information has also been shown to be an indicator of the degree of nonlinearity existing between output variables in flow and transport simulations, with a particular focus on their spatial correlation [4]. As an alternative approach, the concept of entrogram was introduced in [3].…”

Section: Introductionmentioning

confidence: 99%

“…Such proportion can be analytically determined and increases with the number of retained modes. However, for values of the variance of log-conductivity above unity the degree of nonlinearity between input (hydraulic conductivity) and output (flow velocity) increases [4]. A critical issue in this context is to control and constrain a priori the output approximation accuracy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Characterization of flow through random media via Karhunen–Loève expansion: an information theory perspective

Dell’Oca¹,

Porta²

2020

Int J Geomath

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We leverage on Information Theory to assess the fidelity of approximated numerical stochastic groundwater flow simulations. We consider flow in saturated heterogeneous porous media, where the Karhunen-Loève (KL) expansion is used to express the hydraulic conductivity as a spatially correlated random field. We quantify the impact of the KL expansion truncation on the uncertainty associated with punctual values of hydraulic conductivity and flow velocity. In particular, we compare the statistical dependence between variables by considering (a) linear correlation metrics (Pearson coefficient of correlation) and (b) metrics capable of accounting for nonlinear dependence (coefficient of uncertainty based on mutual information). We test the selected metrics by analyzing the relationship between hydraulic conductivity fields generated via Monte Carlo sampling with different levels of truncation of the KL expansion and the corresponding fluid velocity fields, obtained through the numerical solution of Darcy's flow. Our analysis shows that employing linear correlation metrics leads to a general overestimation of the correlation level and IT-based indicators are valuable tools to assess the impact of the KL truncation on the output velocity values. We then analyze the impact of the number of retained modes on the spatial organization of the velocity field. Results indicates that (i) as the number of modes decrease the spatial correlations of the velocity field increases; (ii) linear indicators of spatial correlation are again larger than the nonlinear counterparts.

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Section: Information Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Characterization of flow through random media via Karhunen–Loève expansion: an information theory perspective

Dell’Oca¹,

Porta²

2020

Int J Geomath

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“…Characterization of permeability of porous media plays a major role in a variety of hydrological settings. There are abundant studies documenting that permeability values and their associated statistics depend on a variety of scales, i.e., the measurement support (or data support), the sampling window (domain of investigation), the spatial correlation (degree of structural coherence) and the spatial resolution (rendering the degree of the descriptive detail associated with the characterization of a porous system) (see, e.g., Brace, 1984;Clauser, 1992;Neuman, 1994;Schad and Teutsch, 1994;Rovey and Cherkauer, 1995;Sanchez-Villa et al, 1996;Schulze-Makuch and Cherkauer, 1998;Schulze-Makuch et al, 1999;Wilson, 1999a, b, 2000;Vesselinov et al, 2001a, b;Winter and Tartakovsky, 2001;Hyun et al, 2002;Neuman and Di Federico, 2003;Maréchal et al, 2004;Illman, 2004;Cintoli et al, 2005;Riva et al, 2013;Guadagnini et al, 2013Guadagnini et al, , 2018, and references therein). Among these scales, we focus here on the characteristic length associated with data collection (i.e., support scale).…”

Section: Introductionmentioning

confidence: 99%

Interpretation of multi-scale permeability data through an information theory perspective

Dell’Oca

Guadagnini

Riva

2020

Hydrol. Earth Syst. Sci.

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Abstract. We employ elements of information theory to quantify (i) the information content related to data collected at given measurement scales within the same porous medium domain and (ii) the relationships among information contents of datasets associated with differing scales. We focus on gas permeability data collected over Berea Sandstone and Topopah Spring Tuff blocks, considering four measurement scales. We quantify the way information is shared across these scales through (i) the Shannon entropy of the data associated with each support scale, (ii) mutual information shared between data taken at increasing support scales, and (iii) multivariate mutual information shared within triplets of datasets, each associated with a given scale. We also assess the level of uniqueness, redundancy and synergy (rendering, i.e., information partitioning) of information content that the data associated with the intermediate and largest scales provide with respect to the information embedded in the data collected at the smallest support scale in a triplet. Highlights. Information theory allows characterization of the information content of permeability data related to differing measurement scales. An increase in the measurement scale is associated with quantifiable loss of information about permeability. Redundant, unique and synergetic contributions of information are evaluated for triplets of permeability datasets, each taken at a given scale.

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“…Relaying on IT metrics, Butera et al (2018) assess the relevance of non-linear effects for the characterization of the spatial dependence of flow and solute transport related observables. Pedretti (2017, 2018) develope novel concepts, mutuated by IT, for the characterization of heterogeneity within a porous system and its links to salient solute transport features.…”

Section: Introductionmentioning

confidence: 99%

Interpretation of Multi-scale Permeability Data through an Information Theory Perspective

Dell’Oca¹,

Guadagnini²,

Riva³

2019

Preprint

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Abstract. We employ elements of Information Theory to quantify (i) the information content related to data collected at given measurement scales within the same porous medium domain, and (ii) the relationships among Information contents of datasets associated with differing scales. We focus on gas permeability data collected over a Berea Sandstone and a Topopah Spring Tuff blocks, considering four measurement scales. We quantify the way information is shared across these scales through (i) the Shannon entropy of the data associated with each support scale, (ii) mutual information shared between data taken at increasing support scales, and (iii) multivariate mutual information shared within triplets of datasets, each associated with a given scale. We also assess the level of uniqueness, redundancy and synergy (rendering, i.e., the information partitioning) of information content that the data associated with the intermediate and largest scales provide with respect to the information embedded in the data collected at the smallest support scale in a triplet.

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Mutual information analysis to approach nonlinearity in groundwater stochastic fields

Cited by 7 publications

References 35 publications

Characterization of flow through random media via Karhunen–Loève expansion: an information theory perspective

Characterization of flow through random media via Karhunen–Loève expansion: an information theory perspective

Interpretation of multi-scale permeability data through an information theory perspective

Interpretation of Multi-scale Permeability Data through an Information Theory Perspective

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