The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems

Piret, Cécile; Dissanayake, Neluka; Gierke, John S.; Fornberg, Bengt

doi:10.1007/s11004-019-09820-w

Cited by 8 publications

(5 citation statements)

References 34 publications

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“…Data driven is an another way to enable rapid simulations, where an emulator of the system is constructed upon the HFM solutions of selected collocation points in parameter space without the need to modify the codes. Specifically, some regression techniques, for example, radial basis functions (Piret et al., 2019), Gaussian process regression (GPR) (Yang et al., 2018), and stochastic polynomial chaos expansion (PCE) (Hu et al., 2019), are employed to learn a deterministic or probabilistic input‐output mapping. Because of the nonintrusive feature and ease of implementation, many different data‐driven surrogates have been developed for inversion problems of the hydrological system (Dai et al., 2016; Li & Zhang, 2007; Saad & Ghanem, 2009; Zeng & Zhang, 2010).…”

Section: Introductionmentioning

confidence: 99%

Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

Xiao

Tian

2020

Water Resources Research

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This paper introduces an efficient surrogate model with the aim of accelerating joint estimation of subsurface geological properties and relative permeability parameters for high‐dimensional inversion problems. We fully replace the high‐fidelity model with a set of subdomain linear models through integrating model linearization with smooth local parameterization where the Gaussian geological parameters and non‐Gaussian facies indicators are locally parameterized. These subdomain linear models with smooth local parameterization, referred to as SLM‐SLP, are constructed in each subdomain individually using only a few high‐fidelity model simulations. An adaptive scheme, that is, weighting smooth local parameterization (WSLP), is introduced as well to mitigate the negative effects of inappropriate domain decomposition schemes by adaptively optimizing the domain decomposition strategy. The computational advantages of the proposed algorithm are demonstrated on a synthetic non‐Gaussian facies model and a real‐world high‐dimensional Gaussian model. The amount of computational cost has been drastically reduced while reasonable accuracy remains. Specifically, SLM‐SLP only needs 220 fidelity simulations to optimize 302 parameters. Compared to ensemble smoother with multiple data assimilation (ES‐MDA), SLM‐SLP effectively and efficiently mitigates the ensemble collapse problem in the course of uncertain quantification.

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Section: Introductionmentioning

confidence: 99%

Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

Xiao

Tian

2020

Water Resources Research

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“…RBFs are a family of interpolation functions that were first introduced into the geological literature by Hardy [55] to interpolate scattered topographic data. RBF techniques have been considered good surface interpolators due to their attempt to honor raw data [56] and their ability to provide the smoothest surface of interpolation [57,58], which is ideally suited for geological modeling [59,60]. Implicit geologic modeling using RBFs is also comparable in quality to modeling using popular co-kriging approaches [61,62].…”

Section: Aquifer Geometry and Saltwater Intrusionmentioning

confidence: 99%

Characterization of a Shallow Coastal Aquifer in the Framework of a Subsurface Storage and Soil Aquifer Treatment Project Using Electrical Resistivity Tomography (Port de la Selva, Spain)

et al. 2021

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Water percolation through infiltration ponds is creating significant synergies for the broad adoption of water reuse as an additional non-conventional water supply. Despite the apparent simplicity of the soil aquifer treatment (SAT) approaches, the complexity of site-specific hydrogeological conditions and the processes occurring at various scales require an exhaustive understanding of the system’s response. The non-saturated zone and underlying aquifers cannot be considered as a black box, nor accept its characterization from few boreholes not well distributed over the area to be investigated. Electrical resistivity tomography (ERT) is a non-invasive technology, highly responsive to geological heterogeneities that has demonstrated useful to provide the detailed subsurface information required for groundwater modeling. The relationships between the electrical resistivity of the alluvial sediments and the bedrock and the difference in salinity of groundwater highlight the potential of geophysical methods over other more costly subsurface exploration techniques. The results of our research show that ERT coupled with implicit modeling tools provides information that can significantly help to identify aquifer geometry and characterize the saltwater intrusion of shallow alluvial aquifers. The proposed approaches could improve the reliability of groundwater models and the commitment of stakeholders to the benefits of SAT procedures.

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“…where D is a highly sparse differentiation matrix approximating the left-hand sided operators in (16) and (17), F [•] approximates the residual (18), and g X is a zero vector except at the boundary, where is equal to g(x, y). Newton iterations continue until the tolerance R ψ (i−1) ≤ ∼ 10 −8 is reached.…”

Section: Navier-stokes Equationsmentioning

confidence: 99%

“…Over the last decades, RBF-FD methods have been successfully applied to a wide range of problems in science and engineering. Some of the application areas include the geosciences [16,17,18], combustion modelling [19,20], PDEs on surfaces [21,22,23], interface [24,25] and contact [26] problems, as well as scalable high-performance implementations [27,28,29]. For a complete list of references see monograph [14].…”

Section: Introductionmentioning

confidence: 99%

Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries

Bayona

Sánchez–Sanz

Fernández-Tarrazo

et al. 2021

Applied Mathematical Modelling

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The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems

Cited by 8 publications

References 34 publications

Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

Characterization of a Shallow Coastal Aquifer in the Framework of a Subsurface Storage and Soil Aquifer Treatment Project Using Electrical Resistivity Tomography (Port de la Selva, Spain)

Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries

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