Inverse source problem in a one-dimensional evolution linear transport equation with spatially varying coefficients: application to surface water pollution

Hamdi, Adel; Mahfoudhi, Imed

doi:10.1080/17415977.2013.764871

Cited by 25 publications

(9 citation statements)

References 16 publications

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“…Understanding how different groundwater types mix and how some of the species in these mixtures react is a challenging but very important task. This task is typically performed using complex inverse models representing groundwater mixing processes in the aquifer [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Unsupervised machine learning based on non-negative tensor factorization for analyzing reactive-mixing

Vesselinov

Mudunuru

Karra

et al. 2019

Journal of Computational Physics

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Analysis of reactive-diffusion simulations representing complex mixing processes requires a large number of independent model runs. For each high-fidelity model simulation, the model inputs are varied and the predicted mixing behavior is represented by temporal and spatial changes in species concentration. It is then required to discern how the model inputs (such as diffusivity, dispersion, anisotropy, and velocity field properties) impact the mixing process. This task is challenging and typically involves interpretation of large model outputs representing temporal and spatial changes of species concentration within the model domain. However, the task can be automated and substantially simplified by applying Machine Learning (ML) methods. In this paper, we present an application of an unsupervised ML method (called NTFk) using Non-negative Tensor Factorization (NTF) coupled with a custom clustering procedure based on k-means to reveal the temporal and spatial features in product concentrations. An attractive and unique aspect of the proposed ML method is that it ensures the extracted features are non-negative, which are important to obtain a meaningful deconstruction of the mixing processes. The ML methodology is applied to a large set of high-resolution finite-element model simulations representing anisotropic reaction-diffusion processes in perturbed vortex-based velocity fields. The applied finite-element method ensures that spatial and temporal species concentration are always non-negative, even in the case of high anisotropic contrasts. The simulated reaction is a fast irreversible bimolecular reaction A + B → C, where species A and B react to form species C. The reactive-diffusion model input parameters that control mixing include properties of velocity field (such as vortex structures), anisotropic dispersion, and molecular diffusion. We demonstrate the applicability of the ML feature extraction method to produce a meaningful deconstruction of model outputs to discriminate between different physical processes impacting the reactants, their mixing, and the spatial distribution of the product C. The presented ML analysis allowed us to identify additive temporal and spatial features that characterize mixing behavior. The application of the proposed NTFk approach is not limited to reactive-mixing. NTFk can be readily applied to any observed or simulated datasets that can be 1 arXiv:1805.06454v2 [cs.CE] 21 Feb 2019 represented as tensors and have separable latent signatures or features.

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Section: Introductionmentioning

confidence: 99%

Unsupervised machine learning based on non-negative tensor factorization for analyzing reactive-mixing

Vesselinov

Mudunuru

Karra

et al. 2019

Journal of Computational Physics

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“…In the mathematics and engineering fields, it is popularly known as the "inverse source problem" (ISP) [6,7]. Many methods have been developed in the literature for ISP, such as regularization methods [8,9], simulation-optimization methods [9], and Bayesian inference methods [8].…”

Section: Introductionmentioning

confidence: 99%

Pollution Source Identification for River Chemical Spills by Modular-Bayesian Approach: A Retrospective Study on the ‘Landmark’ Spill Incident in China

2019

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It is important to identify source information after a river chemical spill incident occurs. Among various source inversion approaches, a Bayesian-based framework is able to directly characterize inverse uncertainty using a probability distribution and has recently become of interest. However, the literature has not reported its application to actual spill incidents, and many aspects in practical use have not yet been clearly illustrated, e.g., feasibility for large scale pollution incidents, algorithm parameters, and likelihood functions. This work deduced a complete modular-Bayesian approach for river chemical spills, which combined variance assumptions on a pollutant concentration time series with Adaptive-Metropolis sampling. A retrospective case study was conducted based on the ‘landmark’ spill incident in China, the Songhua River nitrobenzene spill of 2005. The results show that release mass, place, and moment were identified with biases of −26.9%, −7.9%, and 16.9%, respectively. Inverse uncertainty statistics were also quantified for each source parameter. Performance, uncertainty sources, and future work are discussed. This study provides an important real-life case to demonstrate the usefulness of the modular-Bayesian approach in practice and provides valuable references for the setting of parameters for the sampling algorithm and variance assumptions.

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“…Inverse source problems occur in diverse applications, including the diagnosis of brain abnormalities, the control of prosthetic limbs in medical imaging and finding infinitesimal dipole models for antennas. The main goal of inverse source problems is to determine geometrical and/or physical parameters of a target source such as support, location and profile [2,9,12,13,17,25,28,30,32,36].…”

Section: Introductionmentioning

confidence: 99%

A Direct Sampling Method for Recovering Electromagnetic Dipolar Sources

Bousba¹

2019

EAJAM

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An inverse source problem for time-harmonic Maxwell equation is studied and a direct sampling method to recover the location and the moments of electric current dipoles from near-and far-field data at a fixed frequency is developed. The method is based on a new indicator function and requires the evaluation of simple integrals only. It is easily implementable and efficient. Numerical examples demonstrate the robustness of the method with respect to noisy measurements and its capability in identifying the source location and the moments.

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Inverse source problem in a one-dimensional evolution linear transport equation with spatially varying coefficients: application to surface water pollution

Cited by 25 publications

References 16 publications

Unsupervised machine learning based on non-negative tensor factorization for analyzing reactive-mixing

Unsupervised machine learning based on non-negative tensor factorization for analyzing reactive-mixing

Pollution Source Identification for River Chemical Spills by Modular-Bayesian Approach: A Retrospective Study on the ‘Landmark’ Spill Incident in China

A Direct Sampling Method for Recovering Electromagnetic Dipolar Sources

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