Flow and Contaminant Transport Model for Unsaturated Soil

Al-Najjar, M M; Evans, Brian Mark

doi:10.1007/3-540-69876-0_15

Cited by 3 publications

(2 citation statements)

References 1 publication

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“…To demonstrate our framework, we study one of the example problem that was tackled in Meng and Karniadakis [53] with composite neural networks. This particular inverse-PDE problem arises in unsaturated flows as they are central in characterizing contaminant transport [75], soil-atmosphere interaction [76],…”

Section: Nonlinear Inverse-pde Problemmentioning

confidence: 99%

Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion

Basir,

Senocak

2021

Preprint

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Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective function as an unconstrained optimization problem, which is then used to train a deep feed-forward neural network.Here, we show that this specific way of formulating the objective function is the source of severe limitations in the PINN approach when applied to different kinds of PDEs. To address these limitations, we propose a versatile framework that can tackle both inverse and forward problems. The framework is adept at multi-fidelity data fusion and can seamlessly constrain the governing physics equations with proper initial and boundary conditions. The backbone of the proposed framework is a nonlinear, equality-constrained optimization problem formulation aimed at minimizing a loss functional, where an augmented Lagrangian method (ALM) is used to formally convert a constrained-optimization problem into an unconstrainedoptimization problem. We implement the ALM within a stochastic, gradient-descent type training algorithm in a way that scrupulously focuses on meeting the constraints without sacrificing other loss terms. Additionally, as a modification of the original residual layers, we propose lean residual layers in our neural network architecture to address the so-called vanishing-gradient problem. We demonstrate the efficacy and versatility of our physics-and equality-constrained deep-learning framework by applying it to learn the solutions of various multi-dimensional PDEs, including a nonlinear inverse problem from the hydrology field with multi-fidelity data fusion. The results produced with our proposed model match exact solutions very closely for all the cases considered.

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Section: Nonlinear Inverse-pde Problemmentioning

confidence: 99%

Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion

Basir,

Senocak

2021

Preprint

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“…This zone adjusts the water flow from the land surface to the groundwater and vice versa, and it plays a crucial role in the transport of solutes and their retention. The most severe contamination threats to groundwater quality emanate from coincidental surface releases of various types of wastes and products associated with industrial, agricultural, or urban development, such as leachate from municipal landfills [3]. These contaminants are transferred through the vadose zone, which is partially saturated with air and water.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Contaminant Transport through the Vadose Zone: A Continuum Mechanical Approach within the Framework of the Extended Theory of Porous Media (eTPM)

Seyedpour

Thom

Ricken

2023

Water

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The simulation of contaminant transport through the vadose zone enjoys high significance for decision makers and contaminated site planners since the vadose zone can serve as a filter, but many contaminants can be transported from this region to aquifers. The intention of this paper is to utilize the extended Theory of Porous Media (eTPM) to develop a ternary model for the simulation of contaminant transport in the vadose zone whose application is subsequently shown via a numerical example. The simulation was conducted for 140 days, during which the contamination source was removed after 25 days. The results indicate that the contaminant reached the water table after 76 days. The concentration of the contaminant reaching the groundwater was 17% less than that of the contaminant source.

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Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion

Basir

Şenocak

2022

Journal of Computational Physics

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Flow and Contaminant Transport Model for Unsaturated Soil

Cited by 3 publications

References 1 publication

Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion

Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion

Simulation of Contaminant Transport through the Vadose Zone: A Continuum Mechanical Approach within the Framework of the Extended Theory of Porous Media (eTPM)

Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion

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