Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network

Praditia, Timothy; Karlbauer, Matthias; Otte, Sebastian; Oladyshkin, Sergey; Butz, Martin V.; Nowak, Wolfgang

doi:10.1002/essoar.10511934.1

Cited by 2 publications

(3 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All codes used for generating the train , in‐dis‐test , and out‐dis‐test data and reproduce all the results in this paper are preserved at https://doi.org/10.5281/zenodo.7260671, available via the MIT license and developed openly at https://github.com/CognitiveModeling/finn (Praditia et al., 2022).…”

Section: Data Availability Statementmentioning

confidence: 99%

“…We simulate the experimental setup described in Section 2.1 numerically and generate synthetic data sets solving the related (assumed‐to‐be‐true for now) PDE. The numerical simulator is a simple finite difference code with explicit Euler, made available along with our code (Praditia et al., 2022). Three different sorption isotherms, namely the linear, Freundlich, and Langmuir isotherm are used to generate three distinct synthetic data sets, which are then used for a comparison study.…”

Section: Learning Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Water Resources Research

Self Cite

View full text Add to dashboard Cite

Improved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.

show abstract

Section: Data Availability Statementmentioning

confidence: 99%

Section: Learning Experimentsmentioning

confidence: 99%

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Water Resources Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…Shi et al [29] proposed a neural network named FD-Net, which employs finite difference methods to learn partial derivatives and learns the governing PDEs from trajectory data. Praditia et al [30] proposed the FINN by combining deep learning with finite volume methods. The method can accurately handle various types of numerical boundary conditions by effectively managing the fluxes between control volumes.…”

Section: Introductionmentioning

confidence: 99%

RBF-Assisted Hybrid Neural Network for Solving Partial Differential Equations

Li,

Gao,

Ying

2024

Mathematics

View full text Add to dashboard Cite

In scientific computing, neural networks have been widely used to solve partial differential equations (PDEs). In this paper, we propose a novel RBF-assisted hybrid neural network for approximating solutions to PDEs. Inspired by the tendency of physics-informed neural networks (PINNs) to become local approximations after training, the proposed method utilizes a radial basis function (RBF) to provide the normalization and localization properties to the input data. The objective of this strategy is to assist the network in solving PDEs more effectively. During the RBF-assisted processing part, the method selects the center points and collocation points separately to effectively manage data size and computational complexity. Subsequently, the RBF processed data are put into the network for predicting the solutions to PDEs. Finally, a series of experiments are conducted to evaluate the novel method. The numerical results confirm that the proposed method can accelerate the convergence speed of the loss function and improve predictive accuracy.

show abstract

Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network

Abstract: Scientists and engineers have been trying to model physical phenomena occurring in nature for centuries, one of which is the transport of a quantity in space and time through natural media. A few examples include: subsurface fluid flow modeling (e.g.

Cited by 2 publications

References 35 publications

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

RBF-Assisted Hybrid Neural Network for Solving Partial Differential Equations

Contact Info

Product

Resources

About