Construction of elliptic stochastic partial differential equations solver in groundwater flow with convolutional neural networks

Abstract Elliptic stochastic partial differential equations (SPDEs) play an indispensable role in mathematics, engineering and other fields, and its solution methods emerge in endlessly with the progress of science and technology. In this paper, we make use of the convolutional neural networks (CNNs), which are widely used in machine learning, to construct a solver for SPDEs. The SPDEs with Neumann boundary conditions are considered, and two CNNs are employed. One is used to deal with the essential equation, and the other satisfies the boundary conditions. With the help of the length factor, the integrated neural network model can predict the solution of the equations accurately. We show an example of groundwater flow to evaluate the model proposed with Gaussian random field (GRF). The experimental results show that the proposed neural network solver can approximate the traditional numerical algorithm, and has high computational efficiency.

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Applying neural network for identification of land surface model parameters

10.5194/egusphere-egu21-16355 ◽

2021 ◽

Author(s):

Ruslan Chernyshev ◽

Mikhail Krinitskiy ◽

Viktor Stepanenko

Keyword(s):

Neural Network ◽

Machine Learning ◽

Neural Networks ◽

Partial Differential Equations ◽

Differential Equations ◽

Thermodynamic Model ◽

Land Surface ◽

Land Surface Model ◽

Surface Model ◽

Partial Differential

This work is devoted to development of neural networks for identification of partial differential equations (PDE) solved in the land surface scheme of INM RAS Earth System model (ESM). Atmospheric and climate models are in the top of the most demanding for supercomputing resources among research applications. Spatial resolution and a multitude of physical parameterizations used in ESMs continuously increase. Most of parameters are still poorly constrained, many of them cannot be measured directly. To optimize model calibration time, using neural networks looks a promising approach. Neural networks are already in wide use in satellite imaginary (Su Jeong Lee, et al, 2015; Krinitskiy M. et al, 2018) and for calibrating parameters of land surface models (Yohei Sawada el al, 2019). Neural networks have demonstrated high efficiency in solving conventional problems of mathematical physics (Lucie P. Aarts el al, 2001; Raissi M. et al, 2020).&#160;We develop a neural networks for optimizing parameters of nonlinear soil heat and moisture transport equation set. For developing we used Python3 based programming tools implemented on GPUs and Ascend platform, provided by Huawei. Because of using hybrid approach combining neural network and classical thermodynamic equations, the major purpose was finding the way to correctly calculate backpropagation gradient of error function, because model trains and is being validated on the same temperature data, while model output is heat equation parameter, which is typically not known. Neural network model has been runtime trained using reference thermodynamic model calculation with prescribed parameters, every next thermodynamic model step has been used for fitting the neural network until it reaches the loss function tolerance.Literature:1. &#160; &#160; Aarts, L.P., van der Veer, P. &#8220;Neural Network Method for Solving Partial Differential Equations&#8221;. Neural Processing Letters 14, 261&#8211;271 (2001). https://doi.org/10.1023/A:10127841298832. &#160; &#160; Raissi, M., P. Perdikaris and G. Karniadakis. &#8220;Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.&#8221; ArXiv abs/1711.10561 (2017): n. pag.3. &#160; &#160; Lee, S.J., Ahn, MH. & Lee, Y. Application of an artificial neural network for a direct estimation of atmospheric instability from a next-generation imager. Adv. Atmos. Sci. 33, 221&#8211;232 (2016). https://doi.org/10.1007/s00376-015-5084-94. &#160; &#160; Krinitskiy M, Verezemskaya P, Grashchenkov K, Tilinina N, Gulev S, Lazzara M. Deep Convolutional Neural Networks Capabilities for Binary Classification of Polar Mesocyclones in Satellite Mosaics. Atmosphere. 2018; 9(11):426.5. &#160; &#160; Sawada, Y.. &#8220;Machine learning accelerates parameter optimization and uncertainty assessment of a land surface model.&#8221; ArXiv abs/1909.04196 (2019): n. pag.6. &#160; &#160; Shufen Pan et al. Evaluation of global terrestrial evapotranspiration using state-of-the-art approaches in remote sensing, machine learning and land surface modeling. Hydrol. Earth Syst. Sci., 24, 1485&#8211;1509 (2020)7. &#160; &#160; Chaney, Nathaniel & Herman, Jonathan & Ek, M. & Wood, Eric. (2016). Deriving Global Parameter Estimates for the Noah Land Surface Model using FLUXNET and Machine Learning: Improving Noah LSM Parameters. Journal of Geophysical Research: Atmospheres. 121. 10.1002/2016JD024821.&#160;&#160;

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