A Novel Data-driven Numerical Method for Hydrological Modeling of Water Infiltration in Porous Media

• URL: http://arxiv.org/abs/2310.02806v2
• Date: Sat, 17 Aug 2024 16:07:59 GMT
• Title: A Novel Data-driven Numerical Method for Hydrological Modeling of Water Infiltration in Porous Media
• Authors: Zeyuan Song, Zheyu Jiang,
• Abstract summary: Rootzone soil moisture monitoring is essential for sensor-based smart irrigation and agricultural drought prevention. We present a novel data-driven algorithm named the DRW (Data-driven global Random Walk) algorithm.
• Score: 0.4028503203417233
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Root-zone soil moisture monitoring is essential for sensor-based smart irrigation and agricultural drought prevention. Modeling the spatiotemporal water flow dynamics in porous media such as soil is typically achieved by solving an agro-hydrological model, the most important of which being the Richards equation. In this paper, we present a novel data-driven solution algorithm named the DRW (Data-driven global Random Walk) algorithm, which holistically integrates adaptive linearization scheme, neural networks, and global random walk in a finite volume discretization framework. We discuss the need and benefits of introducing these components to achieve synergistic improvements in solution accuracy and numerical stability. We show that the DRW algorithm can accurately solve $n$-dimensional Richards equation with guaranteed convergence under reasonable assumptions. Through examples, we also demonstrate that the DRW algorithm can better preserve the underlying physics and mass conservation of the Richards equation compared to state-of-the-art solution algorithms and commercial solver.

Related papers

• Towards Better Statistical Understanding of Watermarking LLMs [7.68488211412916]
  In this paper, we study the problem of watermarking large language models (LLMs) We consider the trade-off between model distortion and detection ability and it as a constrained optimization problem based on the green-red list of Kirchenbauer et al. We develop an online dual gradient ascent watermarking algorithm in light of this optimization formulation and prove its optimality between model distortion and detection ability.
  arXiv  Detail & Related papers  (2024-03-19T01:57:09Z)
• Flow-based Distributionally Robust Optimization [23.232731771848883]
  We present a framework, called $textttFlowDRO$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets. We aim to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from it. We demonstrate its usage in adversarial learning, distributionally robust hypothesis testing, and a new mechanism for data-driven distribution perturbation differential privacy.
  arXiv  Detail & Related papers  (2023-10-30T03:53:31Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Attention U-Net as a surrogate model for groundwater prediction [13.029731605492252]
  This study proposes a physics-based convolutional encoder-decoder neural network as a surrogate model to calculate the response of the groundwater system. Holding strong promise in cross-domain mappings, encoder-decoder networks are applicable for learning complex input-output mappings of physical systems.
  arXiv  Detail & Related papers  (2022-04-09T17:46:24Z)
• Super-resolution GANs of randomly-seeded fields [68.8204255655161]
  We propose a novel super-resolution generative adversarial network (GAN) framework to estimate field quantities from random sparse sensors. The algorithm exploits random sampling to provide incomplete views of the high-resolution underlying distributions. The proposed technique is tested on synthetic databases of fluid flow simulations, ocean surface temperature distributions measurements, and particle image velocimetry data.
  arXiv  Detail & Related papers  (2022-02-23T18:57:53Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer [0.0]
  We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model.
  arXiv  Detail & Related papers  (2021-07-23T06:41:33Z)
• Resource Allocation via Model-Free Deep Learning in Free Space Optical Communications [119.81868223344173]
  The paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. Under this framework, we propose two algorithms that solve FSO resource allocation problems.
  arXiv  Detail & Related papers  (2020-07-27T17:38:51Z)
• Robust Reinforcement Learning with Wasserstein Constraint [49.86490922809473]
  We show the existence of optimal robust policies, provide a sensitivity analysis for the perturbations, and then design a novel robust learning algorithm. The effectiveness of the proposed algorithm is verified in the Cart-Pole environment.
  arXiv  Detail & Related papers  (2020-06-01T13:48:59Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.