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<p>Random field theory is commonly employed to characterize spatially varying quantities by decomposing them into deterministic and random components. The unknown deterministic part is approximated using algebraic polynomials, but this becomes challenging with sparse and noisy data. This study introduces a framework based on deep neural networks (DNN) for robustly characterizing spatially varying quantities. The DNN, coupled with an efficient regularization technique, determines the deterministic part, while the Karhunen–Lo<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="521_2024_10955_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\grave{e}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>e</mi> <mo>`</mo> </mover> </math></EquationSource> </InlineEquation>ve expansion generates random field samples. The efficacy of this technique is demonstrated using two numerical examples: spatially varying log-normal data and undrained shear strength of the soil. The findings reveal that the DNN-based framework provides robust characterization of the spatially varying quantities with good correlation, even with sparse or noisy data, outperforming conventional regression-based detrending methods. Thus, this paper highlights the application of this framework across a diverse range of engineering domains.</p>

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Artificial neural network to characterize spatially varying quantity through random field approach

  • 期刊论文

  • 发表日期：

    2025年1月4日

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  • Pratyush Kumar

摘要

Random field theory is commonly employed to characterize spatially varying quantities by decomposing them into deterministic and random components. The unknown deterministic part is approximated using algebraic polynomials, but this becomes challenging with sparse and noisy data. This study introduces a framework based on deep neural networks (DNN) for robustly characterizing spatially varying quantities. The DNN, coupled with an efficient regularization technique, determines the deterministic part, while the Karhunen–Lo \(\grave{e}\) e ` ve expansion generates random field samples. The efficacy of this technique is demonstrated using two numerical examples: spatially varying log-normal data and undrained shear strength of the soil. The findings reveal that the DNN-based framework provides robust characterization of the spatially varying quantities with good correlation, even with sparse or noisy data, outperforming conventional regression-based detrending methods. Thus, this paper highlights the application of this framework across a diverse range of engineering domains.