<p>This study proposes a hydraulic tomography neural network (HT-NN) based on a convolutional encoder-decoder neural network (DenseNet) combined with a head data sampling strategy to estimate hydrogeological parameter fields. Numerical experiments demonstrate that HT-NN effectively captures the spatial characteristics of both hydraulic conductivity (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="477_2025_3051_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\({\text{K}}\)</EquationSource> </InlineEquation>) and specific storage (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="477_2025_3051_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({S_s}\)</EquationSource> </InlineEquation>) fields and achieves high accuracy in delineating subsurface heterogeneity. By selecting late- and early-time head data to construct the input matrix, HT-NN substantially improves parameter estimation while significantly reducing computational time. Compared to the successive linear estimator (SLE), HT-NN achieves more accurate parameter estimation and reduces computation time from 28.5&#xa0;h to 0.76&#xa0;s. The simulated heads derived from HT-NN’s estimated parameter fields closely match the reference heads across all experiments. Additionally, adopting a smaller input matrix with a simplified encoder-decoder structure greatly enhances computational efficiency while maintaining estimation accuracy. These findings demonstrate the potential of HT-NN as an efficient and reliable alternative for estimating hydrogeological parameters in heterogeneous aquifer systems.</p>

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Hydraulic heterogeneity estimation with transient hydraulic tomography and convolutional encoder-decoder neural network

  • Yu-Kai Chen,
  • Jui-Pin Tsai,
  • Bo-Tsen Wang,
  • Chia-Hao Chang

摘要

This study proposes a hydraulic tomography neural network (HT-NN) based on a convolutional encoder-decoder neural network (DenseNet) combined with a head data sampling strategy to estimate hydrogeological parameter fields. Numerical experiments demonstrate that HT-NN effectively captures the spatial characteristics of both hydraulic conductivity ( \({\text{K}}\) ) and specific storage ( \({S_s}\) ) fields and achieves high accuracy in delineating subsurface heterogeneity. By selecting late- and early-time head data to construct the input matrix, HT-NN substantially improves parameter estimation while significantly reducing computational time. Compared to the successive linear estimator (SLE), HT-NN achieves more accurate parameter estimation and reduces computation time from 28.5 h to 0.76 s. The simulated heads derived from HT-NN’s estimated parameter fields closely match the reference heads across all experiments. Additionally, adopting a smaller input matrix with a simplified encoder-decoder structure greatly enhances computational efficiency while maintaining estimation accuracy. These findings demonstrate the potential of HT-NN as an efficient and reliable alternative for estimating hydrogeological parameters in heterogeneous aquifer systems.