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This work presents a hybrid modelling framework for simulating Cesium-137 ( \(^{137}\) Cs) transport in variably saturated soils using Physics-Informed Neural Networks (PINNs). The model integrates moisture dynamics from the Richards equation with an advection–diffusion–reaction equation for contaminant transport. Three soil types are considered—sandy loam, black soil and organic—with moisture profiles \(\theta (z,t)\) calculated numerically and used as input to the PINN. We evaluate three strategies for soil-type encoding: scalar, one-hot, and trainable embeddings. Each configuration was assessed using SSIM and RMSE metrics, including generalization tests on unseen soils. Embedding-based encoding provides improved generalization to unseen soils, demonstrating the effectiveness of PINNs in physically consistent and soil-aware modelling of radionuclide transport.

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Soil-Aware Physics-Informed Neural Networks for Modeling ( \(^{137}\) Cs) Migration

  • 会议论文

  • 发表日期：

    2026年

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  • Ilona Kopintsu,
  • Sergei Strijhak

摘要

This work presents a hybrid modelling framework for simulating Cesium-137 ( \(^{137}\) Cs) transport in variably saturated soils using Physics-Informed Neural Networks (PINNs). The model integrates moisture dynamics from the Richards equation with an advection–diffusion–reaction equation for contaminant transport. Three soil types are considered—sandy loam, black soil and organic—with moisture profiles \(\theta (z,t)\) calculated numerically and used as input to the PINN. We evaluate three strategies for soil-type encoding: scalar, one-hot, and trainable embeddings. Each configuration was assessed using SSIM and RMSE metrics, including generalization tests on unseen soils. Embedding-based encoding provides improved generalization to unseen soils, demonstrating the effectiveness of PINNs in physically consistent and soil-aware modelling of radionuclide transport.