用新型神经网络模拟长期非饱和土固结，精度高且计算快。
Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis
- 分段对数时间+滞后兼容损失，解决多尺度时间耦合难题。
- 预测误差低于1e-2，支持长达10^10秒的模拟。
- 适合地质工程中长期固结分析，尤其含气土场景。
本研究提出一种滞后后向兼容物理信息神经网络（LBC-PINN），用于模拟和反演长期荷载下的一维非饱和土固结过程。针对空气与水压在多尺度时间域内耦合消散的挑战，该框架融合对数时间分段、滞后兼容性损失约束及分段迁移学习策略。前向分析中，采用推荐分段方案的LBC-PINN能准确预测孔隙气压与孔隙水压演化过程，其预测结果与有限元法（FEM）对比显示，时间跨度达10^10秒时均方绝对误差低于1e-2。基于特征气相消散时间的简化分段策略显著提升计算效率，同时保持预测精度。敏感性分析表明，该框架在气-水渗透率比从1e-3至1e3范围内均表现稳健。
原文摘要 · Abstract (English)
This study develops a Lagged Backward-Compatible Physics-Informed Neural Network (LBC-PINN) for simulating and inverting one-dimensional unsaturated soil consolidation under long-term loading. To address the challenges of coupled air and water pressure dissipation across multi-scale time domains, the framework integrates logarithmic time segmentation, lagged compatibility loss enforcement, and segment-wise transfer learning. In forward analysis, the LBC-PINN with recommended segmentation schemes accurately predicts pore air and pore water pressure evolution. Model predictions are validated against finite element method (FEM) results, with mean absolute errors below 1e-2 for time durations up to 1e10 seconds. A simplified segmentation strategy based on the characteristic air-phase dissipation time improves computational efficiency while preserving predictive accuracy. Sensitivity analyses confirm the robustness of the framework across air-to-water permeability ratios ranging from 1e-3 to 1e3.
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