用物理定律约束神经网络，精准预测质子交换膜电解水的氢气渗透。
Hard-constraint physics-residual networks for hydrogen crossover prediction and high-pressure extrapolation in PEM water electrolysis
- 将亨利定律、菲克定律和法拉第定律作为模型主干，仅学习残差修正。
- 在200巴高压下预测准确率高达94%，是传统方法的两倍以上。
- 适合需要实时监控与高压安全控制的绿氢生产场景。
氢气渗透是高压质子交换膜水电解（PEMWE）中的关键安全与效率限制因素，但因数据有限、传输物理高度耦合，且工业运行需可靠外推，准确预测仍具挑战。本研究提出硬约束物理残差网络（PR-Net），用于预测氢气渗透，并与纯数据驱动神经网络（NN）及软约束物理信息神经网络（PINN）对比。PR-Net以亨利定律、菲克定律和法拉第定律为确定性主干，仅学习未建模非线性效应的残差修正。基准数据集包含来自八篇同行评审文献的184组观测值，覆盖6种膜材料，压力1–200巴，温度25–85°C，电流密度0.05–5.0 A cm⁻²。PR-Net达到R² = 99.57 ± 0.16%，预测变异性比NN和PINN低9倍。在压力轴外推中，200巴时达R² = 94.02 ± 0.92%，超出训练压力范围2.5倍；而PINN为68.06 ± 5.52%，NN为58.00 ± 8.60%（p < 0.001）。残差分析表明，学习到的修正捕捉了高压气相非理想性，并在约0.23 A cm⁻²处恢复了从菲克扩散主导到法拉第生成主导的传输模式转变。在低功耗嵌入式硬件上计算时间仅为1.08 ± 0.34毫秒，可实现实时监测与自适应过程控制，支持更安全的高压绿氢运行。
原文摘要 · Abstract (English)
Hydrogen crossover is a critical safety and efficiency constraint in high-pressure polymer electrolyte membrane water electrolysis (PEMWE), but accurate prediction remains difficult because data are limited, transport physics are strongly coupled, and industrial operation requires reliable extrapolation beyond observed conditions. This study develops a hard-constraint physics-residual network (PR-Net) for hydrogen crossover prediction in PEMWE and compares it with a purely data-driven neural network (NN) and a soft-constraint physics-informed neural network (PINN). PR-Net embeds Henry's, Fick's, and Faraday's laws as a deterministic backbone and learns only a residual correction for unmodelled nonlinear effects. The benchmark includes 184 observations from eight peer-reviewed sources across six membrane types, covering 1-200 bar, $25-85°C$, and $0.05-5.0 A cm^{-2}$. PR-Net achieves $R^2 = 99.57 \pm 0.16%$, with 9-fold lower prediction variability than NN and PINN. In pressure-axis extrapolation, PR-Net attains $R^2 = 94.02 \pm 0.92%$ at 200 bar, 2.5 times beyond the training pressure range, compared with $68.06 \pm 5.52%$ for PINN and $58.00 \pm 8.60%$ for NN (p < 0.001). Residual analysis indicates that the learned correction captures part of the high-pressure gas-phase non-ideality and recovers a transport-regime transition near $0.23 A cm^{-2}$ between Fickian diffusion-dominated and Faradaic production-dominated transport. With a computation time of $1.08 \pm 0.34 ms$ on low-power embedded hardware, PR-Net provides a practical framework for real-time crossover monitoring, adaptive process control, and safer high-pressure green-hydrogen operation.
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