Accurately predicting the unfrozen water content (UWC) in frozen soils is crucial for modeling various soil processes in cold regions. However, existing empirical and theoretical models suffer limitations due to oversimplified assumptions or limited applicable conditions. Meanwhile, data-driven approaches are typically challenged by insufficient high-quality data and poor alignment with the underlying mechanisms in question. In the present study, a monotonic neural network (MNN) model for generalized UWC prediction was developed by leveraging data interpolation and monotonicity constraints. Experimental UWC data of various soils were collected from the literature and a raw dataset was formed. By first best-fitting each UWC curve in the raw dataset and then data interpolation, a new large dataset was generated and used for model development. A constrained MNN architecture for estimating UWC was constructed by constraining the weights of the neural network. The performance of the MNN was then compared with a standard deep neural network (DNN). The results demonstrated that the statistical characteristics of the generated dataset were comparable to that of the raw dataset. Both the MNN and DNN achieved good performance on the generated dataset. However, compared to DNN, the MNN yielded much more accurate prediction when tested on three new soils. In addition, the MNN was able to consistently give monotonic prediction on the UWC-Temperature relationship, even though both the monotonic and non-monotonic data were used for training. Overall, the monotonicity-constrained MNN can provide a robust and physical mechanisms aligned solution for estimating UWC in frozen soils.

准确预测冻土中的未冻水含量（UWC）对于模拟寒冷地区的各种土壤过程至关重要。然而，现有的经验和理论模型由于假设过于简单或适用条件有限而受到限制。与此同时，数据驱动的方法通常会受到高质量数据不足以及与相关底层机制不一致的挑战。在本研究中，通过利用数据插值和单调性约束，开发了用于广义 UWC 预测的单调神经网络 (MNN) 模型。从文献中收集各种土壤的UWC实验数据，形成原始数据集。首先对原始数据集中的每条 UWC 曲线进行最佳拟合，然后进行数据插值，生成一个新的大型数据集并用于模型开发。通过约束神经网络的权重构建了用于估计 UWC 的约束 MNN 架构。然后将 MNN 的性能与标准深度神经网络 (DNN) 进行比较。结果表明，生成的数据集的统计特征与原始数据集的统计特征相当。MNN 和 DNN 在生成的数据集上都取得了良好的性能。然而，与 DNN 相比，MNN 在三种新土壤上进行测试时产生了更准确的预测。此外，即使使用单调和非单调数据进行训练，MNN 也能够一致地对 UWC-温度关系进行单调预测。总体而言，单调性约束的 MNN 可以为估计冻土中的 UWC 提供稳健且物理机制一致的解决方案。