The development of robust and reliable modeling approaches for crystallization processes is often challenging because of non-idealities in real data arising from various sources of uncertainty. This study investigated the effectiveness of physics-informed recurrent neural networks (PIRNNs) that integrate the mechanistic population balance model with recurrent neural networks under the presence of systematic and model uncertainties. Such uncertainties are represented by using synthetic data containing controlled noise, solubility shift, and limited sampling. The research demonstrates that PIRNNs achieve strong generalization and physical consistency, maintain stable learning behavior, and accurately recover kinetic parameters despite significant stochastic variations in the training data. In the case of systematic errors in the solubility model, the inclusion of physics regularization improved the test performance by more than an order of magnitude compared to purely data-driven models, whereas excessive weighting of physics increased error arising due to the model mismatch. The results also show that PIRNNs are able to recover model parameters and replicate crystallization dynamics even in the limit of very low sampling resolution. These findings validate the robustness of physics-informed machine learning in handling data imperfections and incomplete domain knowledge, providing a potential pathway toward reliable and practical hybrid modeling of crystallization dynamics and industrial process monitoring and control.

翻译：结晶过程建模方法的稳健性与可靠性开发常面临挑战，这源于实际数据中由多种不确定性因素导致的非理想特性。本研究探讨了物理信息循环神经网络在存在系统不确定性与模型不确定性时的有效性，该网络将机理群体平衡模型与循环神经网络相结合。此类不确定性通过使用包含受控噪声、溶解度偏移及有限采样的合成数据进行表征。研究表明，PIRNNs在训练数据存在显著随机波动的情况下，仍能实现强泛化能力与物理一致性，保持稳定的学习行为，并精确恢复动力学参数。在溶解度模型存在系统误差的情况下，引入物理正则化使测试性能较纯数据驱动模型提升超过一个数量级，而过度的物理权重则会因模型失配导致误差增大。结果还表明，即使在极低采样分辨率的条件下，PIRNNs仍能恢复模型参数并复现结晶动力学。这些发现验证了物理信息机器学习在处理数据缺陷与不完整领域知识方面的鲁棒性，为结晶动力学及工业过程监控的可靠实用化混合建模提供了潜在路径。