这篇论文提出了一个结合物理模型和神经网络的混合框架，能从实验数据自动发现本构定律，比传统黑盒模型更具物理一致性。
研究人员提出了一种可微分混合建模框架，专门用于传输过程。该框架集成了JAX有限体积种群平衡求解器与可学习的神经网络组件，能够从真实实验数据中发现本构定律并拟合初始条件。该框架已在种群平衡方程案例中验证，可用于优化实验设置，针对感兴趣的数量进行直接优化。
Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data
Reliable transport models are essential when modelling and optimising many chemical engineering processes, yet, most models assume hand-picked constitutive laws which may not reflect reality, and often assume initial conditions are known exactly. Both restrictions can significantly bias model predictions and lead to systematic error when used in predictive and control settings. Black-box neural surrogate alternatives for modelling can better match real example data, but are confined to the task they were trained on and cannot be interrogated for physical consistency. Here we introduce a general-purpose differentiable hybrid modelling framework for transport processes, specifically for the case of population balance equations. Our framework integrates a JAX finite volume population balance solver with learnable neural network components which are trained to both discover constitutive laws and fit initial conditions from real experimental data, allowing us to better model real experimental transport systems. Furthermore, we use our framework for process optimisation, using its differentiability to allow us to direct optimising experimental settings for quantities of interest. This work highlights the huge potential of such differentiable hybrid modelling frameworks for learning and optimising any given chemical separation which involves mass, energy, and/or momentum transport.