This study presents a systematic machine learning approach for creating efficient hybrid models and discovering sorption uptake models in non-linear advection-diffusion-sorption systems. It demonstrates an effective method to train these complex systems using gradient based optimizers, adjoint sensitivity analysis, and JIT-compiled vector Jacobian products, combined with spatial discretization and adaptive integrators. Sparse and symbolic regression were employed to identify missing functions in the artificial neural network. The robustness of the proposed method was tested on an in-silico data set of noisy breakthrough curve observations of fixed-bed adsorption, resulting in a well-fitted hybrid model. The study successfully reconstructed sorption uptake kinetics using sparse and symbolic regression, and accurately predicted breakthrough curves using identified polynomials, highlighting the potential of the proposed framework for discovering sorption kinetic law structures.

翻译：本研究提出了一种系统化的机器学习方法，用于在非线性对流-扩散-吸附系统中构建高效混合模型并发现吸附摄取模型。该方法通过结合基于梯度的优化器、伴随灵敏度分析、即时编译向量雅可比积，以及空间离散化和自适应积分器，展示了一种有效训练这些复杂系统的途径。采用稀疏回归和符号回归来识别人工神经网络中的缺失函数。在固定床吸附含噪穿透曲线观测的计算机模拟数据集上测试了所提方法的鲁棒性，结果获得了拟合良好的混合模型。研究利用稀疏回归和符号回归成功重建了吸附摄取动力学，并通过识别多项式准确预测了穿透曲线，凸显了该框架在发现吸附动力学定律结构方面的潜力。