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 gradientbased 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机器学习方法，用于构建高效混合模型并发现非线性对流-扩散-吸附系统中的吸附摄取模型。该方法通过结合梯度优化器、伴随敏感性分析及即时编译向量雅可比积，并融合空间离散化与自适应积分器，展示了训练这些复杂系统的有效技术。采用稀疏回归与符号回归来识别人工神经网络中的缺失函数。基于固定床吸附过程的含噪声穿透曲线观测数据的硅内数据集，验证了所提方法的鲁棒性，成功获得了拟合良好的混合模型。通过稀疏回归与符号回归，研究重构了吸附摄取动力学，并利用识别出的多项式准确预测了穿透曲线，凸显了所提出框架在发现吸附动力学定律结构方面的潜力。