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的机器学习方法，用于在非线性平流-扩散-吸附系统中构建高效混合模型并发现吸附摄取模型。该方法展示了一种有效训练这些复杂系统的途径，通过结合基于梯度的优化器、伴随灵敏度分析、即时编译的向量-雅可比积，以及空间离散化和自适应积分器。采用稀疏回归和符号回归来识别人工神经网络中缺失的函数。基于固定床吸附过程中含噪声穿透曲线观测值的合成数据集，对所提方法的鲁棒性进行了测试，结果获得了拟合良好的混合模型。本研究成功利用稀疏回归和符号回归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，凸显了所提框架在发现吸附动力学定律结构方面的潜力。