Accurate modeling of mass front evolution in fixed beds is determined by considering equilibrium data for adsorbed component concentrations. While incorporating thermodynamic-based adsorption isotherms is crucial, their computational demands are high. Thus, pattern recognition methods offer an efficient solution for applying detailed isotherm models. Here, we employ a surrogate model output in the mass balance equations while solving partial differential equations describing column mass fronts, resulting in a hybrid model via a sequential identification approach. We examine lysozyme’s mass front behavior in a silica-packed-bed column across pH 6 to pH 10 in a case study using various ions (Cl\(^{-}\), Br\(^{-}\), and I\(^{-}\)). We establish a Deep Neural Network (DNN) to train a surrogate model using a dataset from a modified non-linear Poisson–Boltzmann equation, incorporating the ionic dispersion potential from Lifshitz Theory. The surrogate model training was archived with 12 hidden layers and used 24,000 pseudo-experimental points (70/30) to exhibit a 0.61% absolute percentage error and R\(^2\) of 0.9999 for test points. The hyper-parameter optimization was essential for the best parity plot results. Results indicate protein elution near isoelectric points due to reduced surface charge density. Additionally, we model mass fronts in a fixed bed at pH 9.0 for different salts. Retention time decreases, and mass front compressibility increases in the order I\(^{-}\) > Br\(^{-}\) > Cl\(^{-}\) due to varying anion polarizability. Results show that elution profiles follow symmetrical behavior, even at higher protein concentration, due to electrolyte concentration gradient. These results demonstrate successful cross-scale linking using DNN.

通过考虑吸附组分浓度的平衡数据来确定固定床中质量前沿演化的准确模型。虽然结合基于热力学的吸附等温线至关重要，但它们的计算要求很高。因此，模式识别方法为应用详细的等温线模型提供了有效的解决方案。在这里，我们在质量平衡方程中采用替代模型输出，同时求解描述柱质量前沿的偏微分方程，通过顺序识别方法产生混合模型。我们在案例研究中使用各种离子 (Cl \(^{-}\)、 Br \(^{-}\)和 I在 pH 6 至 pH 10 范围内检查溶菌酶在二氧化硅填充床柱中的质量前沿行为\(^{-}\) )。我们建立了一个深度神经网络 (DNN)，使用来自修改后的非线性泊松-玻尔兹曼方程的数据集来训练代理模型，并结合了 Lifshitz 理论中的离子色散势。代理模型训练存档有 12 个隐藏层，并使用 24,000 个伪实验点 (70/30)，表现出 0.61% 的绝对百分比误差，测试点的 R \(^2\)为 0.9999。超参数优化对于获得最佳奇偶图结果至关重要。结果表明，由于表面电荷密度降低，蛋白质在等电点附近洗脱。此外，我们还在 pH 9.0 的固定床上针对不同的盐模拟了质量前沿。由于阴离子极化率的变化，保留时间减少，质量前沿压缩性按 I \(^{-}\) > Br \(^{-}\) > Cl \(^{-}\) 的顺序增加。结果表明，由于电解质浓度梯度，即使在较高的蛋白质浓度下，洗脱曲线也遵循对称行为。这些结果证明使用 DNN 可以成功实现跨尺度链接。