Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In particular, DeepONets offer a natural formulation for PDE solving, since the solution of a partial differential equation can be interpreted as an operator mapping an initial condition to its corresponding solution field. In this work, we applied DeepONets in the context of process modeling for adsorption technologies, to assess their feasibility as surrogates for cyclic adsorption process simulation and optimization. The goal is to accelerate convergence of cyclic processes such as Temperature-Vacuum Swing Adsorption (TVSA), which require repeated solution of transient PDEs, which are computationally expensive. Since each step of a cyclic adsorption process starts from the final state of the preceding step, effective surrogate modeling requires generalization across a wide range of initial conditions. The governing equations exhibit steep traveling fronts, providing a demanding benchmark for operator learning. To evaluate functional generalization under these conditions, we construct a mixed training dataset composed of heterogeneous initial conditions and train DeepONets to approximate the corresponding solution operators. The trained models are then tested on initial conditions outside the parameter ranges used during training, as well as on completely unseen functional forms. The results demonstrate accurate predictions both within and beyond the training distribution, highlighting DeepONets as potential efficient surrogates for accelerating cyclic adsorption simulations and optimization workflows.

翻译：深度算子网络作为学习函数空间之间映射关系的各类神经网络中的基础工具正在兴起，并因其逼近非线性算子的能力而受到关注。特别地，DeepONets为偏微分方程求解提供了自然的表述框架，因为偏微分方程的解可被解释为将初始条件映射至相应解场的算子。本工作中，我们将DeepONets应用于吸附技术的流程建模领域，以评估其作为循环吸附过程仿真与优化代理模型的可行性。目标在于加速如温度-真空变压吸附（TVSA）等循环过程的收敛，这类过程需要重复求解瞬态偏微分方程，计算成本高昂。由于循环吸附过程的每一步均从前一步的终态开始，有效的代理建模需要在广泛初始条件下实现泛化。控制方程表现出陡峭的行进锋面，为算子学习提供了严苛的基准。为评估此类条件下的函数泛化能力，我们构建了由异构初始条件组成的混合训练数据集，并训练DeepONets以逼近相应的解算子。随后在训练所用参数范围之外的初始条件以及完全未见过的函数形式上测试训练好的模型。结果表明模型在训练分布内外均能实现精确预测，凸显了DeepONets作为加速循环吸附仿真与优化流程的高效代理模型的潜力。