Physics-informed neural networks (PINNs) have emerged as a promising alternative to purely data-driven neural networks (NNs) for surrogate modeling, particularly in data-scarce scenarios. This study evaluates the performance of hybrid-PINNs against traditional NNs for modeling the adsorption step of a Direct Air Capture (DAC) process. As the complexity of the modeled system increases, larger datasets and longer computational times are required for numerical methods. Therefore, the study aims to develop approaches that minimize data requirements while maintaining accuracy, which is crucial for efficient modeling of complex physical systems. While both AI models can achieve high accuracy with abundant data, the advantages of hybrid-PINNs become more evident as data becomes scarce. In the intermediate and low-data regimes, the physics constraints embedded in hybrid-PINNs significantly improve generalization and predictive accuracy. For extreme low-data conditions, a curriculum learning strategy is implemented, progressively enforcing physics constraints to mitigate underfitting and enhance model stability. Despite these benefits, hybrid-PINNs exhibit a computational cost approximately one order of magnitude higher than traditional NNs as enforcing physics constraints increases training complexity. The results suggest that PINNs hold potential for modeling complex multi-physics problems in DAC and beyond, provided challenges related to gradient balancing and computational efficiency are addressed.

The synergies from integrating direct air capture and CO₂ methanation are assessed and quantified. Three direct air capture and methanation processes with different integration strategies are proposed: only heat integration, direct air capture sorbent regeneration with high‐pressure H₂, and complete integration in a single unit. The heat integration study via pinch analysis evaluated the potential energy demand reduction. Overall autothermal operation is achievable, as the heat generated in methanation often exceeds that required for direct air capture sorbent regeneration. A novel process combining CO₂ adsorption and methanation in one reactor provided the best productivity and energy demand results. However, this design requires complex cycles and strict demands on the sorbent and catalyst, requiring further development and experimental demonstration.

Direct air capture (DAC) is a leading carbon dioxide removal (CDR) technology that extracts CO ₂ directly from ambient air, independent of emission sources.

Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to purely data-driven neural networks (NNs) for surrogate modeling, particularly in data-scarce scenarios. This study evaluates the performance of hybrid-PINNs against traditional NNs for modeling the adsorption step of a Direct Air Capture (DAC) process. As the complexity of the modeled system increases, larger datasets and longer computational times are required for numerical methods. Therefore, the study aims to develop approaches that minimize data requirements while maintaining accuracy, which is crucial for efficient modeling of complex physical systems. While both AI models can achieve high accuracy with abundant data, the advantages of hybrid-PINNs become more evident as data becomes scarce. In the intermediate and low-data regimes, the physics constraints embedded in hybrid-PINNs significantly improves generalization and predictive accuracy. For extreme low-data conditions, a curriculum learning strategy is implemented, progressively enforcing physics constraints to mitigate underfitting and enhance model stability. Despite these benefits, hybrid-PINNs exhibit a computational cost approximately one order of magnitude higher than traditional NNs, as enforcing physics constraints increases training complexity. The results suggest that PINNs hold potential for modeling complex multi-physics problems in DAC and beyond, provided challenges related to gradient balancing and computational efficiency are addressed.

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.

Accurate thermodynamic characterization of CO2 adsorption on solid amine-functionalized sorbents is essential for modeling and optimizing Direct Air Capture (DAC) processes. This study presents a systematic compilation and comprehensive analysis of available adsorption isotherm data for Lewatit® VPOC 1065, one of the most studied benchmark sorbents for DAC applications. Six independent literature datasets were critically evaluated, revealing significant discrepancies in reported adsorption capacities and inconsistencies across the temperature and partial pressure ranges, particularly within the low-pressure regime relevant for DAC. Global fitting of a temperature-dependent Toth model was performed to investigate the capability of this widely used single-mechanism approach to capture experimental trends across the entire dataset. The Toth model demonstrated substantial limitations, particularly at low partial pressures, highlighting inadequacies in representing the complex adsorption behavior of the sorbent. Moreover, comparative analyses indicated that these limitations stem partially from inter-author variability, experimental uncertainties at ultra-low pressures, and potential unknown adsorption mechanisms, e.g. a physisorption - chemisorption dual site mode. Based on these insights, future research directions were identified.