From PINNs to DeepONets: Neural Network-based Approaches for Direct Air Capture Optimization

The awareness of the risks of climate change laid the foundation for the Paris Agreement, a legally binding treaty adopted at the 2015 UN Climate Change Conference (COP21) in Paris. At the European level, the Green Deal establishes clear time targets for GHG emissions and defines carbon capture, storage, and utilization (CCSU) technologies as priority areas. Furthermore, future projections of global emissions show that the utilization of negative emission technologies (NETs) is crucial for achieving Green Deal targets. Among carbon capture and storage technologies, Direct Air Capture plays an active role as an emerging Negative Emission Technology due to its ability to extract CO2 directly from the atmosphere, independently of the source. DAC technologies are peculiar in their low land requirements compared to other CCS approaches, such as BECCS and AR. However, they face other disadvantages, such as higher energy demand and annual cost. This work investigates the feasibility and potential benefits of using neural networks to enhance the optimization of the DAC process through more effective modeling strategies. Under operating conditions, the DAC cycle reaches a dynamic equilibrium, also known as cyclic steady-state (CSS), in which process variables evolve dynamically, while the inlet and outlet conditions of the cycle coincide. When the system is described by partial differential equations (PDEs), determining the CSS requires solving these equations for different initial conditions. Neural networks that can learn to predict PDE solutions for different initial conditions or parameters are well-suited for rapid exploration of the solution space within the desired domain. The research considered two types of feed-forward neural networks: physics-informed neural networks parameterized with respect to the PDE parameters and its initial conditions (P2I2NNs) and deep operator networks (DeepONets). As far as data requirements are concerned, the results showed that physics-based networks can eliminate the need for data collection and preprocessing, providing a mesh-free alternative for solving PDEs. Nonetheless, these networks still suffer from the lack of a solid theoretical foundation and the high complexity of their loss function landscape. Conversely, DeepONet architectures require the collection or generation of large datasets but offer greater stability and faster learning. Using these networks, it was possible to generalize the solution of reference PDEs, such as the convection–diffusion equation and CO₂ adsorption equations, across four classes of initial condition functions: straight linear, sigmoid, gaussian, and exponential. Moreover, the networks demonstrated excellent performance even when tested on functions not observed during the training phase, i.e., sinusoidal functions, and across extended parameter ranges of the training functions. DeepONets owe their generalization capabilities to their intrinsic structure: they are conceived to learn function-to-function mappings, unlike P2I2NNs, which learn pointwise relationships. Future developments of this work include: the solution of coupled equations using MIMO-DeepONet, which allows the simultaneous handling of multiple input and output variables; the comprehensive modeling of all phases of the DAC cycle; and the exploration of the CSS through neural network model-based techniques.