Making Physics‐Informed Neural Networks Theory‐Compliant: The Case of Fischer‐Tropsch Catalyst Modeling

Physics‐Informed Neural Networks (PINNs) accelerate equation solving by merging physics‐based theories with machine learning. Yet, their application in multi‐staged computational workflows unveils reliability issues. This is demonstrated for Fischer‐Tropsch synthesis modeling, by leveraging PINNs for source terms evaluation in the finite‐difference method solving the coupled reaction‐diffusion equations. Subtle inaccuracies of PINNs approximating the functions in close vicinity of their input variables' ranges boundaries, while not captured by traditional neural network assessment methods, are shown to induce unphysical ultimate solutions and convergence failures. A problem‐specific PINN architecture is proposed that has a correct asymptotic behavior and resolves the revealed issues. Combined with a tailored initial guess generation scheme, the proposed modifications are shown to recover the overall stability of the simulations while preserving the speed‐up brought by PINNs as the workflow component. The possible applications of the proposed hybrid solver are discussed in the context of chemical reactor simulations.