Accelerating Thermochemical Equilibrium Calculations with Physics-Informed Neural Networks

Estimating thermochemical equilibrium in multi-component systems is essential for materials science and process engineering, yet computational costs scale poorly with system complexity. This work presents a physics-informed neural network (PINN) approach for scalability from binary to quaternary oxide systems in the CaO-MgO-Al$_2$O$_3$-SiO$_2$ space. Systematic evaluation reveals that selective physics-guided feature engineering improves test $R^2$ by 8.3\%, while embedding the Gibbs-Helmholtz equation as an architectural constraint reduces thermodynamic consistency error by over six orders of magnitude. The proposed two-stage hybrid architecture, comprising a Transformer encoder for phase estimation, and a multi-layer perceptron for property estimation, achieves $R^2 = 0.96$ on binary, $R^2 = 0.94$ on ternary, and $R^2 = 0.90$ on quaternary systems, with inference speeds of ~72 $\mu$s/sample (14--140$\times$ faster than direct calculation). These results demonstrate that PINNs offer a scalable path toward rapid equilibrium estimation where traditional methods become computationally prohibitive.