Operator-Consistent Physics-Informed Learning for Wafer Thermal Reconstruction in Lithography

Thermal field reconstruction in post-exposure bake (PEB) is critical for advanced lithography, yet current physics-informed neural networks (PINNs) suffer from inconsistent accuracy due to a misalignment between geometric coordinates, physical fields, and differential operators. To resolve this, we introduce a novel architecture that unifies these elements on a single computation graph by integrating LSTM-gated mechanisms within a Liquid Neural Network (LNN) backbone. This specific combination of gated liquid layers is necessary to dynamically regulate the network's spectral behavior and enforce operator-level consistency, which ensures stable training and high-fidelity predictions. Applied to a 2D PEB scenario with internal heat generation and convective boundaries, our model formulates residuals via differential forms and a composite loss functional. The results demonstrate rapid convergence, uniformly low errors, strong agreement with FEM benchmarks, and stable training without late-stage oscillations, outperforming existing baselines in accuracy and robustness. Our framework thus establishes a reliable foundation for high-fidelity thermal modeling and offers a transferable strategy for operator-consistent neural surrogates in other physical domains.