Zone-based Physics-Informed Neural Network (Z-PINN) for Addressing Data Scarcity in Ceramic Sintering Processes

Recent advances in artificial intelligence have enabled predictive modeling and control in manufacturing processes. However, industrial datasets often suffer from missing entries and limited availability due to sensor limitations, failures, and high installation costs. Physics-Informed Neural Networks (PINNs) incorporate physical laws into the learning process, offering physically consistent predictions, but their performance deteriorates in complex processes when relying on a single global partial differential equation (PDE) or ordinary differential equation (ODE). To address this limitation, we propose a Zone-based PINN (Z-PINN) framework that divides the process timeline into multiple zones based on a predefined ceramic sintering schedule and trains a separate PINN for each zone. Without modifying the original PINN structure, this approach allows localized learning and improves prediction accuracy while ensuring physical consistency. We evaluate Z-PINN on real ceramic sintering data under three scenarios: short-term missing values, long-term missing values, and full sequence generation from minimal initial inputs. Experimental results show that Z-PINN significantly outperforms the conventional PINN in all cases, achieving lower Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), and producing physically consistent outputs even in data-scarce settings.