Physics-informed neural networks for extrapolating press washer unit operations with heuristic physical knowledge and scarce data

• Developing physics-informed neural networks with scarce data. • Applying physics-informed neural networks for non-routine operations. • Incorporating heuristic physical knowledge into neural networks. • Improving predictive accuracy and model generalizability with meta-learning. • Removing complex correlations to predict twin roll press washer blockage. Extrapolation of process models beyond routine operations is challenging because of the complexity of chemical engineering unit operations, especially for which first-principles models may be unavailable or difficult to formulate. This study investigates to what extent a physics-informed neural network model of a twin roll press washer, incorporating only the generalized heuristic proportionality-based physical relationships that are available, can improve predictive accuracy under non-routine conditions compared to “conventional” data-driven neural network models. The methodology is applied to a case study on predicting roll speed in a twin roll press washer used in pulp and paper production, a key fault-indicating variable for which no established mechanistic or empirical correlations currently exist. To enhance model adaptability, meta-learning is used to treat physical parameters as trainable, allowing the model to adjust them during training and better align physics constraints with observed data. This approach eliminates the need for manual calibration of coefficients in parameterized differential equations, a step that is often impractical in industrial settings due to data scarcity and evolving process conditions. The proposed method achieved a mean squared error of 0.092 RPM 2 , a reduction of nearly 90% compared to purely data-driven models and 30% compared to a fixed-parameter physics-informed neural network model, without significantly increasing training time. The results reinforce the value of the physics-informed neural network modeling approach to process engineering applications and confirm the validity of the proposed novel meta-learning, simple relational physics-based approach.