A physics-informed multimodal transformer model for machining energy consumption prediction

Abstract Machining energy consumption (MEC) prediction is crucial for energy management in manufacturing. Existing methods are commonly classified into physics-based models (PBMs) and data-driven approaches (DDAs), relying on physical knowledge and data learning, respectively. While DDAs alleviate limitations associated with PBMs due to assumptions needed to simplify the complexity, most of them ignore the underlying physical knowledge and may struggle with generalization under varying machining conditions. Moreover, machining data is inherently heterogeneous in modalities, making data fusion another challenge. To address these issues, this paper proposes a physics-informed multimodal transformer (PIMT) model for MEC prediction. Firstly, based on the studies of machining energy nature, a synthetic data augmentation strategy is proposed to incorporate energy-relevant physical principles from PBMs. Secondly, a structured multimodal network is designed to fuse features from diverse data modalities. Then, a transformer with multi-head attention is employed to capture complex temporal dependencies and cross-modal interactions within the fused data. Finally, three groups of comparative experiments are designed to validate and demonstrate the proposed approaches. The results showed that the proposed PIMT model achieves the lowest RMSE (0.048) and MAPE (12.33%), while reducing the training time (152s, 1.7s, and 29.9s) and the number of trainable parameters (49.7%, 51.3% and 67.6%) compared to state-of-the-art methods. Furthermore, the PIMT model consistently produces smaller errors across nearly all evaluation metrics and accurately predicts MEC under continuously varying machining conditions, highlighting its robustness and practical potential.