<p>Accurate prediction of cutting power consumption is crucial for achieving smart manufacturing. Existing methods for predicting cutting power primarily rely on physical models or data-driven models. However, the former struggles to adapt to complex dynamic machining environments, while the latter heavily depends on data quality and lacks interpretability, becoming a bottleneck for achieving smart manufacturing. To address this issue, this paper proposes a multi-modal cutting power online assessment model based on physics-guided error correction. This model incorporates an embedded physics-sensing mechanism, combining tool wear and surface springback characteristics to construct a prior physics model, and dynamically corrects the errors of the physics model through an explicit bias modeling network (MLP). It then combines with multi-source heterogeneous signals, utilizing position encoding, multi-head attention mechanisms, and a physically enhanced bidirectional long short-term memory (BiLSTM) network architecture to deeply mine temporal features. Additionally, an exponentially decaying physical-data dual loss mechanism is introduced, enabling a dynamic transition from physically constrained guidance to data-driven optimization. Experimental results show that the proposed model achieves an accuracy rate of 98%. This model combines physical interpretability and prediction robustness, providing a new method for the online assessment of complex operating conditions in smart manufacturing and laying the foundation for building closed-loop control systems.</p>