As a critical piece of equipment in oil and gas stations, the operating condition of centrifugal compressors directly affects the stability and safety of the production system. To address the issues of poor generalization and limited physical interpretability in compressor fault diagnosis models—caused by complex operating conditions and insufficient fault data—this paper proposes a digital twin-driven fault diagnosis method for centrifugal compressors. First, a digital twin framework for centrifugal compressors is constructed, comprising the stages of data acquisition, mapping, fusion and optimization, and model-driven analysis, enabling the storage and integration of operational information within the digital twin entity. Second, variational mode decomposition (VMD) is employed to decompose time-series signals into intrinsic mode functions with limited bandwidth, thereby mapping compressor status features to thermodynamic state variables. Finally, a physics-informed extended long short-term memory network (PX-LSTM) fault diagnosis model is developed, which embeds key physical features from the compressor’s operational process into the extended long short-term memory network (xLSTM) structure for joint modeling. This design guides the model to learn historical fault features while adhering to the underlying thermodynamic behavior of the system. Experimental results demonstrate that the proposed model outperforms mainstream approaches across multiple operating conditions and fault types, validating its feasibility and effectiveness in oil and gas digital twin systems.