To overcome the limitations of existing cardiac function assessment indices such as ejection fraction (EF) and global longitudinal strain (GLS), we propose a novel AI-based cardiac function index, Acoustic Index, which combines extended dynamic mode decomposition (EDMD) based on Koopman operator theory and a hybrid neural network integrating clinical metadata. Coherent motion patterns are extracted from echocardiographic image sequences, weighted through an attention mechanism, and fused with clinical data using manifold learning to produce a continuous score from 0 (low risk) to 1 (high risk). In a prospective cohort study with 736 patients, we achieved an AUC of 0.89 on an independent validation set, and showed robustness with sensitivity and specificity exceeding 0.8 on independent data in five-fold cross-validation.