用微分方程约束生成心电图，让合成数据更真实可信。

Generating realistic training data for supervised learning remains a significant challenge in artificial intelligence, particularly in domains where large, expert-labeled datasets are scarce or costly to obtain. This is especially true for electrocardiograms (ECGs), where privacy constraints, class imbalance, and the need for physician annotation limit the availability of labeled 12-lead recordings, motivating the development of high-fidelity synthetic ECG data. The primary challenge in this task lies in accurately modeling the intricate biological and physiological interactions among different ECG leads. Although mathematical process models have shed light on these dynamics, effectively incorporating this understanding into generative models is not straightforward. We introduce an innovative method that employs ordinary differential equations (ODEs) to enhance the fidelity of 12-lead ECG data generation. This approach integrates cardiac dynamics directly into the generative optimization process via a novel Euler Loss, producing biologically plausible data that respects real-world variability and inter-lead constraints. Empirical analysis on the G12EC and PTB-XL datasets demonstrates that augmenting training data with MultiODE-GAN yields consistent, statistically significant improvements in specificity across multiple cardiac abnormalities. This highlights the value of enforcing physiological coherence in synthetic medical data.