Scientific Machine Learning (SciML) is a burgeoning field that synergistically combines domain-aware and interpretable models with agnostic machine learning techniques. In this work, we introduce GOKU-UI, an evolution of the SciML generative model GOKU-nets. GOKU-UI not only broadens the original model's spectrum to incorporate other classes of differential equations, such as Stochastic Differential Equations (SDEs), but also integrates attention mechanisms and a novel multiple shooting training strategy in the latent space. These enhancements have led to a significant increase in its performance in both reconstruction and forecast tasks, as demonstrated by our evaluation of simulated and empirical data. Specifically, GOKU-UI outperformed all baseline models on synthetic datasets even with a training set 16-fold smaller, underscoring its remarkable data efficiency. Furthermore, when applied to empirical human brain data, while incorporating stochastic Stuart-Landau oscillators into its dynamical core, it not only surpassed all baseline methods in the reconstruction task, but also demonstrated better prediction of future brain activity up to 15 seconds ahead. By training GOKU-UI on resting state fMRI data, we encoded whole-brain dynamics into a latent representation, learning an effective low-dimensional dynamical system model that could offer insights into brain functionality and open avenues for practical applications such as the classification of mental states or psychiatric conditions. Ultimately, our research provides further impetus for the field of Scientific Machine Learning, showcasing the potential for advancements when established scientific insights are interwoven with modern machine learning.

翻译：科学机器学习是一个新兴领域，它协同融合了领域感知可解释模型与通用机器学习技术。本文提出GOKU-UI——科学机器学习生成模型GOKU-nets的演进版本。GOKU-UI不仅将原始模型的适用范围扩展至随机微分方程等其他类型微分方程，更整合了注意力机制与隐空间中的新型多重打靶训练策略。这些改进显著提升了其在重建和预测任务上的性能，模拟数据和实证数据的评估结果均证实了这一点。具体而言，即使训练集缩减16倍，GOKU-UI在合成数据集上的表现仍超越所有基线模型，展现出卓越的数据效率。此外，当应用于实证人脑数据时，通过在其动态核心中融入随机Stuart-Landau振荡器，该模型不仅在重建任务中超越所有基线方法，更展现出对未来长达15秒脑活动的精准预测能力。通过使用静息态功能磁共振成像数据训练GOKU-UI，我们将全脑动态编码为隐空间表征，学习到一个有效的低维动力系统模型——该模型既能揭示脑功能机制，又为精神状态分类或精神疾病诊断等实际应用开辟了新路径。最终，本研究为科学机器学习领域注入新动力，展示了当现代机器学习与成熟科学认知深度融合时所能实现的突破性进展。