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 modifications 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, our proposed enhancements markedly increased the model's effectiveness in capturing complex brain dynamics. This augmented version not only surpassed all baseline methods in the reconstruction task, but also demonstrated lower prediction error 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 a 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（SciML）是一个新兴领域，它将具有领域知识且可解释的模型与无先验知识的机器学习技术协同结合。本文提出了GOKU-UI模型，这是对SciML生成模型GOKU-nets的改进。GOKU-UI不仅将原始模型的应用范围扩展至随机微分方程（SDEs）等其他类型的微分方程，还整合了注意力机制与潜空间中的新型多重打靶训练策略。这些改进显著提升了模型在重建与预测任务中的表现——基于模拟数据和经验数据的评估结果证明了这一点。值得注意的是，即使训练集缩小16倍，GOKU-UI在合成数据集上的表现仍优于所有基线模型，凸显了其卓越的数据效率。此外，在应用于人类脑电经验数据时，通过将随机Stuart-Landau振子融入动态核心，我们提出的增强方法显著提升了模型捕捉复杂脑动态的能力。增强版模型不仅在重建任务中超越所有基线方法，还能以更低误差预测未来15秒内的脑活动。通过用静息态fMRI数据训练GOKU-UI，我们将全脑动态编码为潜表征，学习得到一个低维动态系统模型——该模型既能揭示脑功能机制，也为精神状态或精神疾病分类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了新动力，展现了将成熟科学洞见与现代机器学习相结合所能实现的突破性进展。