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. The GOKU-UI broadens the original
model's spectrum to incorporate other classes of differential equations, such
as Stochastic Differential Equations (SDEs), and integrates a distributed, i.e.
ubiquitous, inference through 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 32-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 state-of-the-art baseline methods in the reconstruction
task, but also demonstrated better prediction of future brain activity up to 12
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 mental state
or psychiatric condition classification. 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.

本文介绍了 GOKU-UI，一个基于 Scientific Machine Learning（SciML）演化而来的生成模型，它通过在潜空间中使用注意力机制和新型的多发射训练策略，结合不同种类的微分方程，实现分布式推理，显著提高了模型的性能。研究证明，GOKU-UI 具有很高的数据效率，不仅优于基线模型，还能够在重建和预测任务中超越实时方法，并且可以为大脑功能提供有益的见解和开放可行的实际应用，如心理状态或精神状况分类。