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Scientific Machine Learning (SciML) is a burgeoning field thatsynergistically combines domain-aware and interpretable models with agnosticmachine learning techniques. In this work, we introduce GOKU-UI, an evolutionof the SciML generative model GOKU-nets. GOKU-UI not only broadens the originalmodel's spectrum to incorporate other classes of differential equations, suchas Stochastic Differential Equations (SDEs), but also integrates attentionmechanisms and a novel multiple shooting training strategy in the latent space.These modifications have led to a significant increase in its performance inboth reconstruction and forecast tasks, as demonstrated by our evaluation ofsimulated and empirical data. Specifically, GOKU-UI outperformed all baselinemodels on synthetic datasets even with a training set 16-fold smaller,underscoring its remarkable data efficiency. Furthermore, when applied toempirical human brain data, while incorporating stochastic Stuart-Landauoscillators into its dynamical core, our proposed enhancements markedlyincreased the model's effectiveness in capturing complex brain dynamics. Thisaugmented version not only surpassed all baseline methods in the reconstructiontask, but also demonstrated lower prediction error of future brain activity upto 15 seconds ahead. By training GOKU-UI on resting state fMRI data, we encodedwhole-brain dynamics into a latent representation, learning a low-dimensionaldynamical system model that could offer insights into brain functionality andopen avenues for practical applications such as the classification of mentalstates or psychiatric conditions. Ultimately, our research provides furtherimpetus for the field of Scientific Machine Learning, showcasing the potentialfor advancements when established scientific insights are interwoven withmodern machine learning.

Effective Latent Differential Equation Models via Attention and Multiple Shooting