Effective Latent Differential Equation Models via Attention and Multiple Shooting
This work addresses the challenge of efficiently modeling scientific data like brain dynamics for applications in neuroscience, though it appears incremental as an evolution of an existing model.
The authors tackled the problem of modeling complex dynamical systems in Scientific Machine Learning by introducing GOKU-UI, which improved performance in reconstruction and forecast tasks, achieving better results with 16-fold smaller training data on synthetic datasets and lower prediction error up to 15 seconds ahead on human brain data.
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.