The Symbiosis of Deep Learning and Differential Equations -- III

In the deep learning community, a remarkable trend is emerging, where powerful architectures are created by leveraging classical mathematical modeling tools from diverse fields like differential equations, signal processing, and dynamical systems. Differential equations are a prime example: research on neural differential equations has expanded to include a large zoo of related models with applications ranging from time series analysis to robotics control. Score-based diffusion models are among state-of-the-art tools for generative modelling, drawing connections between diffusion models and neural differential equations. Other examples of deep architectures with important ties to classical fields of mathematical modelling include normalizing flows, graph neural diffusion models, Fourier neural operators, architectures exhibiting domain-specific equivariances, and latent dynamical models (e.g., latent NDEs, H3, S4, Hyena). The previous two editions of the Workshop on the Symbiosis of Deep Learning and Differential Equations have promoted the bidirectional exchange of ideas at the intersection of classical mathematical modelling and modern deep learning. On the one hand, this includes the use of differential equations and similar tools to create neural architectures, accelerate deep learning optimization problems, or study theoretical problems in deep learning. On the other hand, the Workshop also explores the use of deep learning methods to improve the speed, flexibility, or realism of computer simulations. Last year, we noted a particularly keen interest from the audience in neural architectures that leveraged classical mathematical models, such as those listed above. We therefore propose that the third edition of this Workshop focus on this theme.