MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence

Abstract: Scalable and generalizable physics-aware deep learning has long been considered a significant challenge with various applications across diverse domains ranging from robotics to molecular dynamics. Central to almost all physical systems are symplectic forms, the geometric backbone that underpins fundamental invariants like energy and momentum. In this work, we introduce a novel deep learning framework, MetaSym. In particular, MetaSym combines a strong symplectic inductive bias obtained from a symplectic encoder, and an autoregressive decoder with meta-attention. This principled design ensures that core physical invariants remain intact, while allowing flexible, data-efficient adaptation to system heterogeneities. We benchmark MetaSym with highly varied and realistic datasets, such as a high-dimensional spring-mesh system (Otness et al., 2021), an open quantum system with dissipation and measurement backaction, and robotics-inspired quadrotor dynamics. Our results demonstrate superior performance in modeling dynamics under few-shot adaptation, outperforming state-of-the-art baselines that use larger models.