MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence

2025-02-23

AI Summary

To address the limited generalizability and scalability of physics-informed modeling, this paper proposes a dynamic modeling framework integrating symplectic geometric priors with meta-learning. Methodologically, it introduces a novel synergistic architecture comprising a symplectic encoder and a meta-attentional autoregressive decoder, embedding physical conservation laws—such as energy and momentum—as inductive biases directly into the network design to ensure physics-consistent few-shot adaptation. Crucially, the framework achieves cross-system transfer without task-specific fine-tuning, demonstrating rapid adaptability across heterogeneous dynamical systems—including spring-mass grids, open quantum systems, and quadrotor dynamics. Experiments show that our approach significantly outperforms large-parameter state-of-the-art models on diverse high-dimensional physics modeling tasks, reducing few-shot adaptation error by 37%–52%. To our knowledge, this is the first work to achieve organic unification of symplectic structure guidance and meta-learning within deep physics-informed learning.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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 architecture, 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 on highly varied 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 with far larger models.

Problem

• Develop scalable physics-aware deep learning
• Preserve symplectic forms in physical systems
• Enable few-shot adaptation in heterogeneous systems

Innovation

• Symplectic encoder ensures physical invariants
• Meta-attention enables data-efficient adaptation
• Autoregressive decoder handles system heterogeneities