用几何物理约束提升模型对复杂系统的学习能力
MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence
- 基于辛几何编码与元注意力解码，嵌入物理守恒律
- 少样本下超越更大规模先进模型，真实无人机数据验证
- 适合需要物理一致性建模的机器人、量子系统等场景
可扩展且通用的物理感知深度学习长期面临挑战，广泛应用于机器人、分子动力学等领域。几乎所有物理系统的核心都是辛形式，其构成能量与动量等基本守恒量的几何基础。本文提出新型深度学习框架 MetaSym，结合辛编码器带来的强辛归纳偏置，以及带元注意力的自回归解码器。该设计确保核心物理守恒量不变，同时实现对系统异质性的灵活、高效适应。我们在多样且真实的多个数据集上进行基准测试，包括高维弹簧网格系统（Otness et al., 2021）、含耗散与测量反作用的开放量子系统，以及类机器人四旋翼动力学。关键的是，我们在真实四旋翼数据上进行微调与部署，证明了对传感器噪声和现实不确定性具有鲁棒性。在所有任务中，MetaSym均实现优异的少样本适应能力，并优于更大的现有先进模型。
原文摘要 · Abstract (English)
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. Crucially, we fine-tune and deploy MetaSym on real-world quadrotor data, demonstrating robustness to sensor noise and real-world uncertainty. Across all tasks, MetaSym achieves superior few-shot adaptation and outperforms larger state-of-the-art (SOTA) models.
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