论文标题
大约是不完美对称动力学的近似网络
Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
论文作者
论文摘要
将对称性作为归纳偏置纳入神经网络体系结构已导致动态建模的概括，数据效率和身体一致性的提高。诸如CNN或e象神经网络之类的方法使用重量绑定来强制执行诸如偏移不变性或旋转率的对称性。但是，尽管物理定律遵守了许多对称性，但实际动态数据很少符合严格的数学对称性，这是由于嘈杂或不完整的数据或基础动力学系统中的对称性破坏特征。我们探索近似模棱两可的网络，这些网络偏向于保存对称性，但并非严格限制这样做。通过放松的均衡约束，我们发现我们的模型可以在模拟的湍流域和现实世界多流射流流中均超过对称性偏差和基线的两个基准。
Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use weight tying to enforce symmetries such as shift invariance or rotational equivariance. However, despite the fact that physical laws obey many symmetries, real-world dynamical data rarely conforms to strict mathematical symmetry either due to noisy or incomplete data or to symmetry breaking features in the underlying dynamical system. We explore approximately equivariant networks which are biased towards preserving symmetry but are not strictly constrained to do so. By relaxing equivariance constraints, we find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.
