Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
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发表时间：
2022-01
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通讯作者：
Rui Wang;R. Walters;Rose Yu
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作者：
Rui Wang;R. Walters;Rose Yu
将对称性作为神经网络架构的归纳偏差，导致了动力学建模中泛化、数据效率和物理一致性的改进。诸如CNN或等变神经网络之类的方法使用权重绑定来强制对称性，例如移位不变性或旋转等变性。然而，尽管物理定律服从许多对称性，但现实世界的动力学数据很少符合严格的数学对称性，这要么是由于噪声或不完整的数据，要么是由于基础动力学系统中的对称性破缺特征。我们探讨近似等变网络偏向于保持对称性，但不严格限制这样做。通过放松等方差约束，我们发现，我们的模型可以优于两个基线没有对称性偏差和基线过于严格的对称性在模拟的湍流域和现实世界的多流射流。
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.