Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
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发表时间：
2020-02
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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
最近的工作表明，相对于数值求解器，深度学习可以加快物理动力学的预测。然而，有限的物理精度和无法在分布偏移下进行泛化限制了它在现实世界中的适用性。我们建议通过将对称性引入到深度神经网络中来提高精度和泛化能力。具体地说，我们采用了各种方法，每种方法都是为实施不同的对称而量身定做的。我们的模型在理论上和实验上都对对称群变换引起的分布漂移具有较强的稳健性，并且具有良好的样本复杂性。我们展示了我们的方法在各种物理动力学上的优势，包括瑞利-贝纳德对流和真实世界的洋流和温度。这是第一次将等变神经网络用于预测物理动力学。
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under the distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into deep neural networks. Specifically, we employ a variety of methods each tailored to enforce a different symmetry. Our models are both theoretically and experimentally robust to distributional shift by the symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh-Benard Convection and real-world ocean currents and temperatures. This is the first time that equivariant neural networks have been used to forecast physical dynamics.