论文标题
将对称性纳入深度动力学模型以改善概括
Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
论文作者
论文摘要
最近的工作表明，深度学习可以加速相对于数值求解器的物理动力学预测。但是，有限的身体准确性和无法在分配偏移下概括其对现实世界的适用性。我们建议通过将对称性纳入卷积神经网络来提高准确性和概括。具体而言，我们采用各种定制的方法来强制执行不同的对称性。我们的模型在理论上和实验上都可以通过对称组转换进行分布转移，并具有良好的样本复杂性。我们证明了方法对各种物理动态的优势，包括雷利·贝纳德对流以及现实世界中的洋流和温度。与图像或文本应用程序相比，我们的工作是朝着将模棱两可的神经网络应用于具有复杂动力学的高维系统的重要一步。我们以\ url {https://github.com/rose-stl-lab/equivariant-net}开放源仿真，数据和代码。
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 distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into convolutional 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 symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh Bénard convection and real-world ocean currents and temperatures. Compared with image or text applications, our work is a significant step towards applying equivariant neural networks to high-dimensional systems with complex dynamics. We open-source our simulation, data, and code at \url{https://github.com/Rose-STL-Lab/Equivariant-Net}.
