论文标题
基于物理学的多项式神经网络，用于从一个或几个样本中对动力学系统进行动力学系统的一次性学习
Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples
论文作者
论文摘要
本文讨论了一种将先前的物理知识纳入神经网络的方法，以提高数据效率和预测模型的概括。如果系统的动力学大致遵循给定的微分方程，则可以使用泰勒映射方法来初始化多项式神经网络的权重。这允许从一个真实系统动力学的一个训练样本中微调模型。本文描述了具有简单的摆和全球X射线源之一的真实实验的实际结果。实际上证明了所提出的方法允许从嘈杂，有限和部分观察结果中恢复复杂的物理，并为以前看不见的输入提供了有意义的预测。当缺乏培训数据时，难以应用最先进的模型时，该方法主要针对物理系统的学习。
This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given differential equation, the Taylor mapping method can be used to initialize the weights of a polynomial neural network. This allows the fine-tuning of the model from one training sample of real system dynamics. The paper describes practical results on real experiments with both a simple pendulum and one of the largest worldwide X-ray source. It is demonstrated in practice that the proposed approach allows recovering complex physics from noisy, limited, and partial observations and provides meaningful predictions for previously unseen inputs. The approach mainly targets the learning of physical systems when state-of-the-art models are difficult to apply given the lack of training data.
