  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.
