# Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples

arXiv: https://arxiv.org/abs/2005.11699 · HTML: https://mlsanity.com/paper/2005.11699/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2020.

## Built on by (most cited first, 2 of 2)

- [One-shot learning for solution operators of partial differential equations](https://mlsanity.com/paper/2104.05512/) (2021)
- [One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators](https://mlsanity.com/paper/2604.15181/) (2026)

## Abstract (arXiv)

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.