Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples
This approach addresses the challenge of applying state-of-the-art models to physical systems where training data is scarce, offering a data-efficient solution for domains like physics and engineering.
The paper tackles the problem of learning dynamical systems from extremely limited data by incorporating prior physical knowledge into polynomial neural networks, enabling fine-tuning from just one training sample and demonstrating successful recovery of complex physics from noisy, partial observations in experiments like a pendulum and a large X-ray source.
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.