We present a machine learning based method for learning first integrals of systems of ordinary differential equations from given trajectory data. The method is model-agnostic in that it does not require explicit knowledge of the underlying system of differential equations that generated the trajectories. As a by-product, once the first integrals have been learned, also the system of differential equations will be known. We illustrate our method by considering several classical problems from the mathematical sciences.

翻译：我们提出了一种基于机器学习的方法，用于从给定轨迹数据中学习常微分方程组的第一积分。该方法具有模型无关性，即无需明确知晓生成轨迹的底层微分方程组。作为副产品，一旦学会了第一积分，微分方程组也将随之获知。我们通过考虑数学科学中的若干经典问题来展示该方法。