We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of autoencoder to identify the unobserved latent random variables. In our approach, we design an encoding function to discover the latent variables, which are modeled as unit Gaussian, and a decoding function to reconstruct the future states of the system. Both the encoder and decoder are expressed as deep neural networks (DNNs). Once the DNNs are trained by the trajectory data, the decoder serves as a predictive model for the unknown stochastic system. Through an extensive set of numerical examples, we demonstrate that the method is able to produce long-term system predictions by using short bursts of trajectory data. It is also applicable to systems driven by non-Gaussian noises.

翻译：本文提出了一种数值方法，用于从轨迹数据中学习未知随机动力系统的精确预测模型。该方法旨在逼近底层系统的未知流映射。其采用自编码器的思想来识别未观测到的潜在随机变量。在我们的方法中，我们设计了一个编码函数来发现被建模为单位高斯分布的潜在变量，以及一个解码函数来重建系统的未来状态。编码器和解码器均表示为深度神经网络。一旦深度神经网络通过轨迹数据训练完成，解码器即可作为未知随机系统的预测模型。通过大量数值算例，我们证明该方法能够利用短时轨迹数据实现长期系统预测，并且适用于由非高斯噪声驱动的系统。