We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to leverage a priori physics knowledge as inductive bias, and we design the diffusion term to represent a distance-aware estimate of the uncertainty in the learned model's predictions -- it matches the system's underlying stochasticity when evaluated on states near those from the training dataset, and it predicts highly stochastic dynamics when evaluated on states beyond the training regime. The proposed neural SDEs can be evaluated quickly enough for use in model predictive control algorithms, or they can be used as simulators for model-based reinforcement learning. Furthermore, they make accurate predictions over long time horizons, even when trained on small datasets that cover limited regions of the state space. We demonstrate these capabilities through experiments on simulated robotic systems, as well as by using them to model and control a hexacopter's flight dynamics: A neural SDE trained using only three minutes of manually collected flight data results in a model-based control policy that accurately tracks aggressive trajectories that push the hexacopter's velocity and Euler angles to nearly double the maximum values observed in the training dataset.

本文提出了一种使用神经随机微分方程学习控制动力学模型的框架和算法，能够构建模型预测控制算法以及模型基的增强学习领域中的仿真器，在模拟机器人系统中得到良好的应用。

如何从三分钟数据中学习和泛化：物理约束和不确定性感知的神经随机微分方程