Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to predict time series accurately, their uncertainty quantification properties remain unexplored. We report the empirical finding that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. As a remedy, we develop a computationally affordable deterministic scheme for expressing the likelihood of a sequence, when dynamics is governed by a NSDE, which is applicable to both training and prediction. Our method introduces a bidirectional moment matching scheme, one vertical along the neural net layers, and one horizontal along the time direction, which benefits from an original combination of effective approximations. We observe in multiple experiments that the uncertainty calibration quality of our method can be matched by Monte Carlo sampling only after introducing at least five times more computation cost. Thanks to the numerical stability of deterministic training, our method also provides improvement in prediction accuracy.

翻译：神经物理差异(NSDEs) 模型是神经网络中随机过程的漂移和扩散功能的模型。 虽然已知NSDEs准确预测时间序列,但其不确定性量化特性仍未被探索。 我们报告的经验发现,从NSDEs获得经充分校准的不确定性估计是计算上令人望而生畏的。作为一种补救措施,我们开发了一个计算上可承受的确定性计划,以表达序列的可能性,当动态由适用于培训和预测的NSDE(NSDE)管理时,动态由该NSA(NSDE)管理,同时适用于培训和预测。我们的方法引入了双向时时刻匹配方案,一个沿神经网层垂直,一个沿时间方向横向,从有效近似原始组合中受益。我们观察到,我们方法的不确定性校准质量只有在引入至少五倍的计算成本之后,才能与Monte Carlo取样相匹配。由于确定性培训的数字稳定性,我们的方法也提高了预测的准确性。