Neural networks used for multi-interaction trajectory reconstruction lack the
ability to estimate the uncertainty in their outputs, which would be useful to
better analyse and understand the systems they model. In this paper we extend
the Factorised Neural Relational Inference model to output both a mean and a
standard deviation for each component of the phase space vector, which together
with an appropriate loss function, can account for uncertainty. A variety of
loss functions are investigated including ideas from convexification and a
Bayesian treatment of the problem. We show that the physical meaning of the
variables is important when considering the uncertainty and demonstrate the
existence of pathological local minima that are difficult to avoid during
training.

本文扩展了 Factorised Neural Relational Inference 模型，加入了输出每个相空间向量部分的均值和标准差以及相应的损失函数，以解决神经网络在多交互轨迹重建中缺乏输出不确定性估计的问题。本文研究了多种损失函数，包括凸函数和 Bayesian 方法，并且我们发现在考虑不确定性时，变量的物理意义非常重要，且存在难以避免的病态局部最小值问题。