Uncertainty in Neural Relational Inference Trajectory Reconstruction

TL;DR

This paper enhances neural relational inference models by enabling uncertainty estimation in trajectory reconstruction, improving interpretability and robustness in modeling multi-interaction systems.

Contribution

It introduces a method to output both mean and standard deviation in neural relational inference, incorporating uncertainty estimation into trajectory reconstruction.

Findings

Uncertainty-aware models improve trajectory analysis.

Physical meaning of variables affects uncertainty estimation.

Pathological local minima pose training challenges.

Abstract

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.