Uncertainty in Neural Relational Inference Trajectory Reconstruction
This work addresses uncertainty estimation for researchers analyzing complex systems modeled by neural networks, but it is incremental as it builds on existing models.
The paper tackles the problem of uncertainty estimation in neural networks for multi-interaction trajectory reconstruction by extending the Factorised Neural Relational Inference model to output mean and standard deviation, investigating various loss functions including convexification and Bayesian approaches, and demonstrating issues like pathological local minima during training.
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.