# Dimension reduction based on atomic level stresses


**Discussions**
* The color represents the von Mises atomic stress. It’s clear that, due to the random dropout method exciting particles not directly associated with the vacancy, several particles away from the vacancy remain strained even after the structure around the vacancy has relaxed to a new minimum.
* In contrast, when the penalty is assigned solely to particles with the highest atomic stress, and the penalty atom list is only updated after identifying a new energy minimum, particles far from the defect no longer experience residual stresses, as only the relevant particles are influenced by the penalty.
* One possibility is that introducing randomness may help simulating thermal effects in studies at higher temperatures. For this purpose, the probability distribution used to select penalized particles should incorporate temperature and atomic-level stress as inputs.
* Another important consideration is whether a single, system-level potential energy landscape remains suitable for describing the behavior of multiple defects. For instance, if two vacancies are present in the system, it’s possible that as one vacancy crosses an energy barrier, the other could still be midway through the uphill process. This raises ambiguity as to whether the detected energy barrier truly corresponds to the vacancy migration energy, complicating the interpretation of the results.
* When zooming in on the steps approaching the energy minimum, we notice that the potential energy doesn't always reach the minimum, causing a slight slide in the subsequent step. This also leads to artificial residual stress.
To address this issue, an additional energy minimization step can be applied after the convergence criteria are satisfied, ensuring the inherent state trajectory is saved with minimal residual stress.