The Large Hadron Collider at CERN has collected a vast amount of data at the highest energies ever achieved in a laboratory setting. This data has allowed for the discovery of the Higgs boson and the precise measurements of properties of the Standard Model of particle physics. No new particles have been discovered beyond the Standard Model, and despite an impressive physics program, there remain many extensions that have not been excluded. Many extensions to the Standard Model predict the existence of new particles that decay into a pair of visible particles, which would appear as a peak in the invariant dijet mass spectrum. The standard approach to searching for such resonances is to perform a bump hunt, where the invariant mass spectrum is examined for a peak. This approach is limited in its sensitivity as it only utilizes the information contained in the invariant mass spectrum.

This thesis presents a search that extends the bump hunt by including up to six additional variables that are sensitive to the presence of physics beyond the Standard Model. Narrow width new physics models are searched for in the dijet invariant mass spectrum using 139~fb$^{-1}$ of proton-proton collision data collected by the ATLAS detector at a center-of-mass energy of $\sqrt{s} = 13$~TeV. Events that contain at least two large radius jets at high transverse momentum are selected. The search uses two different interpolation techniques for producing background estimates over the six additional variables. This search is the first of its kind and thus requires extensive development and validation of the analysis strategy. The development of the analysis, and the challenges that were faced, are laid out in detail. Limits are set on the production of twenty different possible new physics processes, many of which have not been studied by any other analysis. Many of the challenges that need to be addressed in future iterations of such a search are also discussed in detail, as well as avenues for interpreting the results of such a search.

In addition, studies using machine learning techniques to improve different aspects of high energy physics analyses are presented.