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To reconstruct the impact parameter distributions from the selected eventssample or centrality, which is defined by two-observables, at intermediateenergy heavy ion collisions, we extend the approach proposed by Das \textit{etal.} [Phys. Rev. C 97, 014905 (2018)], Rogly \textit{et al.} [Phys. Rev. C 98,024902 (2018)], and Frankland \textit{et al.} [Phys. Rev. C 104, 034609(2021)]. Based on deep investigations of the fluctuation mechanism, we foundthat the intrinsic fluctuations are mainly generated in the microscopicstochasticity of initialization and nucleon-nucleon collisions in thenonequilibrium process of heavy ion collisions, and this leads the observablesto fluctuate with respect to impact parameter in a Gaussian form. In this work,the multiplicity of the charged particles and the total transverse momentum ofthe light charged particles are used simultaneously to model-independentlyreconstruct the impact parameter distributions for selected events orcentrality based on the Bayesian method. For sorting the centrality with twoobservables, we propose to use the $K$-means clustering method (an unsupervisedmachine learning algorithm), which can automatically sort events when the classnumber is given. Furthermore, the reconstructed impact parameter distributionsfrom data of the two observables can be used to learn the correlation betweenmultiplicity and transverse momentum at different centralities, which may beuseful for understanding the fragmentation mechanism.

Bayesian reconstruction of impact parameter distributions from two observables for intermediate energy heavy ion collisions