Significant efforts have been recently made to obtain the three-dimensional (3D) structure of the genome with the goal of understanding how structures may affect gene regulation and expression. Chromosome conformational capture techniques such as Hi-C, have been key in uncovering the quantitative information needed to determine chromatin organization. Complementing these experimental tools, co-polymers theoretical methods are necessary to determine the ensemble of three-dimensional structures associated to the experimental data provided by Hi-C maps. Going beyond just structural information, these theoretical advances also start to provide an understanding of the underlying mechanisms governing genome assembly and function. Recent theoretical work, however, has been focused on single chromosome structures, missing the fact that, in the full nucleus, interactions between chromosomes play a central role in their organization. To overcome this limitation, MiChroM (Minimal Chromatin Model) has been modified to become capable of performing these multi-chromosome simulations. It has been upgraded into a fast and scalable software version, which is able to perform chromosome simulations using GPUs via OpenMM Python API, called Open-MiChroM. To validate the efficiency of this new version, analyses for GM12878 individual autosomes were performed and compared to earlier studies. This validation was followed by multi-chain simulations including the four largest human chromosomes (C1-C4). These simulations demonstrated the full power of this new approach. Comparison to Hi-C data shows that these multiple chromosome interactions are essential for a more accurate agreement with experimental results. Without any changes to the original MiChroM potential, it is now possible to predict experimentally observed inter-chromosome contacts. This scalability of Open-MiChroM allow for more audacious investigations, looking at interactions of multiple chains as well as moving towards higher resolution chromosomes models.