The packing of nucleosomes regulates gene expression through genome condensation and expansion, but the specific structures and their thermodynamic stabilities remain unresolved. In this work, we employ the use of a meso-scale model of chromatin, referred to as "1-Cylinder-per-Nucleosome," or 1CPN, in combination with nonlinear manifold learning to identify and characterize the structure and free energy of metastable states of short chromatin segments. Our results reveal the intrinsic formation of two previously characterized tetranucleosomal conformations, the "α-tetrahedron" and the "β-rhombus," which have been suggested to play a role in inducing chromatin compaction or elongation, respectively. Building upon these findings, we leverage convolutional neural networks and molecular dynamics simulations to design a deep convolutional denoising autoencoder (DAE) capable of providing nucleosome-level resolution of scanning transmission electron microscopy images of chromatin (ChromSTEM). Our DAE is trained on synthetic images generated from simulations of the chromatin fiber using the 1CPN model of chromatin, thereby learning structural features driven by the physics of chromatin folding. We find that our DAE outperforms other well-known denoising algorithms without degradation of structural features and allows for the resolution of individual nucleosomes and organized domains within chromatin-dense regions. Lastly, we investigate how post-translational modifications (PTMs), modeled as modifications to the nucleosome interaction potential, affect the construction of these motifs and, consequently, the chromatin fiber as a whole. Our study provides important insight into chromatin folding and highlights the value of interdisciplinary approaches in this field.