Machine learning (ML) is transforming computational chemistry by accelerating molecular simulations, property prediction, and inverse design. Central to this transformation is mathematical optimization, which underpins nearly every stage of model development, from training neural networks and tuning hyperparameters to navigating chemical space for molecular discovery. This review presents a structured overview of optimization techniques used in ML for computational chemistry, including gradient-based methods (e.g., SGD and Adam), probabilistic approaches (e.g., Monte Carlo sampling and Bayesian optimization), and spectral methods. We classify optimization targets into model parameter optimization, hyperparameter selection, and molecular optimization and analyze their application across supervised, unsupervised, and reinforcement learning frameworks. Additionally, we examine key challenges such as data scarcity, limited generalization, and computational cost, outlining how mathematical strategies like active learning, meta-learning, and hybrid physics-informed models can address these issues. By bridging optimization methodology with domain-specific challenges, this review highlights how tailored optimization strategies enhance the accuracy, efficiency, and scalability of ML models in computational chemistry.

The ornaments from the Serbian medieval frescoes belong to the religious decorative art with the restricted set of possible motifs, frequently related to a cross, and thus the basic motifs can fit in a very limited number of symmetry groups. The main criterion for the quality of such ornamental art could be the richness and variety of patterns obtained from a very small number of symmetry groups, proving the creativity of their authors-their ability to create variety with a very restricted number of initial symmetry groups. Here we analyze these ornaments and their symmetry group and give an introductions to further work on automated symmetry group recognition and pattern reconstruction.