Mathematical Optimization in Machine Learning for Computational Chemistry
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...
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MDPI AG
2025-07-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/13/7/169 |
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| author | Ana Zekić |
| author_facet | Ana Zekić |
| author_sort | Ana Zekić |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0dc44aef6bf543dc9d98f61c137a0e47 |
| institution | DOAJ |
| issn | 2079-3197 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj-art-0dc44aef6bf543dc9d98f61c137a0e472025-08-20T03:08:00ZengMDPI AGComputation2079-31972025-07-0113716910.3390/computation13070169Mathematical Optimization in Machine Learning for Computational ChemistryAna Zekić0Department of Mathematical Sciences, Faculty of Technology and Metallurgy, University of Belgrade, 11000 Belgrade, SerbiaMachine 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.https://www.mdpi.com/2079-3197/13/7/169mathematical optimizationmachine learning in chemistrycomputational chemistryBayesian optimization |
| spellingShingle | Ana Zekić Mathematical Optimization in Machine Learning for Computational Chemistry Computation mathematical optimization machine learning in chemistry computational chemistry Bayesian optimization |
| title | Mathematical Optimization in Machine Learning for Computational Chemistry |
| title_full | Mathematical Optimization in Machine Learning for Computational Chemistry |
| title_fullStr | Mathematical Optimization in Machine Learning for Computational Chemistry |
| title_full_unstemmed | Mathematical Optimization in Machine Learning for Computational Chemistry |
| title_short | Mathematical Optimization in Machine Learning for Computational Chemistry |
| title_sort | mathematical optimization in machine learning for computational chemistry |
| topic | mathematical optimization machine learning in chemistry computational chemistry Bayesian optimization |
| url | https://www.mdpi.com/2079-3197/13/7/169 |
| work_keys_str_mv | AT anazekic mathematicaloptimizationinmachinelearningforcomputationalchemistry |