{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T04:52:06Z","timestamp":1788238326735,"version":"build-2803163510"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T00:00:00Z","timestamp":1781222400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:00:00Z","timestamp":1787702400000},"content-version":"vor","delay-in-days":75,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Supercritical carbon dioxide (SC-CO\u2082) is widely used as an environmentally friendly solvent in pharmaceutical processing, where accurate prediction of drug solubility is essential for efficient formulation design, extraction processes, and process optimization. However, predicting solubility behavior in supercritical systems remains challenging due to the nonlinear interactions between thermodynamic conditions and molecular properties. In this study, a hybrid artificial intelligence framework is developed to predict the solubility of active pharmaceutical ingredients (APIs) in SC-CO\u2082 using a curated dataset of more than 350 experimentally reported measurements. The proposed framework integrates interpretable deep learning (TabNet) and histogram-based gradient boosting (HGB) with three metaheuristic optimization algorithms, namely the Attack-Leave Optimizer (ALO), Energy Valley Optimizer (EVO), and Botox Optimization Algorithm (BOA), to improve hyperparameter tuning and predictive performance. Model evaluation was conducted using multiple statistical indicators, five-fold cross-validation, prediction interval bootstrapping, and multi-objective Pareto front analysis to assess accuracy and robustness. Among the evaluated configurations, the EVO-tuned TabNet model demonstrated the best predictive performance, achieving a coefficient of determination of\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:{R}^{2}=0.982$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    along with narrow prediction intervals, indicating strong generalization capability within the studied thermodynamic domain. Statistical analysis using the Kruskal\u2013Wallis test confirmed significant differences between optimizer performances (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:p&lt;0.05$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ). These findings demonstrate that the proposed hybrid pipeline enhances predictive accuracy and interpretability within the thermodynamic domain represented by the compiled dataset. The framework therefore provides a statistically supported computational tool for assisting solvent selection and formulation analysis in supercritical systems, while broader generalization would benefit from future expansion of experimental solubility datasets.\n                  <\/jats:p>","DOI":"10.1038\/s41598-026-51115-8","type":"journal-article","created":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T07:54:53Z","timestamp":1781250893000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimization algorithm for improving the prediction accuracy of API solubility in green solvent"],"prefix":"10.1038","volume":"16","author":[{"given":"Ali","family":"Alasiri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmed A.","family":"Lahiq","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdullah A.","family":"Alshehri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,12]]},"reference":[{"key":"51115_CR1","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1038\/s41598-024-84263-w","volume":"15","author":"AF Wali","year":"2025","unstructured":"Wali, A. F. et al. Determination of the solubility of methyldopa in supercritical carbon dioxide for drug delivery applications: thermal analysis. Sci. Rep. 15, 923 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR2","doi-asserted-by":"publisher","first-page":"107150","DOI":"10.1016\/j.ejps.2025.107150","volume":"211","author":"B Goovaerts","year":"2025","unstructured":"Goovaerts, B. et al. Tiny-TIM intestinal fluids versus human intestinal fluids: A comparison of their composition and solubilizing capacity for poorly soluble drugs. Eur. J. Pharm. Sci. 211, 107150 (2025).","journal-title":"Eur. J. Pharm. Sci."},{"key":"51115_CR3","doi-asserted-by":"publisher","DOI":"10.5599\/admet.2626","author":"A Avdeef","year":"2025","unstructured":"Avdeef, A. Often neglected steps in transforming drug solubility from single measurement in pure water to physiologically-appropriate solubility-pH. ADMET DMPK. https:\/\/doi.org\/10.5599\/admet.2626 (2025).","journal-title":"ADMET DMPK"},{"key":"51115_CR4","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s40262-025-01472-w","volume":"64","author":"K Rodriguez-Fernandez","year":"2025","unstructured":"Rodriguez-Fernandez, K. et al. Solubility-Limited Absorption Identified by a Simplified PBPK Model for the Prediction of Positive Food Effect for BCS II\/IV Drugs. Clin. Pharmacokinet. 64, 369\u2013372 (2025).","journal-title":"Clin. Pharmacokinet."},{"key":"51115_CR5","doi-asserted-by":"publisher","first-page":"109004","DOI":"10.1016\/j.jmgm.2025.109004","volume":"137","author":"AM Veselinovi\u0107","year":"2025","unstructured":"Veselinovi\u0107, A. M. et al. Las Vegas algorithm in the prediction of intrinsic solubility of drug-like compounds. J. Mol. Graph Model. 137, 109004 (2025).","journal-title":"J. Mol. Graph Model."},{"key":"51115_CR6","doi-asserted-by":"publisher","first-page":"4451","DOI":"10.1038\/s41598-025-88817-4","volume":"15","author":"G Sodeifian","year":"2025","unstructured":"Sodeifian, G. et al. Solubility of gemcitabine (an anticancer drug) in supercritical carbon dioxide green solvent: Experimental measurement and thermodynamic modeling. Sci. Rep. 15, 4451 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR7","doi-asserted-by":"publisher","first-page":"4590","DOI":"10.1038\/s41598-025-87383-z","volume":"15","author":"G Sodeifian","year":"2025","unstructured":"Sodeifian, G., Alwi, R. S., Derakhsheshpour, R. & Ardestani, N. S. Determination of 5-fluorouracil anticancer drug solubility in supercritical CO 2 using semi-empirical and machine learning models. Sci. Rep. 15, 4590 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR8","doi-asserted-by":"publisher","first-page":"19456","DOI":"10.1038\/s41598-025-04596-y","volume":"15","author":"L Jiang","year":"2025","unstructured":"Jiang, L. et al. Analysis of a nonsteroidal anti inflammatory drug solubility in green solvent via developing robust models based on machine learning technique. Sci. Rep. 15, 19456 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR9","unstructured":"Tripathi, G. AI-driven predictive modeling for enhancing drug solubility and stability in pharmaceutical formulations."},{"key":"51115_CR10","doi-asserted-by":"publisher","first-page":"4043","DOI":"10.1021\/acs.jcim.5c00432","volume":"65","author":"DM Makarov","year":"2025","unstructured":"Makarov, D. M. et al. Improved Solubility Predictions in scCO2 Using Thermodynamics-Informed Machine Learning Models. J. Chem. Inf. Model. 65, 4043\u20134056 (2025).","journal-title":"J. Chem. Inf. Model."},{"key":"51115_CR11","doi-asserted-by":"publisher","first-page":"5192","DOI":"10.1038\/s41598-025-89858-5","volume":"15","author":"Z Bahrami","year":"2025","unstructured":"Bahrami, Z., Bashipour, F. & Baghban, A. Application of machine learning approach to estimate the solubility of some solid drugs in supercritical CO2. Sci. Rep. 15, 5192 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR12","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1208\/s12249-025-03051-5","volume":"26","author":"S Patel","year":"2025","unstructured":"Patel, S. et al. Machine Learning-Based Prediction of Drug Solubility in Lipidic Environments: The Sol_ME Tool for Optimizing Lipid-Based Formulations with a Preliminary Apalutamide Case Study. AAPS PharmSciTech. 26, 50 (2025).","journal-title":"AAPS PharmSciTech"},{"key":"51115_CR13","doi-asserted-by":"publisher","first-page":"114720","DOI":"10.1016\/j.ejpb.2025.114720","volume":"211","author":"A Roosta","year":"2025","unstructured":"Roosta, A., Esmaeilzadeh, F. & Haghbakhsh, R. Predicting the solubility of drugs in supercritical carbon dioxide using machine learning and atomic contribution. Eur. J. Pharm. Biopharm. 211, 114720 (2025).","journal-title":"Eur. J. Pharm. Biopharm."},{"key":"51115_CR14","doi-asserted-by":"publisher","first-page":"2586335","DOI":"10.1080\/21645515.2025.2586335","volume":"21","author":"B Liu","year":"2025","unstructured":"Liu, B. et al. Pharmacovigilance analysis of FcRn antagonists in the treatment of myasthenia gravis: A disproportionality analysis based on the FAERS database. Hum. Vaccin Immunother. 21, 2586335 (2025).","journal-title":"Hum. Vaccin Immunother"},{"key":"51115_CR15","doi-asserted-by":"publisher","first-page":"603615","DOI":"10.3389\/fimmu.2020.603615","volume":"11","author":"X Tang","year":"2021","unstructured":"Tang, X. et al. Indicator regularized non-negative matrix factorization method-based drug repurposing for COVID-19. Front. Immunol. 11, 603615 (2021).","journal-title":"Front. Immunol."},{"key":"51115_CR16","doi-asserted-by":"publisher","first-page":"e11667","DOI":"10.1002\/advs.202511667","volume":"12","author":"Q Zhu","year":"2025","unstructured":"Zhu, Q. et al. Rethinking the AI paradigm for solubility prediction of drug\u2013like compounds with dual-perspective modeling and experimental validation. Adv. Sci. 12, e11667 (2025).","journal-title":"Adv. Sci."},{"key":"51115_CR17","doi-asserted-by":"publisher","first-page":"2085","DOI":"10.1039\/D4DD00065J","volume":"3","author":"MA Ghanavati","year":"2024","unstructured":"Ghanavati, M. A., Ahmadi, S. & Rohani, S. A machine learning approach for the prediction of aqueous solubility of pharmaceuticals: A comparative model and dataset analysis. Digit. Discov. 3, 2085\u20132104 (2024).","journal-title":"Digit. Discov"},{"key":"51115_CR18","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.cherd.2024.07.050","volume":"209","author":"N Mac Fhionnlaoich","year":"2024","unstructured":"Mac Fhionnlaoich, N. et al. A hybrid approach to aqueous solubility prediction using COSMO-RS and machine learning. Chem. Eng. Res. Des. 209, 67\u201371 (2024).","journal-title":"Chem. Eng. Res. Des."},{"key":"51115_CR19","doi-asserted-by":"publisher","first-page":"8426","DOI":"10.1021\/acs.jcim.4c02399","volume":"65","author":"M Ali","year":"2025","unstructured":"Ali, M. et al. Advancing Aqueous Solubility Prediction: A Machine Learning Approach for Organic Compounds Using a Curated Data Set. J. Chem. Inf. Model. 65, 8426\u20138434 (2025).","journal-title":"J. Chem. Inf. Model."},{"key":"51115_CR20","doi-asserted-by":"crossref","unstructured":"Xue, N., Zhang, Y. & Liu, S. Evaluation of machine learning models for aqueous solubility prediction in drug discovery. in: 2024 7th International Conference on Artificial Intelligence and Big Data (ICAIBD) 26\u201333 (IEEE, 2024).","DOI":"10.1109\/ICAIBD62003.2024.10604556"},{"key":"51115_CR21","doi-asserted-by":"publisher","first-page":"e0330598","DOI":"10.1371\/journal.pone.0330598","volume":"20","author":"B Pan","year":"2025","unstructured":"Pan, B. et al. A water solubility prediction algorithm based on the StackBoost model. PLoS One. 20, e0330598 (2025).","journal-title":"PLoS One"},{"key":"51115_CR22","doi-asserted-by":"publisher","first-page":"28880","DOI":"10.1038\/s41598-025-13090-4","volume":"15","author":"M Alqarni","year":"2025","unstructured":"Alqarni, M. & Alqarni, A. Development of several machine learning based models for determination of small molecule pharmaceutical solubility in binary solvents at different temperatures. Sci. Rep. 15, 28880 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR23","doi-asserted-by":"publisher","first-page":"32411","DOI":"10.1038\/s41598-025-17642-6","volume":"15","author":"HF Alotaibi","year":"2025","unstructured":"Alotaibi, H. F. et al. Raloxifene solubility in supercritical CO2 and correlation of drug solubility via hybrid machine learning and gradient based optimization. Sci. Rep. 15, 32411 (2025).","journal-title":"Sci. Rep."},{"key":"51115_CR24","first-page":"1","volume":"8","author":"O Dewangan","year":"2024","unstructured":"Dewangan, O. & Prakash, V. V. Enhanced ResNet50 Model for Aqueous Solubility Prediction of Drug Compounds Using Deep Learning Techniques. Integr. Biomed. Res. 8, 1\u20136 (2024).","journal-title":"Integr. Biomed. Res."},{"key":"51115_CR25","doi-asserted-by":"publisher","first-page":"6956","DOI":"10.1021\/acs.molpharmaceut.5c00939","volume":"22","author":"A Mathers","year":"2025","unstructured":"Mathers, A., Fulem, M. A. & parameter-fitted PC-SAFT framework for solubility extrapolation in drug\u2013polymer systems. Mol. Pharm. 22, 6956\u20136963 (2025).","journal-title":"Mol. Pharm."},{"key":"51115_CR26","doi-asserted-by":"publisher","first-page":"114284","DOI":"10.1016\/j.fluid.2024.114284","volume":"590","author":"M Askarizadeh","year":"2025","unstructured":"Askarizadeh, M. et al. Solubility of teriflunomide in supercritical carbon dioxide and co-solvent investigation. Fluid Phase Equilib. 590, 114284 (2025).","journal-title":"Fluid Phase Equilib."},{"key":"51115_CR27","doi-asserted-by":"publisher","first-page":"126295","DOI":"10.1016\/j.molliq.2024.126295","volume":"415","author":"F Razmimanesh","year":"2024","unstructured":"Razmimanesh, F. et al. Measuring the solubility of tacrolimus in supercritical carbon dioxide (binary and ternary systems), comparing the performance of machine learning models with conventional models. J. Mol. Liq. 415, 126295 (2024).","journal-title":"J. Mol. Liq"},{"key":"51115_CR28","doi-asserted-by":"publisher","first-page":"103034","DOI":"10.1016\/j.jcou.2025.103034","volume":"93","author":"Z Laggoune","year":"2025","unstructured":"Laggoune, Z., Masmoudi, Y., Sajadian, S. A. & Badens, E. Sirolimus solubility in supercritical carbon dioxide: Measurement and modeling. J. CO2 Util. 93, 103034 (2025).","journal-title":"J. CO2 Util."},{"key":"51115_CR29","doi-asserted-by":"publisher","first-page":"106510","DOI":"10.1016\/j.supflu.2024.106510","volume":"218","author":"H Peyrovedin","year":"2025","unstructured":"Peyrovedin, H. et al. Studying the rifampin solubility in supercritical CO2 with\/without co-solvent: Experimental data, modeling and machine learning approach. J. Supercrit Fluids. 218, 106510 (2025).","journal-title":"J. Supercrit Fluids"},{"key":"51115_CR30","doi-asserted-by":"publisher","first-page":"106031","DOI":"10.1016\/j.supflu.2023.106031","volume":"201","author":"NS Ardestani","year":"2023","unstructured":"Ardestani, N. S. et al. Solubility of famotidine in supercritical carbon dioxide: Experimental measurement and thermodynamic modeling. J. Supercrit Fluids. 201, 106031 (2023).","journal-title":"J. Supercrit Fluids"},{"key":"51115_CR31","doi-asserted-by":"publisher","first-page":"113877","DOI":"10.1016\/j.fluid.2023.113877","volume":"573","author":"M Bazaei","year":"2023","unstructured":"Bazaei, M. et al. Measurement and thermodynamic modeling of solubility of Erlotinib hydrochloride, as an anti-cancer drug, in supercritical carbon dioxide. Fluid Phase Equilib. 573, 113877 (2023).","journal-title":"Fluid Phase Equilib."},{"key":"51115_CR32","doi-asserted-by":"publisher","first-page":"113880","DOI":"10.1016\/j.fluid.2023.113880","volume":"574","author":"RS Alwi","year":"2023","unstructured":"Alwi, R. S. et al. Experimental study and thermodynamic modeling of clonazepam solubility in supercritical carbon dioxide. Fluid Phase Equilib. 574, 113880 (2023).","journal-title":"Fluid Phase Equilib."},{"key":"51115_CR33","doi-asserted-by":"publisher","first-page":"105858","DOI":"10.1016\/j.supflu.2023.105858","volume":"194","author":"SA Sajadian","year":"2023","unstructured":"Sajadian, S. A., Peyrovedin, H., Zomorodian, K. & Khorram, M. Using the supercritical carbon dioxide as the solvent of Nystatin: Studying the effect of co-solvent, experimental and correlating. J. Supercrit Fluids. 194, 105858 (2023).","journal-title":"J. Supercrit Fluids"},{"key":"51115_CR34","doi-asserted-by":"publisher","first-page":"106165","DOI":"10.1016\/j.supflu.2023.106165","volume":"206","author":"F Arabgol","year":"2024","unstructured":"Arabgol, F., Amani, M., Ardestani, N. S. & Sajadian, S. A. Experimental and thermodynamic investigation of gemifloxacin solubility in supercritical CO2 for the production of nanoparticles. J. Supercrit Fluids. 206, 106165 (2024).","journal-title":"J. Supercrit Fluids"},{"key":"51115_CR35","doi-asserted-by":"publisher","first-page":"34210","DOI":"10.1039\/D3RA05484E","volume":"13","author":"A Rojas","year":"2023","unstructured":"Rojas, A. et al. Improving and measuring the solubility of favipiravir and montelukast in SC-CO 2 with ethanol projecting their nanonization. RSC Adv. 13, 34210\u201334223 (2023).","journal-title":"RSC Adv."},{"key":"51115_CR36","doi-asserted-by":"crossref","unstructured":"Li, W. TabNet for high-dimensional tabular data: advancing interpretability and performance with feature fusion. in: IET Conference Proceedings CP915 168\u2013173 (IET, 2025).","DOI":"10.1049\/icp.2025.1030"},{"key":"51115_CR37","doi-asserted-by":"publisher","first-page":"2194","DOI":"10.3390\/math13132194","volume":"13","author":"NL Fitriyani","year":"2025","unstructured":"Fitriyani, N. L. et al. A Novel Approach Utilizing Bagging, Histogram Gradient Boosting, and Advanced Feature Selection for Predicting the Onset of Cardiovascular Diseases. Mathematics 13, 2194 (2025).","journal-title":"Mathematics"},{"key":"51115_CR38","doi-asserted-by":"publisher","first-page":"2450081","DOI":"10.1080\/10298436.2025.2450081","volume":"26","author":"J Fu","year":"2025","unstructured":"Fu, J. Cost assessment and strength properties estimation of high-performance concrete using a histogram gradient boosting model integrated with individual and ensemble optimisation algorithm. Int. J. Pavement Eng. 26, 2450081 (2025).","journal-title":"Int. J. Pavement Eng."},{"key":"51115_CR39","doi-asserted-by":"publisher","DOI":"10.22266\/ijies2023.0630.19","author":"PD Kusuma","year":"2023","unstructured":"Kusuma, P. D. & Hasibuan, F. C. Attack-leave optimizer: A new metaheuristic that focuses on the guided search and performs random search as alternative. Int. J. Intell. Eng. Syst. https:\/\/doi.org\/10.22266\/ijies2023.0630.19 (2023).","journal-title":"Int. J. Intell. Eng. Syst."},{"key":"51115_CR40","doi-asserted-by":"publisher","first-page":"521","DOI":"10.3390\/fractalfract9080521","volume":"9","author":"IS Fathi","year":"2025","unstructured":"Fathi, I. S., El-Saeed, A. R., Hassan, G. & Aly, M. Fractional Chebyshev Transformation for Improved Binarization in the Energy Valley Optimizer for Feature Selection. Fractal Fract. 9, 521 (2025).","journal-title":"Fractal Fract."},{"key":"51115_CR41","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1007\/s13042-024-02397-9","volume":"16","author":"S Purbey","year":"2025","unstructured":"Purbey, S., Khan, N., Singh, B. K. & Balan, S. K. Adam energy valley optimization-based routing and RF-Spinalnet enabled medical data classification in IoT. Int. J. Mach. Learn. Cybern. 16, 2377\u20132399 (2025).","journal-title":"Int. J. Mach. Learn. Cybern"},{"key":"51115_CR42","doi-asserted-by":"crossref","unstructured":"Mahmodvand, N., Salehi, M., Yarahmadi, M. & Damia, A. Feature selection optimization in high-dimensional data: A hybrid approach based on botox optimization algorithm and Q-learning. in: 2025 11th International Conference on Web Research (ICWR) 438\u2013445 (IEEE, 2025).","DOI":"10.1109\/ICWR65219.2025.11006196"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51115-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51115-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51115-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:08:17Z","timestamp":1787702897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51115-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,12]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["51115"],"URL":"https:\/\/doi.org\/10.1038\/s41598-026-51115-8","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,12]]},"assertion":[{"value":"21 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"26794"}}