{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:32:13Z","timestamp":1787027533401,"version":"3.56.0"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP26103739"],"award-info":[{"award-number":["AP26103739"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Monitoring the concentration of Total Volatile Fatty Acids (TVFA (M)) is critical for ensuring the stability and efficiency of the Anaerobic Digestion (AD) process although conventional laboratory methods are often time-consuming and hinder real-time control. This study develops soft sensors based on machine learning techniques to predict TVFA (M) levels using readily available parameters such as pH, pCO2, and Total Ammoniacal Nitrogen (TAN). A primary contribution of this work is the comprehensive benchmarking of the proposed approach against current State-of-the-Art (SOTA) deep learning and machine learning models including XGBoost, Random Forest, TorchMLP, and the advanced RealTabPFN-v2.5. Experimental results demonstrate that the RealTabPFN-v2.5 model outperforms other modern algorithms by achieving the highest accuracy with an R2 of 0.889 and the lowest error rate with an RMSE of 0.0079. SHAP (SHapley Additive exPlanations) analysis was employed to interpret the model\u2019s predictions, identifying pH as the most influential factor in TVFA (M) prediction and confirming that the model\u2019s decision-making process aligns with established biological principles. These findings highlight the significant potential of integrating SOTA machine learning models into intelligent monitoring systems for the automation and optimization of biogas production processes.<\/jats:p>","DOI":"10.3390\/a19020127","type":"journal-article","created":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T10:35:37Z","timestamp":1770287737000},"page":"127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Benchmarking Tabular Foundation Models for Total Volatile Fatty Acid Prediction in Anaerobic Digestion"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4089-6337","authenticated-orcid":false,"given":"Bibars","family":"Amangeldy","sequence":"first","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technologies and Artificial Intelligence, Al Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1919-3570","authenticated-orcid":false,"given":"Zhanel","family":"Baigarayeva","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technologies and Artificial Intelligence, Al Farabi Kazakh National University, Almaty 050040, Kazakhstan"},{"name":"LLP \u201cKazakhstan R&D Solutions\u201d, Almaty 050056, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3039-6715","authenticated-orcid":false,"given":"Nurdaulet","family":"Tasmurzayev","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technologies and Artificial Intelligence, Al Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7279-9910","authenticated-orcid":false,"given":"Assiya","family":"Boltaboyeva","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technologies and Artificial Intelligence, Al Farabi Kazakh National University, Almaty 050040, Kazakhstan"},{"name":"LLP \u201cKazakhstan R&D Solutions\u201d, Almaty 050056, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baglan","family":"Imanbek","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technologies and Artificial Intelligence, Al Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marlen","family":"Maulenbekov","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"LLP \u201cKazakhstan R&D Solutions\u201d, Almaty 050056, Kazakhstan"},{"name":"Institute of Automation and Information Technology, Satbayev University, Almaty 050013, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sarsenbek","family":"Zhussupbekov","sequence":"additional","affiliation":[{"name":"Department of Automation and Control, Energo University, Almaty 050013, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0843-8053","authenticated-orcid":false,"given":"Waldemar","family":"Wojcik","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Institute of Electronics and Information Technology, Politechnika Lubelska, 20-618 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mergul","family":"Kozhamberdieva","sequence":"additional","affiliation":[{"name":"Joldasbekov Institute of Mechanics and Engineering, Almaty 050010, Kazakhstan"},{"name":"Faculty of Information Technologies and Artificial Intelligence, Al Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Akzhan","family":"Konysbekova","sequence":"additional","affiliation":[{"name":"JSC \u201cResearch Institute of Cardiology and Internal Diseases\u201d, Almaty 050000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sevillano, C.A., Pesantes, A.A., Pe\u00f1a Carpio, E., Mart\u00ednez, E.J., and G\u00f3mez, X. 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