The integration of computational intelligence techniques into pharmaceutical wastewater treatment offers promising opportunities to improve process efficiency and minimize operational costs. This study compares the predictive capabilities of Response Surface Methodology (RSM) and Artificial Neural Network (ANN) models in forecasting the rejection efficiencies of caffeine and paracetamol using AFC 40 and AFC 80 nanofiltration (NF) membranes. Experiments were conducted under varying operating conditions, including transmembrane pressure, feed concentration, and flow rate. The predictive performance of both models was evaluated using statistical metrics such as the Coefficient of Determination (R2), Root Mean Square Error (RMSE), Marquardt's Percentage Squared Error Deviation (MPSED), Hybrid fractional error function (HYBRID), and Average Absolute Deviation (AAD). Both models demonstrated strong predictive accuracy, with R2 values of 0.9867 and 0.9832 for RSM and ANN, respectively, in AFC 40 membranes, and 0.9769 and 0.9922 in AFC 80 membranes. While both approaches closely matched the experimental results, the ANN model consistently yielded lower error values and higher R2 values, indicating superior predictive performance. These findings support the application of ANNs as a robust modelling tool in optimizing NF membrane processes for pharmaceutical removal.

Department of Chemical Engineering Nnamdi Azikiwe University Awka 5025 Nigeria

Institute of Environmental and Chemical Engineering Faculty of Chemical Technology University of Pardubice Studentská 573 532 10 Pardubice Czech Republic

Institute of Metallurgy Clausthal University of Technology Robert Koch Straße 42 38678 Clausthal Zellerfeld Germany

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Wilkinson J.L., Boxall A.B.A., Kolpin D.W., Leung K.M.Y., Lai R.W.S., Galbán-Malagón C., Adell A.D., Mondon J., Metian M., Marchant R.A., et al. Pharmaceutical pollution of the world’s rivers. Proc. Natl. Acad. Sci. USA. 2022;119:e2113947119. doi: 10.1073/pnas.2113947119. PubMed DOI PMC

Majumder A., Gupta B., Gupta A.K. Pharmaceutically active compounds in aqueous environment: A status, toxicity and insights of remediation. Environ. Res. 2019;176:108542. doi: 10.1016/j.envres.2019.108542. PubMed DOI

Guo Y., Qi P.S., Liu Y.Z. A Review on Advanced Treatment of Pharmaceutical Wastewater. IOP Conf. Ser. Earth Environ. Sci. 2017;63:12025. doi: 10.1088/1755-1315/63/1/012025. DOI

Obotey Ezugbe E., Rathilal S. Membrane Technologies in Wastewater Treatment: A Review. Membranes. 2020;10:89. doi: 10.3390/membranes10050089. PubMed DOI PMC

Khayet M., Seman M.N.A., Hilal N. Response surface modeling and optimization of composite nanofiltration modified membranes. J. Membr. Sci. 2010;349:113–122. doi: 10.1016/j.memsci.2009.11.031. DOI

Hilal N., Al-Zoubi H., Mohammad A.W., Darwish N.A. Nanofiltration of highly concentrated salt solutions up to seawater salinity. Desalination. 2005;184:315–326. doi: 10.1016/j.desal.2005.02.062. DOI

Anike O., Cuhorka J., Ezeogu N., Mikulášek P. Separation of Antibiotics Using Two Commercial Nanofiltration Membranes—Experimental Study and Modelling. Membranes. 2024;14:248. doi: 10.3390/membranes14120248. PubMed DOI PMC

U.S. Food and Drug Administration, FDA. Don’t Overuse Acetaminophen. [(accessed on 24 October 2024)]; Available online: https://www.fda.gov/consumers/consumer-updates/dont-overuse-acetaminophen.

Ivanova D., Tzvetkov G., Kaneva N. Degradation of Paracetamol in Distilled and Drinking Water via Ag/ZnO Photocatalysis under UV and Natural Sunlight. Water. 2023;15:3549. doi: 10.3390/w15203549. DOI

Emami M.R.S., Amiri M.K., Zaferani S.P.G. Removal efficiency optimization of Pb2+ in a nanofiltration process by MLP-ANN and RSM. Korean J. Chem. Eng. 2021;38:316–325. doi: 10.1007/s11814-020-0698-8. DOI

Alghooneh A., Razavi S.M.A., Mousavi S.M. Nanofiltration treatment of tomato paste processing wastewater: Process modeling and optimization using response surface methodology. Desalination Water Treat. 2016;57:9609–9621. doi: 10.1080/19443994.2015.1041054. DOI

Mojarrad M., Noroozi A., Zeinivand A., Kazemzadeh P. Response surface methodology for optimization of simultaneous Cr (VI) and as (V) removal from contaminated water by nanofiltration process. Environ. Prog. Sustain. Energy. 2018;37:434–443. doi: 10.1002/ep.12704. DOI

Ghaemi N., Madaeni S.S., Daraei P., Rajabi H., Shojaeimehr T., Rahimpour F., Shirvani B. PES mixed matrix nanofiltration membrane embedded with polymer wrapped MWCNT: Fabrication and performance optimization in dye removal by RSM. J. Hazard. Mater. 2015;298:111–121. doi: 10.1016/j.jhazmat.2015.05.018. PubMed DOI

Srivastava A., K A., Nair A., Ram S., Agarwal S., Ali J., Singh R., Garg M.C. Response surface methodology and artificial neural network modelling for the performance evaluation of pilot-scale hybrid nanofiltration (NF) & reverse osmosis (RO) membrane system for the treatment of brackish ground water. J. Environ. Manag. 2021;278:111497. doi: 10.1016/j.jenvman.2020.111497. PubMed DOI

Abadikhah H., Zokaee Ashtiani F., Fouladitajar A. Nanofiltration of oily wastewater containing salt; experimental studies and optimization using response surface methodology. Desalination Water Treat. 2015;56:2783–2796. doi: 10.1080/19443994.2014.966331. DOI

Gasemloo S., Khosravi M., Sohrabi M.R., Dastmalchi S., Gharbani P. Response surface methodology (RSM) modeling to improve removal of Cr (VI) ions from tannery wastewater using sulfated carboxymethyl cellulose nanofilter. J. Clean. Prod. 2019;208:736–742. doi: 10.1016/j.jclepro.2018.10.177. DOI

Rajkumar K., Muthukumar M. Response surface optimization of electro-oxidation process for the treatment of C.I. Reactive Yellow 186 dye: Reaction pathways. Appl. Water Sci. 2017;7:637–652. doi: 10.1007/s13201-015-0276-0. DOI

Koç B., Kaymak-Ertekİn F. Response surface methodology and food processing applications. GIDA-J. Food. 2010;35:63–70.

Aydar A.Y. Statistical Approaches with Emphasis on Design of Experiments Applied to Chemical Processes. Volume 7. InTech; Rijeka, Croatia: 2018. Utilization of response surface methodology in optimization of extraction of plant materials; pp. 157–169.

Jomy J., Prabhu D. Custom design approach of design of experiment as a tool for the optimisation of parameters for corrosion inhibition study of (+)-arabinogalactan on AISI 5140 steel. Corros. Eng. Sci. Technol. 2024;60:62–76. doi: 10.1177/1478422X241272083. DOI

Peydayesh M., Bagheri M., Mohammadi T., Bakhtiari O. Fabrication optimization of polyethersulfone (PES)/polyvinylpyrrolidone (PVP) nanofiltration membranes using Box–Behnken response surface method. RSC Adv. 2017;7:24995–25008. doi: 10.1039/C7RA03566G. DOI

Okonkwo C.P., Ajiwe V.I.E., Obiadi M.C., Okwu M.O., Ayogu J.I. Production of biodiesel from the novel non-edible seed of Chrysobalanus icaco using natural heterogeneous catalyst: Modeling and prediction using Artificial Neural Network. J. Clean. Prod. 2023;385:135631. doi: 10.1016/j.jclepro.2022.135631. DOI

Okwu M.O., Tartibu L.K., Samuel O.D., Omoregbee H.O., Ivbanikaro A.E. Predictive Ability of Response Surface Methodology (RSM) and Artificial Neural Network (ANN) to Approximate Biogas Yield in a Modular Biodigester. Springer International Publishing; Cham, Switzerland: 2021. pp. 202–215.

Al-Abri M., Hilal N. Artificial neural network simulation of combined humic substance coagulation and membrane filtration. Chem. Eng. J. 2008;141:27–34. doi: 10.1016/j.cej.2007.10.005. DOI

Ibrahim M., Haider A., Lim J.W., Mainali B., Aslam M., Kumar M., Shahid M.K. Artificial neural network modeling for the prediction, estimation, and treatment of diverse wastewaters: A comprehensive review and future perspective. Chemosphere. 2024;362:142860. doi: 10.1016/j.chemosphere.2024.142860. PubMed DOI

Addar F.Z., Farah M., Belfaquir M., Tahaikt M., Taky M., Elmidaoui A. Comparison of response surface method and artificial neural network in predicting fluoride removal by nanofiltration. Desalination Water Treat. 2023;297:215–226.

Aydiner C., Demir I., Yildiz E. Modeling of flux decline in crossflow microfiltration using neural networks: The case of phosphate removal. J. Membr. Sci. 2005;248:53–62. doi: 10.1016/j.memsci.2004.07.036. DOI

Abbi B., Touazit A., Gliti O., Igouzal M., Pontie M., Lemenand T., Charki A. Modelling Salt Rejection in Nanofiltration and Reverse Osmosis Membranes Using the Spiegler-Kedem Model Enhanced by a Bio-Inspired Metaheuristic Algorithms: Particle Swarm Optimization and Grey Wolf Optimization. J. Sustain. Dev. Energy Water Environ. Syst.—JSDEWES. 2025;13:1130565. doi: 10.13044/j.sdewes.d13.0565. DOI

Scaffaro R., Gammino M., Maio A. Hierarchically Structured Hybrid Membranes for Continuous Wastewater Treatment via the Integration of Adsorption and Membrane Ultrafiltration Mechanisms. Polymers. 2023;15:156. doi: 10.3390/polym15010156. PubMed DOI PMC

Scaffaro R., Gammino M. 3D wet-electrospun “branch leaf” graphene oxide polycaprolactone fibers structure for enhancing oil-water separation treatment performance in a multi-scale design. Sustain. Mater. Technol. 2025;43:e01200. doi: 10.1016/j.susmat.2024.e01200. DOI

Samuel O.D., Okwu M.O. Comparison of Response Surface Methodology (RSM) and Artificial Neural Network (ANN) in modelling of waste coconut oil ethyl esters production. Energy Sources Part A Recovery Util. Environ. Eff. 2019;41:1049–1061. doi: 10.1080/15567036.2018.1539138. DOI

Silva G.F., Camargo F.L., Ferreira A.L.O. Application of response surface methodology for optimization of biodiesel production by transesterification of soybean oil with ethanol. Fuel Process. Technol. 2011;92:407–413. doi: 10.1016/j.fuproc.2010.10.002. DOI

Onu C.E., Nwabanne J.T., Ohale P.E., Asadu C.O. Comparative analysis of RSM, ANN and ANFIS and the mechanistic modeling in eriochrome black-T dye adsorption using modified clay. S. Afr. J. Chem. Eng. 2021;36:24–42. doi: 10.1016/j.sajce.2020.12.003. DOI

Addar F., Qaid S., Zeggar H., El Hajji H., Tahaikt M., Elmidaoui A., Taky M. Ultrafiltration of Moroccan Valencia orange juice: Juice quality, optimization by custom designs and membranefouling. Sustain. Agri Food Environ. Res.-Discontin. 2023;11 doi: 10.7770/safer-V11N1-art2722. DOI

Zheng Y., Wang A. Removal of heavy metals using polyvinyl alcohol semi-IPN poly (acrylic acid)/tourmaline composite optimized with response surface methodology. Chem. Eng. J. 2010;162:186–193. doi: 10.1016/j.cej.2010.05.027. DOI

Gherasim C.-V., Mikulášek P. Influence of operating variables on the removal of heavy metal ions from aqueous solutions by nanofiltration. Desalination. 2014;343:67–74. doi: 10.1016/j.desal.2013.11.012. DOI

Fang J., Deng B. Arsenic Rejection by Nanofiltration Membranes: Effect of Operating Parameters and Model Analysis. Environ. Eng. Sci. 2014;31:496–506. doi: 10.1089/ees.2013.0460. DOI

Ghorbani A., Bayati B., Drioli E., Macedonio F., Kikhavani T., Frappa M. Modeling of Nanofiltration Process Using DSPM-DE Model for Purification of Amine Solution. Membranes. 2021;11:230. doi: 10.3390/membranes11040230. PubMed DOI PMC

Garcia-Ivars J., Martella L., Massella M., Carbonell-Alcaina C., Alcaina-Miranda M.-I., Iborra-Clar M.-I. Nanofiltration as tertiary treatment method for removing trace pharmaceutically active compounds in wastewater from wastewater treatment plants. Water Res. 2017;125:360–373. doi: 10.1016/j.watres.2017.08.070. PubMed DOI

Onu C.E., Ohale P.E., Ekwueme B.N., Obiora-Okafo I.A., Okey-Onyesolu C.F., Onu C.P., Ezema C.A., Onu O.O. Modeling, optimization, and adsorptive studies of bromocresol green dye removal using acid functionalized corn cob. Clean. Chem. Eng. 2022;4:100067. doi: 10.1016/j.clce.2022.100067. DOI

Arulsudar N., Subramanian N., Murthy R. Comparison of artificial neural network and multiple linear regression in the optimization of formulation parameters of leuprolide acetate loaded liposomes. J. Pharm. Pharm. Sci. 2005;8:243–258. PubMed

Fetimi A., Dâas A., Benguerba Y., Merouani S., Hamachi M., Kebiche-Senhadji O., Hamdaoui O. Optimization and prediction of safranin-O cationic dye removal from aqueous solution by emulsion liquid membrane (ELM) using artificial neural network-particle swarm optimization (ANN-PSO) hybrid model and response surface methodology (RSM) J. Environ. Chem. Eng. 2021;9:105837. doi: 10.1016/j.jece.2021.105837. DOI

Ohale P.E., Onu C.E., Nwabanne J.T., Aniagor C.O., Okey-Onyesolu C.F., Ohale N.J. A comparative optimization and modeling of ammonia–nitrogen adsorption from abattoir wastewater using a novel iron-functionalized crab shell. Appl. Water Sci. 2022;12:193. doi: 10.1007/s13201-022-01713-4. DOI