Comparison of optimizers (Adam, RMSprop, SGD and Adagrad) in a neural network for mineral resource classification: a case study in a copper deposit in Peru

Document Type : Research Paper

Authors

1 Department of Mining Engineering, Faculty of Engineering, National University of Trujillo, Trujillo, Perú,

2 Faculty of Chemical Engineering, National University of the Altiplano, Puno, Perú.

10.22059/ijmge.2025.393902.595243

Abstract

TThis study has compared the performance of various optimizers in mineral resource classification using a multilayer perceptron artificial neural network (MLP) applied to a copper deposit in Peru. The optimizers Adam (Adaptive moment estimation), RMSprop (Root mean square propagation), SGD (Stochastic gradient descent), and Adagrad (Adaptive gradient algorithm) were evaluated to assess their impact on the spatial continuity of block classification. A total of 318,443 blocks were estimated using ordinary kriging, based on key variables including estimated grade, kriging variance, average sample distance, number of composited samples, the kriging Lagrangian, and geological confidence. The methodology involved a mixed multivariable block-by-block clustering using the k-prototypes algorithm, followed by block smoothing through an artificial neural network with different optimizers. Results show that the Adam optimizer achieved the highest overall accuracy (93%), outperforming both RMSprop and SGD (92%), as well as Adagrad (90%). In addition, Adam yielded a more homogeneous classification of mineral resources. It categorized 75,869 blocks as measured (1,395.99 Mt total tonnage, 5.40 Mt fine copper), 120,039 as indicated (2,208.72 Mt and 6.56 Mt fine copper), and 122,535 as inferred (2,254.64 Mt and 6.29 Mt fine copper). In conclusion, the model trained with the Adam optimizer demonstrated superior precision and stability in mineral resource classification, effectively mitigating the “spotty dog effect” and improving the geological coherence of the block model

Keywords

Main Subjects


[1]    Coates, D. (1985). Mineral resources. In Geology and Society, 19–46.
[2]    Dubiński, J. (2013). Sustainable Development of Mining Mineral Resources. Journal of Sustainable Mining, 12(1), 1-6. doi:https://doi.org/10.7424/jsm130102.



[3]    Ericsson, M., Löf, O. (2019). Mining’s contribution to national economies between 1996 and 2016. Mineral Economics, 32, 223-250. doi:https://doi.org/10.1007/s13563-019-00191-6.
[4]    Van Gosen, B., Verplanck, P., Long, K., Gambogi, J., Seal, R. (2014). The Rare-Earth Elements: Vital to Modern Technologies and Lifestyles. US Geological Survey: Reston, VA, USA.
[5]    Henckens, MLCM., Biermann, FHB., Driessen, PPJ. (2019). Mineral resources governance: A call for the establishment of an International Competence Center on Mineral Resources Management. Resour Conserv Recycl, 141, 255-263. doi:https://doi.org/10.1016/j.resconrec.2018.10.033.
[6]    Crowson, PCF. (2011). Mineral reserves and future minerals availability. Mineral Economics, 24, 1-6. doi:https://doi.org/10.1007/s13563-011-0002-9.
[7]    Zerzour, O., Gadri, L., Hadji, R., Mebrouk, F., Hamed, Y. (2021). Geostatistics-Based Method for Irregular Mineral Resource Estimation, in Ouenza Iron Mine, Northeastern Algeria. Geotechnical and Geological Engineering, 39, 3337-3346. doi:https://doi.org/10.1007/s10706-021-01695-1.
[8]    Hartman, HL., Mutmansky, JM. (2002). Introductory mining engineering. Introductory Mining Engineering.
[9]    CIM. (2019). Estimation of mineral resources & mineral reserves best practice guidelines. Canadian Institute of Mining.
[10] JORC Code. (2012). Australasian code for reporting of exploration results, mineral resources and ore reserves. AusIMM 44.
[11]   SAMREC. (2016). The South African code for the reporting of exploration results, mineral resources and mineral reserves (the SAMREC Code. South African Mineral Resource Committee.
[12] Goodfellow, RC., Dimitrakopoulos, R. (2016). Global optimization of open pit mining complexes with uncertainty. Applied Soft Computing Journal, 40, 292-304. doi:https://
doi.org/10.1016/j.asoc.2015.11.038.
[13] Menin, R., Diedrich, C., Reuwsaat, JD., De Paula, WF. (2017). Drilling Grid Analysis for Defining Open-Pit and Underground Mineral Resource Classification through Production Data. Geostatistics Valencia 2016, 271-285. doi:https://doi.org/
10.1007/978-3-319-46819-8_18.
[14] Battalgazy, N., Madani, N. (2019). Categorization of mineral resources based on different geostatistical simulation algorithms: a case study from an iron ore deposit. Nat Resour Res, 28:1329–1351. doi:https://doi.org/10.1007/s11053-019-09474-9.
[15] Afzal, P., Gholami, H., Madani, N., Yasrebi, A., Sadeghi, B. (2023). Mineral Resource Classification Using Geostatistical and Fractal Simulation in the Masjed Daghi Cu–Mo Porphyry Deposit, NW Iran. Minerals, 13(3), 370. doi:https://doi.org/10.3390/min13030370.
[16] Guardiano, E., Parker, H., Isaaks, E. (1995). Prediction of Recoverable Reserves Using Conditional Simulation: A Case Study for the Fort Knox Gold Project, Alaska. Unpublished Technical Report; Mineral Resource Development Inc.: Port Moresby, Papua New Guinea.
[17] Kingston, G. (1977). Reserve classification of identified nonfuel mineral resources by the bureau of mines minerals availability system. Journal of the International Association for Mathematical Geology, 9, 273–279. doi:https://doi.org/
10.1007/BF02272389.
[18] Dimitrakopoulos, R., Chou, C., Godoy, M. (2008). Resource / Reserve Classification with Integrated Geometric and Local Grade Variability Measures. Cosmo 08.
[19] Asghari, O., Esfahani, NM. (2014). Erratum to: A new approach for the geological risk evaluation of coal resources through a geostatistical simulation. Arabian Journal of Geosciences, 7, 839. doi:https://doi.org/10.1007/s12517-013-1262-1.
[20] Peattie, R., Dimitrakopoulos, R. (2013). Forecasting Recoverable Ore Reserves and Their Uncertainty at Morila Gold Deposit, Mali: An Efficient Simulation Approach and Future Grade Control Drilling. Math Geosci, 45, 1005-1020. doi:https://
doi.org/10.1007/s11004-013-9478-x.
[21] Tajvidi, E., Monjezi, M., Asghari, O., Emery, X., Foroughi, S. (2015). Application of joint conditional simulation to uncertainty quantification and resource classification. Arabian Journal of Geosciences, 8, 455-463. doi:https://doi.org/
10.1007/s12517-013-1133-9.
[22] Deustch, C., Leaungthong, O., Ortiz, J. (2007). Case for geometric criteria in resources and reserves classifcation. Trans Soc Min Metall Explor 322.
[23] Dominy, S., Stephenson, P., Annels, A. (2001). Classification and reporting of mineral resources for high-nugget effect gold vein deposits. Exploration and Mining Geology, 10, 215–233.
[24] Dohm, C. (2005). Quantifiable Mineral Resource Classification: A Logical Approach. Geostatistics Banff 2004, 333-342. doi:https://doi.org/10.1007/978-1-4020-3610-1_34.
[25]  Cevik, IS., Leuangthong, O., Caté, A., Ortiz, JM. (2021). On the Use of Machine Learning for Mineral Resource Classification. Min Metall Explor, 38, 2055-2073. doi:https://doi.org/
10.1007/s42461-021-00478-9.
[26]  Stephenson, P., Stoker, P. (2001). Mineral resource and ore reserve estimation - the AusIMM guide to good practice (monograph 23). Miner Eng, 14(9). doi:https://doi.org/
10.1016/s0892-6875(01)80033-9.
[27] Owusu, S. (2019). Critical Review of Mineral Resource Classification Techniques in the Gold Mining Industry. Insights in Mining Science & Technology, 1(3), 555564. doi:https://doi.org/10.19080/imst.2019.01.555564.
[28] Machuca-Mory, D., Deutsch, C. (2006). A Program for Robust Calculation of Drillhole Spacing in Three Dimensions.
[29] Delaunay, B. (1934). Sur la sphere vide. Bulletin de l’Académie des Sciences de l’URSS 6.
[30] Wilde, B., Deutsch, C V. (2010). Data spacing and uncertainty: Quantification and complications. IAMG 2010 Budapest - 14th Annual Conference of the International Association for Mathematical Geosciences.
[31] Emery, X., Ortiz, JM., Rodríguez, JJ. (2006). Quantifying uncertainty in mineral resources by use of classification schemes and conditional simulations. Math Geol, 38, 445-464. doi:https://doi.org/10.1007/s11004-005-9021-9.
[32]  Mucha, J., Wasilewska-Błaszczyk, M., Augus̈cik, J. (2015). Categorization of mineral resources based upon geostatistical estimation of the continuity of changes of resource parameters. Proceedings of IAMG 2015 - 17th Annual Conference of the International Association for Mathematical Geosciences.
[33]  Taghvaeenezhad, M., Shayestehfar, M., Moarefvand, P., Rezaei, A. (2020). Quantifying the criteria for classification of mineral resources and reserves through the estimation of block model uncertainty using geostatistical methods: a case study of Khoshoumi Uranium deposit in Yazd, Iran. Geosystem Engineering, 23(4), 216-225. doi:https://doi.org/
10.1080/12269328.2020.1748524.
[34]  Nowak, M., Leuangthong, O. (2019). Optimal drill hole spacing for resource classification. Mining Goes Digital - Proceedings of the 39th international symposium on Application of Computers and Operations Research in the Mineral Industry, APCOM 2019. doi:https://doi.org/10.1201/9780429320774-14.
[35]  Journel, AG. (1983). Nonparametric estimation of spatial distributions. Journal of the International Association for Mathematical Geology, 15, 445-468. doi:https://doi.org/
10.1007/BF01031292.
[36]  Jelvez, E., Ortiz, J., Morales, N., Askari, H., Nelis, G. (2023). A Multi-Satage Methodology for Long-Term Open-Pit Mine Production Planning under Ore Grade Uncertainty. Mathematics, 11(18).
[37]  Ribeiro, DT., Filho, CGM., de Souza, LE., Costa, JFCL., de Almeida D del PM. (2012). Utilização de critérios geoestatísticos para comparação de malha de sondagem visando à maximização da quantidade de recursos. Revista Escola de Minas, 65(1). doi:https://doi.org/10.1590/S0370-44672012000100016.
[38]  Madani, N. (2020). Mineral resource classification based on uncertainty measures in geological domains. Springer Series in Geomechanics and Geoengineering, 157-164. doi:https://doi.org/10.1007/978-3-030-33954-8_19.
[39]  Wawruch, TM., Betzhold, JF. (2005). Mineral Resource Classification Through Conditional Simulation. Geostatistics Banff 2004, 479-489. doi:https://doi.org/10.1007/978-1-4020-3610-1_48.
[40] Isatelle, F., Rivoirard, J. (2019). Mineral Resources classification of a nickel laterite deposit: Comparison between conditional simulations and specific areas. J South Afr Inst Min Metall, 119(10). doi:https://doi.org/10.17159/2411-9717/660/2019.
[41]  Silva, DSF., Boisvert, JB. (2014). Mineral resource classification: A comparison of new and existing techniques. J South Afr Inst Min Metall 114.
[42] Arik, A. (2002). Comparison of resource classification methodologies with a new approach. 30th International Symposium on the Application of Computers and Operations Research in the Mineral Industry.
[43]  Abzalov, M. (2016). Methodology of the mineral resource classification. Modern Approaches in Solid Earth Sciences, 355-363. doi:https://doi.org/10.1007/978-3-319-39264-6_28.
[44] Caers, J. (2011). Modeling Uncertainty in the Earth Sciences. Modeling Uncertainty in the Earth Sciences. doi:https://doi.org/10.1002/9781119995920.
[45]  Pyrcz, M., Deutsch, C. (2014). Geostatistical Reservoir Modeling (2nd Edition). Oxford University Press.
[46]  Hernández, H. (2024). A semiautomatic multi criteria method for mineral resources classification. Applied Earth Science: Transactions of the Institutions of Mining and Metallurgy, 133, 211–223
[47]  Zuo, M., Wang, T. (2021). Research on reserve classification of solid mineral resources in China and western countries. IOP Conf Ser Earth Environ Sci, 631. doi:https://doi.org/10.1088/1755-1315/631/1/012044.
[48] Duggan, S., Grills, A., Stiefenhofer, J., Thurston, M. (2017). Development of a best-practice mineral resource classification system for the de Beers group of companies. J South Afr Inst Min Metall, 117(12). doi:https://doi.org/10.17159/2411-9717/2017/v117n12a6.
[49] Mohanlal, K., Stevenson, P. (2010). Anglo American Platinum’s approach to resource classification case study—Boschkoppie/Styldrift minewide UG2 project. The 4th International Platinum Conference, Platinum in Transition ‘Boom or Bust.
[50]  Rocha V, A., Bassani, MA. (2023). Practical application of a multi-layer scorecard workflow (MLSW) for comprehensive mineral resource classification. Applied Earth Science: Transactions of the Institute of Mining and Metallurgy. doi:https://doi.org/10.1080/25726838.2023.2244775.
[51]  Ortiz, J., Deutsch, C. (2003). A practical way to summarize uncertainty for classifcation. Centre for computational geostatistics, report fve, University of Alberta 14.
[52]  Glacken, I., Snowden, D. (2001). Mineral resource estimation, In Edwards, A. C.
[53]  Revuelta, MB. (2018). Mineral Resources :From Exploration to Sustainability Assessment.
[54]  Da Rocha, MM., Yamamoto, JK. (2000). Comparison between kriging variance and interpolation variance as uncertainty measurements in the Capanema iron mine, State of Minas Gerais-Brazil. Natural Resources Research, 9, 223-235. doi:https://doi.org/10.1023/a:1010195701968.
[55]  Rossi, ME., Deutsch, C V. (2014). Mineral Resource Estimation. doi:https://doi.org/10.1007/978-1-4020-5717-5.
[56]  Emery, X. (2008). Uncertainty modeling and spatial prediction by multi-Gaussian kriging: Accounting for an unknown mean value. Comput Geosci, 34(11), 1431-1442. doi:https://doi.org/
10.1016/j.cageo.2007.12.011.
[57]  McManus, S., Rahman, A., Horta, A., Coombes, J. (2020). Applied Bayesian Modeling for Assessment of Interpretation Uncertainty in Spatial Domains. Statistics for Data Science and Policy Analysis, 3-13. doi:https://doi.org/10.1007/978-981-15-1735-8_1.
[58]  Riquelme, ÁI., Ortiz, JM. (2021). Uncertainty Assessment over any Volume without Simulation: Revisiting Multi-Gaussian Kriging. Math Geosci, 53, 1375-1405. doi:https://doi.org/10.1007/s11004-020-09907-9.
[59]  Fouedjio, F., Klump, J. (2019). Exploring prediction uncertainty of spatial data in geostatistical and machine learning approaches. Environ Earth Sci, 78(38). doi:https://doi.org/10.1007/s12665-018-8032-z.
[60]  Mery, N., Marcotte, D. (2022). Assessment of Recoverable Resource Uncertainty in Multivariate Deposits Through a Simple Machine Learning Technique Trained Using Geostatistical Simulations. Natural Resources Research, 31, 767-783. doi:https://doi.org/10.1007/s11053-022-10028-9.
[61]  Lindi, OT., Aladejare, AE., Ozoji, TM., Ranta, J-P. (2024). Uncertainty Quantification in Mineral Resource Estimation. Natural Resources Research, 33, 2503–2526.
[62]  Mery, N., Emery, X., Cáceres, A., Ribeiro, D., Cunha, E. (2017). Geostatistical modeling of the geological uncertainty in an iron ore deposit. Ore Geol Rev, 88, 336-351. doi:https://
doi.org/10.1016/j.oregeorev.2017.05.011.
[63]  Stephenson, PR., Allman, A., Carville, DP., Stoker, PT., Mokos, P., Tyrrell, J., Burrows, T. (2006). Mineral resource classification - It’s time to shoot the ’spotted dog’! Australasian Institute of Mining and Metallurgy Publication Series.
[64]  Dumakor-Dupey, NK., Arya, S. (2021). Machine learning—a review of applications in mineral resource estimation. Energies (Basel). doi:https://doi.org/10.3390/en14144079.
[65]  Solomatine, DP., Shrestha, DL. (2009). A novel method to estimate model uncertainty using machine learning techniques. Water Resour Res, 45(12). doi:https://doi.org/
10.1029/2008WR006839.
[66]  Li, T., Xia, Q., Ouyang, Y., Zeng, R., Liu, Q., Li, T. (2024). Prospectivity and Uncertainty Analysis of Tungsten Polymetallogenic Mineral Resources in the Nanling Metallogenic Belt, South China: A Comparative Study of AdaBoost, GBDT, and XgBoost Algorithms. Natural Resources Research, 33, 1049–1071.
[67]  Zhao, J., Chi, H., Shao, Y., Peng, X. (2022). Application of AdaBoost Algorithms in Fe Mineral Prospectivity Prediction: A Case Study in Hongyuntan–Chilongfeng Mineral District, Xinjiang Province, China. Natural Resources Research, 31, 2001–2022.
[68]  Farhadi, S., Tatullo, S., Boveiri Konari, M., Afzal, P. (2024). Evaluating StackingC and ensemble models for enhanced lithological classification in geological mapping. Journal of Geochemical Exploration, 260, 107441. doi: https://doi.org/10.1016/j.gexplo.2024.107441.
[69]  Farhadi, S., Afzal, P., Boveiri Konari, M., Daneshvar Saein, L., Sadeghi, B. (2022). Combination of Machine Learning Algorithms with Concentration-Area Fractal Method for Soil Geochemical Anomaly Detection in Sediment-Hosted Irankuh Pb-Zn Deposit, Central Iran. Minerals, 12(6), 689. doi: https://doi.org/10.3390/min12060689.
[70]  Cotrina, M.A., Marquina, J.J., Riquelme, A.I. (2025). Comparison of Machine Learning Techniques for Mineral Resource Categorization in a Copper Deposit in Peru. Natural Resources Research. doi: https://doi.org/10.1007/s11053-025-10505-x.
[71]  Desai, C. (2020). Comparative Analysis of Optimizers in Deep Neural Networks. Int J Innov Sci Res Technol 5.
[72]  Hassan, E., Shams, MY., Hikal, NA., Elmougy, S. (2023). The effect of choosing optimizer algorithms to improve computer vision tasks: a comparative study. Multimed Tools Appl, 82, 16591-16633. doi:https://doi.org/10.1007/s11042-022-13820-0.
[73]  Nanni, L., Maguolo, G., Lumini, A. (2021). Exploiting Adam-like Optimization Algorithms to Improve the Performance of Convolutional Neural Networks. Computer Science. doi:https://doi.org/https://doi.org/10.48550/arXiv.2103.14689.
[74]  Hernández, H., Alberdi, E., Goti, A., Oyarbide-Zubillaga, A. (2023). Application of the k-Prototype Clustering Approach for the Definition of Geostatistical Estimation Domains. Mathematics, 11(3), 740. doi:https://doi.org/
10.3390/math11030740.
[75]  Bianchi, M., Zheng, C. (2009). SGeMS: A free and versatile tool for three-dimensional geostatistical applications. Ground Water. doi:https://doi.org/10.1111/j.1745-6584.2008.00522.x.
[76]  Remy, N. (2005). S-GeMS: The Stanford Geostatistical Modeling Software: A Tool for New Algorithms Development. doi:https://doi.org/10.1007/978-1-4020-3610-1_89.
[77]  Ali, Rezaei., Hossein, Hassani., Parviz, Moarefvand., Abbas, Golmohammadi. (2019) Grade 3D Block Modeling and Reserve Estimation of the C-North Iron Skarn Ore Deposit, Sangan, NE Iran. Global Journal of Earth Science and Engineering, 6(2019). doi:https://doi.org/10.15377/2409-5710.2019.06.4.
[78]  Heuvelink, GBM., Pebesma, EJ. (2002). Is The Ordinary Kriging Variance A Proper Measure Of Interpolation Error? The fifth international symposium on spatial accuracy assessment in natural resources and environmental sciences.
[79]  da Silva, CZ., Nisenson, J., Boisvert, J. (2022). Grade Control with Ensembled Machine Learning: A Comparative Case Study at the Carmen de Andacollo Copper Mine. Natural Resources Research, 31, 785-800. doi:https://doi.org/10.1007/s11053-022-10029-8.
[80] Tülay., BAYRAMİN, T. (2016). Assessment of ınverse distance weighting (ıdw) ınterpolation on spatial variability of selected soil properties in the Cukurova plain. Tarım Bilimleri Dergisi. doi:https://doi.org/10.1501/tarimbil_0000001396.
[81]  Estrada-Gil, JK., Fernández-López, JC., Hernández-Lemus, E., Silva-Zolezzi, I., Hidalgo-Miranda, A., Jiménez-Sánchez, G., Vallejo-Clemente, EE. (2007). GPDTI: A genetic programming decision tree induction method to find epistatic effects in common complex diseases. Bioinformatics. doi:https://doi.org/
10.1093/bioinformatics/btm205.
[82] Marinos, V., Marinos, P., Hoek, E. (2005). The geological strength index: Applications and limitations. Bulletin of Engineering Geology and the Environment. doi:https://doi.org/10.1007/s10064-004-0270-5.
[83]  Emery, X. (2009). The kriging update equations and their application to the selection of neighboring data. Comput Geosci, 13, 269-280. doi:https://doi.org/10.1007/s10596-008-9116-8.
[84] Adhikary, SK., Muttil, N., Yilmaz, AG. (2016). Genetic Programming-Based Ordinary Kriging for Spatial Interpolation of Rainfall. J Hydrol Eng, 21(2). doi:https://doi.org/
10.1061/(asce)he.1943-5584.0001300.
[85]  Marquina-Araujo, JJ., Cotrina-Teatino, MA., Cruz-Galvez, JA., Noriega-Vidal, EM., Vega-Gonzalez, JA. (2024). Application of Autoencoders Neural Network and K-Means Clustering for the Definition of Geostatistical Estimation Domains. Mathematical Modelling of Engineering Problems, 11,1207–1218.
[86]  Dorman, KS., Maitra, R. (2022). An efficient k-modes algorithm for clustering categorical datasets. Stat Anal Data Min. doi:https://doi.org/10.1002/sam.11546.
[87]  Marquina, J., Cotrina, M., Mamani, J., Noriega, E., Vega, J., Cruz, J. (2024). Copper Ore Grade Prediction using Machine Learning Techniques in a Copper Deposit. Journal of Mining and Environment, 15,1011–1027.
[88] Cotrina, M., Marquina, J., Mamani, J., Arango, S., Gonzalez, J., Ccatamayo, J., Noriega E. (2024). Predictive model using machine learning to determine fuel consumption in CAT-777F mining equipment. Int J Min Miner Eng, 15, 147–160.
[89] Cotrina, M., Marquina, J., Noriega, E., Mamani, J., Ccatamayo, J., Gonzalez, J., Arango, S. (2024). Predicting Open Pit Mine Production using Machine Learning Techniques: A Case Study in Peru. Journal of Mining and Environment, 15, 1345–1355.
[90] Joseph, FJJ., Nonsiri, S., Monsakul, A. (2021). Keras and TensorFlow: A Hands-On Experience. EAI/Springer Innovations in Communication and Computing. doi:https://doi.org/10.1007/978-3-030-66519-7_4.
[91]  Kingma, DP., Ba, JL. (2015). Adam: A method for stochastic optimization. 3rd International Conference on Learning Representations, ICLR 2015 - Conference Track Proceedings.
[92] Elshamy, R., Abu-Elnasr, O., Elhoseny, M., Elmougy, S. (2023). Improving the efficiency of RMSProp optimizer by utilizing Nestrove in deep learning. Sci Rep, 13, 8814.
[93]  Tian, Y., Zhang, Y., Zhang, H. (2023). Recent Advances in Stochastic Gradient Descent in Deep Learning. Mathematics, 11, 682.
[94] Lydia, AA., Francis, FS. (2019). Adagrad - An Optimizer for Stochastic Gradient Descent. INTERNATIONAL JOURNAL OF INFORMATION AND COMPUTING SCIENCE 6.
[95]  Yacouby, R., Axman, D. (2020). Probabilistic Extension of Precision, Recall, and F1 Score for More Thorough Evaluation of Classification Models. doi:https://doi.org/
10.18653/v1/2020.eval4nlp-1.9.
[96]  Dalianis, H. (2018). Evaluation Metrics and Evaluation. Clinical Text Mining. doi:https://doi.org/10.1007/978-3-319-78503-5_6.