{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:41:54Z","timestamp":1760060514292,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,31]],"date-time":"2025-08-31T00:00:00Z","timestamp":1756598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad del Quindio","award":["1054"],"award-info":[{"award-number":["1054"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In this paper, we propose a deep learning-based surrogate model for Multivariate Empirical Mode Decomposition (MEMD) using Long Short-Term Memory (LSTM) networks, aimed at efficiently extracting Intrinsic Mode Functions (IMFs) from electroencephalographic (EEG) signals. Unlike traditional data-driven methods, our approach leverages temporal sequence modeling to learn the decomposition process in an end-to-end fashion. We further enhance the decomposition targets by employing Noise-Assisted MEMD (NA-MEMD), which stabilizes mode separation and mitigates mode mixing effects, leading to better supervised learning signals. Extensive experiments on synthetic and real EEG data demonstrate the superior performance of the proposed LSTM surrogate over conventional feedforward neural networks and standard MEMD-based targets. Specifically, the LSTM trained on NA-MEMD outputs achieved the lowest mean squared error (MSE) and the highest signal-to-noise ratio (SNR), significantly outperforming the feedforward baseline, even when compared using the Power Spectral Density (PSD). These results confirm the effectiveness of combining LSTM architectures with noise-assisted decomposition strategies to approximate nonlinear signal analysis tasks such as MEMD. The proposed surrogate model offers a fast and accurate alternative to classical empirical methods, enabling real-time and scalable EEG analysis.<\/jats:p>","DOI":"10.3390\/info16090754","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T13:01:13Z","timestamp":1756818073000},"page":"754","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Deep LSTM Surrogates for MEMD: A Noise-Assisted Approach to EEG Intrinsic Mode Function Extraction"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1559-3537","authenticated-orcid":false,"given":"Pablo Andres","family":"Mu\u00f1oz-Gutierrez","sequence":"first","affiliation":[{"name":"Electronic Instrumentation Technology Program, Universidad del Quind\u00edo, Armenia 630003, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9050-666X","authenticated-orcid":false,"given":"Diego Fernando","family":"Ramirez-Jimenez","sequence":"additional","affiliation":[{"name":"Electronic Engineering Program, Universidad del Quind\u00edo, Armenia 630003, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6228-2731","authenticated-orcid":false,"given":"Eduardo","family":"Giraldo","sequence":"additional","affiliation":[{"name":"Research Group in Automatic Control, Electrical Engineering Department, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Soler, A., Mu\u00f1oz-Guti\u00e9rrez, P.A., Bueno-L\u00f3pez, M., Giraldo, E., and Molinas, M. (2020). Low-Density EEG for Neural Activity Reconstruction Using Multivariate Empirical Mode Decomposition. Front. Neurosci., 14.","DOI":"10.3389\/fnins.2020.00175"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ymssp.2016.03.010","article-title":"Multivariate empirical mode decomposition and its application to fault diagnosis of rolling bearing","volume":"81","author":"Lv","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zuo, Y., Wang, X., and Zhang, B. (2023, January 28\u201330). Power System Dominant Oscillation Mode Analysis Based on Multivariate Empirical Mode Decomposition. Proceedings of the 2023 3rd International Conference on Energy Engineering and Power Systems (EEPS), Dali, China.","DOI":"10.1109\/EEPS58791.2023.10257119"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1350007","DOI":"10.1142\/S1793536913500076","article-title":"EMD via MEMD: Multivariate Noise-Aided Computation of Standard EMD","volume":"05","author":"Park","year":"2013","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1016\/j.sigpro.2017.08.001","article-title":"Time-frequency decomposition of multivariate multicomponent signals","volume":"142","year":"2018","journal-title":"Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102180","DOI":"10.1016\/j.jocs.2023.102180","article-title":"Efficient GPU implementation of the multivariate empirical mode decomposition algorithm","volume":"74","author":"Wang","year":"2023","journal-title":"J. Comput. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8691","DOI":"10.1109\/ACCESS.2017.2705136","article-title":"GPU-Accelerated Multivariate Empirical Mode Decomposition for Massive Neural Data Processing","volume":"5","author":"Mujahid","year":"2017","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"132457","DOI":"10.1016\/j.jhydrol.2024.132457","article-title":"Deep Bayesian surrogate models with adaptive online sampling for ensemble-based data assimilation","volume":"649","author":"Zhang","year":"2025","journal-title":"J. Hydrol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103588","DOI":"10.1016\/j.advengsoft.2023.103588","article-title":"DNN surrogate model based cable force optimization for cantilever erection construction of large span arch bridge with concrete filled steel tube","volume":"189","author":"Zhou","year":"2024","journal-title":"Adv. Eng. Softw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"132697","DOI":"10.1016\/j.jhydrol.2025.132697","article-title":"Forecasting Multi-Step-Ahead Street-Scale Nuisance Flooding using a seq2seq LSTM Surrogate Model for Real-Time Application in a Coastal-Urban City","volume":"656","author":"Roy","year":"2025","journal-title":"J. Hydrol."},{"key":"ref_11","first-page":"903","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. London. Ser. Math. Phys. Eng. Sci."},{"key":"ref_12","first-page":"1291","article-title":"Multivariate empirical mode decomposition","volume":"466","author":"Rehman","year":"2010","journal-title":"Proc. R. Soc. Math. Phys. Eng. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1109\/TSP.2011.2106779","article-title":"Filter Bank Property of Multivariate Empirical Mode Decomposition","volume":"59","author":"Mandic","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jcp.2018.02.037","article-title":"Non-intrusive reduced order modeling of nonlinear problems using neural networks","volume":"363","author":"Hesthaven","year":"2018","journal-title":"J. Comput. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110013","DOI":"10.1016\/j.asoc.2023.110013","article-title":"DNN surrogates for turbulence closure in CFD-based shape optimization","volume":"134","author":"Kontou","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_16","first-page":"20170844","article-title":"Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks","volume":"474","author":"Vlachas","year":"2018","journal-title":"Proc. R. Soc. Math. Phys. Eng. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"108553","DOI":"10.1016\/j.compchemeng.2023.108553","article-title":"Bayesian LSTM framework for the surrogate modeling of process engineering systems","volume":"181","year":"2024","journal-title":"Comput. Chem. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"115778","DOI":"10.1109\/ACCESS.2020.3004173","article-title":"Tracking of Flexible Brush Tip on Real Canvas: Silhouette-Based and Deep Ensemble Network-Based Approaches","volume":"8","author":"Joolee","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","unstructured":"Nasreddine, W. (2025, July 30). Epileptic EEG Dataset. Available online: https:\/\/data.mendeley.com\/datasets\/5pc2j46cbc\/1."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/9\/754\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:36:31Z","timestamp":1760034991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/9\/754"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,31]]},"references-count":19,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["info16090754"],"URL":"https:\/\/doi.org\/10.3390\/info16090754","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2025,8,31]]}}}