{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T10:48:07Z","timestamp":1783162087870,"version":"3.54.6"},"reference-count":48,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFB2002300"],"award-info":[{"award-number":["2018YFB2002300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61971399"],"award-info":[{"award-number":["61971399"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018527","name":"Key Research Program of Frontier Science, Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["ZDBS-LY-JSC028"],"award-info":[{"award-number":["ZDBS-LY-JSC028"]}],"id":[{"id":"10.13039\/501100018527","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Reservoir computing (RC) is an attractive paradigm of a recurrent neural network (RNN) architecture, owning to the ease of training and existing neuromorphic implementation. Its simulated performance matches other digital algorithms on a series of benchmarking tasks, such as prediction tasks and classification tasks. In this article, we propose a novel RC structure based on the coupled MEMS resonators with the enhanced dynamic richness to optimize the performance of the RC system both on the system level and data set level. Moreover, we first put forward that the dynamic richness of RC comprises linear dynamic richness and nonlinear dynamic richness, which can be enhanced by adding delayed feedbacks and nonlinear nodes, respectively. In order to set forth this point, we compare three typical RC structures, a single-nonlinearity RC structure with single-feedback, a single-nonlinearity RC structure with double-feedbacks, and the couple-nonlinearity RC structure with double-feedbacks. Specifically, four different tasks are enumerated to verify the performance of the three RC structures, and the results show the enhanced dynamic richness by adding delayed feedbacks and nonlinear nodes. These results prove that coupled MEMS resonators offer an interesting platform to implement a complex computing paradigm leveraging their rich dynamical features.<\/jats:p>","DOI":"10.3390\/s21092961","type":"journal-article","created":{"date-parts":[[2021,4,25]],"date-time":"2021-04-25T02:12:57Z","timestamp":1619316777000},"page":"2961","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Enhancing Performance of Reservoir Computing System Based on Coupled MEMS Resonators"],"prefix":"10.3390","volume":"21","author":[{"given":"Tianyi","family":"Zheng","sequence":"first","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wuhao","family":"Yang","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Sun","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingyin","family":"Xiong","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0996-0011","authenticated-orcid":false,"given":"Zhitian","family":"Li","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5347-0124","authenticated-orcid":false,"given":"Xudong","family":"Zou","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1145\/3065386","article-title":"ImageNet classification with deep convolutional neural networks","volume":"60","author":"Krizhevsky","year":"2017","journal-title":"Commun. ACM"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Feldkamp, L.A., Prokhorov, D.V., Eagen, C.F., and Yuan, F. (1998). Enhanced multi-stream Kalman filter training for recurrent networks. Nonlinear Modeling, Springer.","DOI":"10.1007\/978-1-4615-5703-6_2"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Graves, A., Mohamed, A.-R., and Hinton, G. (2013, January 26\u201331). Speech recognition with deep recurrent neural networks. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638947"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mo, W., Gutterman, C.L., Li, Y., Zussman, G., and Kilper, D.C. (2018, January 11\u201315). Deep neural network based dynamic resource reallocation of BBU pools in 5G C-RAN ROADM networks. Proceedings of the Optical Fiber Communication Conference, San Diego, CA, USA.","DOI":"10.1364\/OFC.2018.Th1B.4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1162\/089976602760407955","article-title":"Real-time computing without stable states: A new framework for neural computation based on perturbations","volume":"14","author":"Maass","year":"2002","journal-title":"Neural Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1109\/72.410363","article-title":"Gradient calculations for dynamic recurrent neural networks: A survey","volume":"6","author":"Pearlmutter","year":"1995","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1126\/science.1091277","article-title":"Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication","volume":"304","author":"Jaeger","year":"2004","journal-title":"Science"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1162\/ARTL_a_00080","article-title":"Locomotion without a brain: Physical reservoir computing in tensegrity structures","volume":"19","author":"Caluwaerts","year":"2013","journal-title":"Artif. Life"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-017-02337-y","article-title":"Reservoir computing using dynamic memristors for temporal information processing","volume":"8","author":"Du","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1038\/s41928-019-0313-3","article-title":"Temporal data classification and forecasting using a memristor-based reservoir computing system","volume":"2","author":"Moon","year":"2019","journal-title":"Nat. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms1476","article-title":"Information processing using a single dynamical node as complex system","volume":"2","author":"Appeltant","year":"2011","journal-title":"Nat. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Degrave, J., Caluwaerts, K., Dambre, J., and Wyffels, F. (October, January 28). Developing an embodied gait on a compliant quadrupedal robot. Proceedings of the 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany.","DOI":"10.1109\/IROS.2015.7354014"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Riou, M., Araujo, F.A., Torrejon, J., Tsunegi, S., Khalsa, G., Querlioz, D., Bortolotti, P., Cros, V., Yakushiji, K., and Fukushima, A. (2017, January 2\u20136). Neuromorphic computing through time-multiplexing with a spin-torque nano-oscillator. Proceedings of the 2017 IEEE International Electron Devices Meeting (IEDM), San Francisco, CA, USA.","DOI":"10.1109\/IEDM.2017.8268505"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"024049","DOI":"10.1103\/PhysRevApplied.12.024049","article-title":"Temporal pattern recognition with delayed-feedback spin-torque nano-oscillators","volume":"12","author":"Riou","year":"2019","journal-title":"Phys. Rev. Appl."},{"key":"ref_15","first-page":"1","article-title":"Role of non-linear data processing on speech recognition task in the framework of reservoir computing","volume":"10","author":"Araujo","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3241","DOI":"10.1364\/OE.20.003241","article-title":"Photonic information processing beyond Turing: An optoelectronic implementation of reservoir computing","volume":"20","author":"Larger","year":"2012","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1038\/srep00287","article-title":"Optoelectronic reservoir computing","volume":"2","author":"Paquot","year":"2012","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Antonik, P., Hermans, M., Haelterman, M., and Massar, S. (2016, January 6\u20139). Towards adjustable signal generation with photonic reservoir computers. Proceedings of the International Conference on Artificial Neural Networks, Barcelona, Spain.","DOI":"10.1007\/978-3-319-44778-0_44"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"22381","DOI":"10.1038\/srep22381","article-title":"Fully analogue photonic reservoir computer","volume":"6","author":"Duport","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms2368","article-title":"Parallel photonic information processing at gigabyte per second data rates using transient states","volume":"4","author":"Brunner","year":"2013","journal-title":"Nat. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1364\/OPTICA.2.000438","article-title":"High-performance photonic reservoir computer based on a coherently driven passive cavity","volume":"2","author":"Vinckier","year":"2015","journal-title":"Optica"},{"key":"ref_22","first-page":"1","article-title":"All-optical reservoir computing on a photonic chip using silicon-based ring resonators","volume":"24","author":"Sciamanna","year":"2018","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"013077","DOI":"10.1103\/PhysRevResearch.3.013077","article-title":"Quantum reservoir computing with a single nonlinear oscillator","volume":"3","author":"Govia","year":"2021","journal-title":"Phys. Rev. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"152132","DOI":"10.1063\/1.5038038","article-title":"Reservoir computing with a single delay-coupled non-linear mechanical oscillator","volume":"124","author":"Dion","year":"2018","journal-title":"J. Appl. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Coulombe, J.C., York, M.C., and Sylvestre, J. (2017). Computing with networks of nonlinear mechanical oscillators. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0178663"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"H Hasan, M., Al-Ramini, A., Abdel-Rahman, E., Jafari, R., and Alsaleem, F. (2020). Colocalized Sensing and Intelligent Computing in Micro-Sensors. Sensors, 20.","DOI":"10.3390\/s20216346"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1109\/JMEMS.2020.2978467","article-title":"Microfabricated Neuroaccelerometer: Integrating Sensing and Reservoir Computing in MEMS","volume":"29","author":"Barazani","year":"2020","journal-title":"J. Microelectromechanical Syst."},{"key":"ref_28","unstructured":"Appeltant, L. (2012). Reservoir Computing Based on Delay-Dynamical Systems. [Ph.D. Thesis, Vrije Universiteit Brussel\/Universitat de les Illes Balears]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"10211","DOI":"10.1364\/OE.26.010211","article-title":"Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection","volume":"26","author":"Hou","year":"2018","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.optcom.2018.10.014","article-title":"Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers","volume":"433","author":"Hou","year":"2019","journal-title":"Opt. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"27431","DOI":"10.1364\/OE.27.027431","article-title":"Reservoir computing system with double optoelectronic feedback loops","volume":"27","author":"Chen","year":"2019","journal-title":"Opt. Express"},{"key":"ref_32","first-page":"40","article-title":"Parallel information processing using a reservoir computing system based on mutually coupled semiconductor lasers","volume":"126","author":"Hou","year":"2020","journal-title":"Appl. Phys. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.cosrev.2009.03.005","article-title":"Reservoir computing approaches to recurrent neural network training","volume":"3","author":"Jaeger","year":"2009","journal-title":"Comput. Sci. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Kovac, A.D., Koall, M., Pipa, G., and Toutounji, H. (2016). Persistent memory in single node delay-coupled reservoir computing. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0165170"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/TNNLS.2014.2311855","article-title":"Delay-based reservoir computing: Noise effects in a combined analog and digital implementation","volume":"26","author":"Soriano","year":"2014","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Thiruvenkatanathan, P., Yan, J., Lee, J.-Y., and Seshia, A. (200, January 21\u201325). Enhancing parametric sensitivity using mode localization in electrically coupled MEMS resonators. Proceedings of the TRANSDUCERS 2009-2009 International Solid-State Sensors, Actuators and Microsystems Conference, Denver, CO, USA.","DOI":"10.1109\/SENSOR.2009.5285444"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.sna.2005.03.038","article-title":"Electrically coupled MEMS bandpass filters: Part I: With coupling element","volume":"122","author":"Pourkamali","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_38","unstructured":"Jaeger, H. (2002). Tutorial on Training Recurrent Neural Networks, Covering BPPT, RTRL, EKF and the\" Echo State Network\" Approach, GMD-Forschungszentrum Informationstechnik."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"8679","DOI":"10.1364\/OE.24.008679","article-title":"Laser dynamical reservoir computing with consistency: An approach of a chaos mask signal","volume":"24","author":"Nakayama","year":"2016","journal-title":"Opt. Express"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1162\/neco.2009.01-09-947","article-title":"Connectivity, dynamics, and memory in reservoir computing with binary and analog neurons","volume":"22","author":"Schrauwen","year":"2010","journal-title":"Neural Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1162\/089976604323057443","article-title":"Real-time computation at the edge of chaos in recurrent neural networks","volume":"16","author":"Bertschinger","year":"2004","journal-title":"Neural Comput."},{"key":"ref_42","first-page":"1","article-title":"Parameters optimization method for the time-delayed reservoir computing with a nonlinear duffing mechanical oscillator","volume":"11","author":"Zheng","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_43","unstructured":"(2021, March 01). Instruments-Developed, Texas. 46-Word Speaker-Dependent Isolated Word Corpus (TI46), NIST Speech Disc, September 1991. Available online: https:\/\/catalog.ldc.upenn.edu\/LDC93S9."},{"key":"ref_44","unstructured":"Lyon, R. (1982, January 3\u20135). A computational model of filtering, detection, and compression in the cochlea. Proceedings of the ICASSP\u201982. IEEE International Conference on Acoustics, Speech, and Signal Processing, Paris, France."},{"key":"ref_45","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"Hinton","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1038\/s42256-019-0110-8","article-title":"Human action recognition with a large-scale brain-inspired photonic computer","volume":"1","author":"Antonik","year":"2019","journal-title":"Nat. Mach. Intell."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Schuldt, C., Laptev, I., and Caputo, B. (2004, January 26). Recognizing human actions: A local SVM approach. Proceedings of the 17th International Conference on Pattern Recognition, Cambridge, UK.","DOI":"10.1109\/ICPR.2004.1334462"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-019-47747-8","article-title":"Hydrodynamic object identification with artificial neural models","volume":"9","author":"Lakkam","year":"2019","journal-title":"Sci. Rep."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/9\/2961\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:51:52Z","timestamp":1760161912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/9\/2961"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,23]]},"references-count":48,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["s21092961"],"URL":"https:\/\/doi.org\/10.3390\/s21092961","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,23]]}}}