The DOI matches its Crossref record; 40 of the 41 references it cites were found in a registry or an index.
DISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA
Abstract
Artificial neural networks (ANNs) are often used for short term discrete time predictions of experimental data. In this paper we focus on the capability of such nets to correctly identify long term behavior and, in particular, observed bifurcations. As we show, the usual discrete time mapping approach is (precisely because of its discrete nature) often incapable of reproducing observed bifurcation sequences. If the interest is only in periodic or temporally more complicated behavior, a Poincaré map extracted from the experimental time series can be used to circumvent this problem. A complete dynamic picture including bifurcations of steady states can, however, only be captured by a continuous-time model. We present an ANN configuration which couples a “nonlinear principal component” network for data processing (Kramer, 1991, Usui et al., 1990) with a composite ANN based on a simple integrator scheme. This ANN is able to correctly reconstruct the bifurcation diagram of our experimental data. All time series we process stem from the potentiostatic electrodissolution of Cu in phosphoric acid solution. As the applied potential is varied, the electrodissolution rate changes from steady behavior to periodic oscillations, followed by a sequence of period doublings to apparently chaotic motion, and then returns to simple oscillations via a reverse cascade of period doublings.
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“Indeed, hybrid modeling techniques and applications have been growing in number since the early 90's (Psichogios and Ungar 1992; Rico-Martínez et al. 1992; Thompson and Kramer 1994)”
From Perspectives on the integration between first-principles and data-driven modeling (2022) · cites this paper as Rico-Martínez et al. 1992
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Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Self-citationLearning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu, L., Jin, P., Pang, G., Zhang, Z., & Karniadakis, G. E. (2021) · Nature Machine Intelligence · doi:10.1038/s42256-021-00302-5 · Cited by 4,338
Machine Learning for Fluid Mechanics
Brunton, S. L., Noack, B. R., & Koumoutsakos, P. (2020) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010719-060214 · Cited by 3,063
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential EquationsPreprint
Raissi, M. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1801.06637 · Cited by 604
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Vlachas, P. R., Byeon, W., Koumoutsakos, P., Wan, Z. Y., & Sapsis, T. P. (2018) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 424
Metadata
- Authors
- RICO-MARTÍNEZ, R., KRISCHER, K., KEVREKIDIS, I. G., KUBE, M. C., & HUDSON, J. L.
- Affiliations
- a Department of Chemical Engineering , Princeton University , Princeton, NJ, 08544-5263
- Princeton University (US)
- University of Virginia (US)
- Venue
- Chemical Engineering Communications
- Publisher
- Informa UK Limited
- Published
- 1992-11
- Volume
- 118
- Issue
- 1
- Pages
- 25-48
- ISSN
- 0098-6445 (ISSN-L)
- 1563-5201
- OpenAlex
- W1976068300
- Cited by
- 144
- References
- 41
- Citations by year
- 2026: 4 · 2025: 16 · 2024: 20 · 2023: 18 · 2022: 11 · 2021: 10 · 2020: 6 · 2019: 7 · 2018: 5 · 2015: 1
- FWCI
- 3.12
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Chemical Engineering Communications (publishedVersion)
- Funders
- David and Lucile Packard Foundation
- Deutsche Forschungsgemeinschaft
- Defense Advanced Research Projects Agency
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Dynamics and Pattern Formation
- Keywords
- bifurcation diagrams, period doubling, Poincaré map, continuous-time neural networks, artificial neural networks, chaotic oscillations, periodic oscillations, phosphoric acid solutions, potentiostatic measurements, nonlinear signal processing
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