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Couturier R, Dionis E, Guérin S, Guyeux C, Sugny D. Characterization of a Driven Two-Level Quantum System by Supervised Learning. ENTROPY (BASEL, SWITZERLAND) 2023; 25:446. [PMID: 36981334 PMCID: PMC10048282 DOI: 10.3390/e25030446] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Revised: 02/26/2023] [Accepted: 02/27/2023] [Indexed: 06/18/2023]
Abstract
We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.
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Affiliation(s)
- Raphaël Couturier
- Université de Franche-Comté, CNRS, Institut FEMTO-ST, F-90000 Belfort, France
| | - Etienne Dionis
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS-Université de Bourgogne, 9 Av. A. Savary, BP 47 870, CEDEX, F-21078 Dijon, France
| | - Stéphane Guérin
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS-Université de Bourgogne, 9 Av. A. Savary, BP 47 870, CEDEX, F-21078 Dijon, France
| | - Christophe Guyeux
- Université de Franche-Comté, CNRS, Institut FEMTO-ST, F-90000 Belfort, France
| | - Dominique Sugny
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS-Université de Bourgogne, 9 Av. A. Savary, BP 47 870, CEDEX, F-21078 Dijon, France
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Binti Hasan NAS, Balasubramanian P. Exact Solution for the Kinetic Equations of First Order Reversible Reaction Systems through Flow Graph Theory Approach. Ind Eng Chem Res 2013. [DOI: 10.1021/ie303501t] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nurul Amira Syakilla Binti Hasan
- Chemical
Engineering Department, Universiti Teknologi
PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan,
Malaysia
| | - Periyasamy Balasubramanian
- Chemical
Engineering Department, Universiti Teknologi
PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan,
Malaysia
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Spegazzini N, Siesler HW, Ozaki Y. Activation and Thermodynamic Parameter Study of the Heteronuclear C═O···H–N Hydrogen Bonding of Diphenylurethane Isomeric Structures by FT-IR Spectroscopy Using the Regularized Inversion of an Eigenvalue Problem. J Phys Chem A 2012; 116:7797-808. [DOI: 10.1021/jp211968s] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Nicolas Spegazzini
- Department of Chemistry, School of
Science and Technology, Kwansei Gakuin University, Gakuen 2-1, Sanda, Hyogo 669-1337, Japan
| | - Heinz W. Siesler
- Department of Physical Chemistry, University of Duisburg-Essen, D 45117 Essen, Germany
| | - Yukihiro Ozaki
- Department of Chemistry, School of
Science and Technology, Kwansei Gakuin University, Gakuen 2-1, Sanda, Hyogo 669-1337, Japan
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Spegazzini N, Siesler HW, Ozaki Y. Modeling of Isomeric Structure of Diphenyl Urethane by FT-IR Spectroscopy During Synthesis from Phenylisocyanate and Phenol as an Inverse Kinetic Problem. J Phys Chem A 2011; 115:8832-44. [DOI: 10.1021/jp202227d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nicolas Spegazzini
- Department of Chemistry, School of Science and Technology, Kwansei Gakuin University, Gakuen 2-1, Sanda, Hyogo 669-1337, Japan
| | - Heinz W. Siesler
- Department of Physical Chemistry, University of Duisburg-Essen, D 45117 Essen, Germany
| | - Yukihiro Ozaki
- Department of Chemistry, School of Science and Technology, Kwansei Gakuin University, Gakuen 2-1, Sanda, Hyogo 669-1337, Japan
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Feng XJ, Rabitz H, Turinici G, Le Bris C. A closed-loop identification protocol for nonlinear dynamical systems. J Phys Chem A 2007; 110:7755-62. [PMID: 16789759 DOI: 10.1021/jp056189o] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency.
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Affiliation(s)
- Xiao-jiang Feng
- Department of Chemistry, Princeton University, New Jersey 08544, USA
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Bieniasz LK, Rabitz H. Extraction of Parameters and Their Error Distributions from Cyclic Voltammograms Using Bootstrap Resampling Enhanced by Solution Maps: Computational Study. Anal Chem 2006; 78:8430-7. [PMID: 17165836 DOI: 10.1021/ac061167z] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The conventional determination of model parameter errors in least-squares regression of experimental cyclic voltammetric data assumes validity of local approximations (e.g., linearization) in the parameter space and normal distributions of the data and parameter errors. Such assumptions may not always be satisfied in practice. Bootstrap resampling techniques present a more universally applicable approach to error estimation, which until now has not been used in cyclic voltammetric studies, owing to the high costs of the required voltammogram simulations. We demonstrate that the burden of computing voltammograms can be significantly reduced by the use of high-dimensional model representation (HDMR) solution mapping techniques, thereby making it feasible to apply the bootstrap data analysis in cyclic voltammetry. We perform computational experiments with bootstrap resampling, enhanced by HDMR maps, for a typical cyclic voltammetric model (i.e., the Eqrev Cirr Eqrev reaction mechanism at a planar macroelectrode under semi-infinite, pure diffusion transport conditions). The experiments reveal that the bootstrap distributions of the estimated parameters provide a satisfactory quantification of the parameter errors and can also be used for detecting statistical correlations of the parameters.
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Affiliation(s)
- Lesław K Bieniasz
- Institute of Physical Chemistry of the Polish Academy of Sciences, Department of Electrochemical Oxidation of Gaseous Fuels, ul. Zagrody 13, 30-318 Cracow, Poland
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Shenvi N, Geremia JM, Rabitz H. Efficient chemical kinetic modeling through neural network maps. J Chem Phys 2006; 120:9942-51. [PMID: 15268013 DOI: 10.1063/1.1718305] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An approach to modeling nonlinear chemical kinetics using neural networks is introduced. It is found that neural networks based on a simple multivariate polynomial architecture are useful in approximating a wide variety of chemical kinetic systems. The accuracy and efficiency of these ridge polynomial networks (RPNs) are demonstrated by modeling the kinetics of H(2) bromination, formaldehyde oxidation, and H(2)+O(2) combustion. RPN kinetic modeling has a broad range of applications, including kinetic parameter inversion, simulation of reactor dynamics, and atmospheric modeling.
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Affiliation(s)
- Neil Shenvi
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
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Hayes MY, Li B, Rabitz H. Estimation of Molecular Properties by High-Dimensional Model Representation. J Phys Chem A 2005; 110:264-72. [PMID: 16392864 DOI: 10.1021/jp053197w] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Additivity models have been widely employed to approximate unknown molecular properties based on previously measured or calculated data for similar molecules. This paper proposes an improved formulation of additivity, which is based on high-dimensional model representation (HDMR). HDMR is a general function-mapping technique that expresses the output of a multivariate system in terms of a hierarchy of cooperative effects among its input variables. HDMR rests on the general observation that, for many physical systems, only relatively low-order input variable cooperativity is significant. A molecule is expressed as a multivariate system by defining binary-valued input variables corresponding to the presence or absence of a chemical bond, with the molecular property as the output. Conventional additivity decomposes a molecular property into contributions from nonoverlapping subcomponents of fixed size. On the other hand, HDMR decomposes a molecular property into the exact contributions from the full hierarchy of its variable-sized subcomponents and contains additivity as a special case. The complete hierarchical structure of HDMR can in many cases lead to a much more accurate estimate than conventional additivity. Also, when full group additivity is not possible, HDMR gives an expression for a lower-order approximation for the missing group additivity value, greatly expanding the scope of HDMR compared to additivity. The component terms in an HDMR approximation have well-defined physical significance. Moreover, HDMR gives an exact expression for the truncation error in any given HDMR approximation, also with a well-defined physical significance. The HDMR model is tested for the enthalpy of formation of a broad range of organic molecules, and its advantages over additivity are illustrated.
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Affiliation(s)
- Michael Y Hayes
- Department of Chemistry, Princeton University, 207 Frick Laboratory, Princeton, New Jersey 08544-1009, USA
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Leistritz L, Suesse T, Haueisen J, Hilgenfeld B, Witte H. Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity. ACTA ACUST UNITED AC 2005; 99:58-65. [PMID: 16039101 DOI: 10.1016/j.jphysparis.2005.06.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.
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Affiliation(s)
- L Leistritz
- Institute of Medical Statistics, Computer Sciences and Documentation, Friedrich Schiller University Jena, Bachstr. 18, D-07740 Jena, Germany.
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Tang W, Zhang L, Linninger AA, Tranter RS, Brezinsky K. Solving Kinetic Inversion Problems via a Physically Bounded Gauss−Newton (PGN) Method. Ind Eng Chem Res 2005. [DOI: 10.1021/ie048872n] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Weiyong Tang
- Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
| | - Libin Zhang
- Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
| | - Andreas A. Linninger
- Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
| | - Robert S. Tranter
- Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
| | - Kenneth Brezinsky
- Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
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