High dimensional model representations

Journal of Physical Chemistry A

Volumn 105, Issue 33, 2001, Pages

  Li, Genyuan ^a   Rosenthal, Carey ^b   Rabitz, Herschel ^a  

^a PRINCETON UNIVERSITY   (United States)

^b DREXEL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HIGH DIMENSIONAL MODELS;

ATMOSPHERIC RADIATION; ERROR ANALYSIS; MATHEMATICAL MODELS; MOLECULES; PROBLEM SOLVING; QUANTUM THEORY; REACTION KINETICS; SOLAR RADIATION;

PHYSICAL CHEMISTRY;

EID: 42849083056     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp010450t     Document Type: Review

References (45)

1. Diaconis, P.; Shahshahani, M. On Nonlinear Functions of Linear Combinations. SIAM J. Sci. Stat. Comput. 1984, 5, 175-191.
2. Friedman, J.; Stuetzle, W. Projection Pursuit Regression. J. Am. Stat. Assoc. 1981, 76, 817-823.
3. Huber, P. Projection Persuit. Ann. Statist. 1985, 13, 435-525.
4. Stone, C. J. Additive Regression and Other Nonparametric Models. Ann. Stat. 1985, 13, 689-705.
5. Parker, D. Learning Logic. Working paper No. 47; Center for Computational Research in Economics and Management Science, Massachusetts Institute of Technology: Cambridge, MA, 1985.
6. Piggio, T.; Girosi, F. Networks for Approximation and Learning. Proc. IEEE 1990, 78, 1481-1497.
7. Girosi; F.; Poggio, T. Representation Properties of Networks: Kolmogorov's Theorem is Irrelevant. Neural Comput. 1989, 1, 465-469.
8. Lorentz, G. G.; Golitschek, M. V.; Makovoz, Y. Constructive Approximation; Springer: New York, 1996.
9. Frisch, H. L.; Borzi, C.; Ord, G.; Percus, J. K.; Williams, G. O. Approximate Representation of Functions of Several Variables in Terms of Functions of One Variable. Phys. Rev. Lett. 1989, 63, 927-929.
10. Gorban, A. N. Approximation of Continuous Functions of Several Variables by an Arbitrary Nonlinear Continuous Function of One Variable, Linear Functions, and Their Superpositions. Appl. Math. Lett. 1998, 11, 45-49.
11. Rabitz, H.; Alis, O. F.; Shorter, J.; Shim, K. Efficient Input-output Model Representations. Comput. Phys. Commun. 1999, 117, 11-20.
12. Alis, O.; Rabitz, H. General Foundations of High Dimensional Model Representations. J. Math. Chem. 1999, 25, 197-233.
13. 1-β-γ Alloys. Phys. Rev. B. 1998, 58, 1940-1946.
14. Shorter, J.; Precila, C. Ip.; Rabitz, H. An Efficient Chemical Kinetics Solver using High Dimensional Model Representations. J. Phys. Chem. A. 1999, 103, 7192-7198.
15. Alis, O.; Rabitz, H. Efficient Implementation of High Dimensional Model Representations. In Mathematical and Statistical Methods for Sensitivity Analysis; Saltelli, A., Ed.; John Wiley and Sons: New York, 2000.
16. Ghanem, R. G.; Spanos, P. D. Stochastic Finite Elements: A Spectral Approach; Springer-Verlag: New York, 1991.
17. Wang, S.; Jaffe, P. R.; Li, G.; Wang, S. W.; Rabitz, H. Simulating Bioremediation of Uranium-Contaminated Aquifers; Uncertainty Assessments of Model Parameters. J. Contam. Hydrol. 2001. Submitted for publication.
18. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in FORTRAN, Cambridge University Press: New York, 1992; p 299-319.
19. Gordon, W. J. Distributive Lattices and the Approximation of Multivariate Functions. In Proceedings of the Symposium of the Approximation with Special Emphasis on Spline Functions; Schoenberg, I. J., Ed.; Academic Press: New York, 1969; pp 223-277.
20. Sobol, I. M. Sensitivity Estimates for Nonlinear Mathematical Models. Mathematical Modelling and Computational Experiments 1993, 1, 407-414.
21. Hastie, T. J.; Tibshirani, R. J. Generalized Additive Models; Chapman and Hall: London, 1990; p 112.
22. Hollebeek, T.; Ho, T. S.; Rabitz, H. J. Chem. Phys. 1997, 106, 7223-7227.
23. Li, G.; Wang, S. W.; Rabitz, H.; Rosenthal, C. High Dimensional Model Representations Generated from Low Dimensional Data Samples I: mp-Cut-HDMR. J. Math. Chem. 2001. In press.
24. Wang, S. W.; Levy, H., II; Li, G.; Rabitz, H. Fully Equivalent Operational Models generated by a monomial preconditioning method for Atmospheric Chemical Kinetics within Global Chemistry-transport Models. J. Geophys. Res. 2000. Submitted for publication.
25. Rabitz, H.; Pierce, L.; Li, B.; Carey, J. Mapping Protein Functionality: Revealing Patterns in High-Dimensional Sequence Space. Science 2000, Submitted for publication.
26. 1-y-z. J. Appl. Phys. 1999, 85, 7705-7715.
27. Rabitz, H.; Shim, K. Multicomponent Semiconductor Material Discovery Guided by a Generalized Correlated Function Expansion. J. Chem. Phys. 1999, 111, 10640-10651.
28. Sandberg, W. S.; Terwilliger, T. C. Engineering Multiple Properties of a Protein by Combinatorial Mutagenesis. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 8367-8371.
29. Sandberg, W. S.; Schlunk, P. M.; Zabin, H. B.; Terwilliger, T. C. Relationship between in Vivo Activity and in Vitro Measures of Function and Stability of a Protein. Biochem. 1995, 34, 11970-11978.
30. Shenvi, N.; Geremia, J. M.; Rabitz, H. A Genetic Algorithm Solution to the Substituent Ordering Problem in Library Optimization. Manuscript in preparation.
31. Geremia, J. M.; Rabitz, H.; Rosenthal, C. Constructing Global Functional Maps between Molecular Potentials and Quantum Observables. J. Chem. Phys. 2001. In press.
32. Geremia, J. M.; Rabitz, H. A Global, Nonlinear Method for Extracting Potentials from Spectral Data: The Singlet and Triplet States of Na2. J. Chem. Phys. 2001. Submitted for publication.
33. Shenvi, N.; Geremia, J. M.; Rabitz, H. Nonlinear Kinetics Parameter Identification by HDMR Map Inversion. Manuscript in preparation.
34. Geremia, J. M.; Rabitz, H. A Global, Nonlinear Algorithm for Inverting Quantum Mechanical Observations. Phys. Rev. A 2001. Submitted for publication.
35. Geremia, J. M.; Rabitz, H. The Ar-HCl Potential Energy Surface From a Global Map-Facilitated Inversion of State-to-State Rotationally Resolved Differential Scattering Cross Sections and Rovibrational Spectral Data. J. Chem. Phys. 2001. Submitted for publication.
36. Geremia, J. M.; Zhu, W.; Rabitz, H. Incorporating Physical Implementation Concerns into Closed Loop Quantum Control Experiments. J. Chem. Phys. 2000, 113, 10841-10848.
37. Geremia, J. M.; Weiss, E.; Rabitz, H. Achieving the Laboratory Control of Quantum Dynamics Phenomena Using Nonlinear Functional Maps. Chem. Phys. 2001. In press.
38. Geremia, J. M.; Rabitz, H. An Efficient Optimal Identification Algorithm: The Synthesis of Quantum Optimal Control and Map-Facilitated Inversion. Chem. Phys. 2001. To be submitted.
39. Biteen, J.; Geremia, J. M.; Rabitz, H. Closed-Loop Quantum Control Utilizing Time Domain Maps. Manuscript in preparation.
40. Biteen, J.; Geremia, J. M.; Rabitz, H. Quantum Optimal Quantum Control Field Design Using Logarithmic Maps. Manuscript in preparation.
41. Wang, S. W.; Levy, H., II; Li, G.; Rabitz, H. Fully Equivalent Operational Models for Atmospheric Chemical Kinetics within Global Chemistry-transport Models. J. Geophys. Res. 1999, 104, D23, 30417-30426.
42. Faliks, A.; Yetter, R. A.; Floudas, C. A.; Bernasek, S. L.; Fransson, M.; Rabitz, H. Optimal Control of Catalytic Methanol Conversion to Formaldehyde. J. Phys. Chem. A 2000. In press.
43. Li, G.; Wang, S. W.; Rabitz, H.; Wang, S. K.; Jaffe, P. Global Uncertainty Assessments by High Dimensional Model Representations (HDMR). Chem. Eng. Sci. 2001. To be submitted.
44. Shorter, J.; Rabitz, H. Radiation Transport Simulation by Means of a Fully Equivalent Operational Model, Geophys. Res. Lett. 2000, 27, 3485-3488.
45. Faliks, A.; Alis, O.; Rabitz, H. A Nonparametric Approach to Pricing Derivative Securities via High Dimensional Model Representations. Manuscript in preparation.