Research
Potential of Mean Force (PMF)
The PMF is an energy representation of the probability of being in a state, which is defined by a function of the atomic positions. From the PMF expected transition times between states can be calculated as well as binding energies.
This project entailed the study of the different methods for calculating the PMF of a molecule. Focus is placed on the Weighted Histogram Analysis Method (WHAM) and the Adaptive Biasing Force (ABF) method recently developed by Eric Darve and others. The primary motivation was to understand the mechanics and implementation of the different methods. Both methods were implemented using the NAMD 2.5 TCL interface and custom post processing programs. A presentation I gave on the WHAM method for CS491MH can be found on my UIUC projects page.
Recently we wrote a paper on using the weighted residual method (WRM) to compute the PMF. One motivation behind this work was to see if we could reduce the statistical problems with sampling in bins of decreasing size. This led to the consideration of higher order approximations to the PMF, both in terms of a global spectral (GS) approximation and a spectral element (SE) approximation. This approach has the advantage that it allows p-refinement which leads to faster convergence rate in terms of the truncation (not statistical) error. These methods do indeed reduce the statistical error arising from a small bin size, indeed for GS approximations there is only one large bin. However, the statistical error still remains as averages of basis functions are needed to compute the approximation. Regardless, the convergence rate still goes as 1/sqrt(N) where N is the number of samples. The GS approximations appear to have an advantage in that they are more robust in the number of degrees of freedom chosen, meaning the parameterization of the solution space makes less difference. In addition to benefits gained from the higher order approximation, it was possible to write both TI and a single window direct histogram approach as a weighted residual method. This seems to unify the two, at least to some degree. Finally, it is possible to handle multiple windows in the WRM by using an appropriately chosen weight function. For more details I refer you to the paper.
Poisson Boltzmann Equation (PBE)
The PBE computes the electrostatic effects of an implicit solvent in a molecular simulation. The goal is to find rapid solution techniques, accurate enough to model the effect of the solvent on a MD simulation without having to explicitly represent the water molecules.
Publications
- E. C. Cyr, Numerical Methods for Computing the Free-Energy of Coarse-Grained Molecular Systems, PhD Thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, November 2008. (Abstract)
- E. C. Cyr and S. D. Bond, Using the Method of Weighted Residuals to Compute Potentials of Mean Force, Journal of Computational Physics, 225:714-729, 2007. (Abstract/Text)
- Giunta, A.A., Swiler, L.P., Brown, S.L., Eldred, M.S., Richards, M.D., and Cyr, E.C. , "The Surfpack Software Library for Surrogate Modeling of Sparse Irregularly Spaced Multidimensional Data," paper AIAA-2006-7049 in the Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA, Sept. 6-8, 2006. (Abstract/Text)
- C.L. Cox, E.C. Cyr, E.B. Duffy, J.B. von Oehsen, and B.A. Malloy, An Efficient C++ Finite Element Viscoelastic Flow Code Exploiting Generative Programming Techniques, Luxfem 2003 International Conference on Finite element for process, Luxembourg, Nov. 13-14, 2003.
- J.B. von Oehsen, C.L. Cox, E.C. Cyr, and B.A. Malloy, Using Design Patterns and XML to Construct an Extensible Finite Element System, Proceedings of the International Conference on Computational Science, Part III, April 21-24, 2002, Lecture Notes in Computer Science, 2331, Springer-Verlag 2002, pp. 735-744. (Abstract/Text)
- J.B. von Oehsen, E.C. Cyr, C.L. Cox, and B.A. Malloy, An Internet-Accessible Software Package for Modeling Viscoelastic Flow, Internet Accessible Mathematical Computation 2002 Workshop, Lille France, July 7, 2002. (Abstract/Text)
Presentations
- Goal-Oriented Adaptivity for the Poisson-Boltzmann Equation West Lafayette, IN, Purdue University, Computational and Applied Mathematics Seminar, December 5, 2008 (Presentation).
- Nonequilibrium Weighted Residual Approximations to the Potential of Mean Force, Banff, AB, Canada, BIRS: Mathematical and Numerical Methods for Free Energy Calculations in Molecular Systems, June 16, 2008 (Poster).
- Goal-Oriented Adaptivity for the Poisson-Boltzmann Equation, Urbana, IL, UIUC CSE Symposium, April 15, 2008 (Presentation).
- A Comparison of Maximum Likelihood and Weighted Residual Approximations to the Potential of Mean Force, Minneapolis, MN, IMA Summer Program: Classical and Quantum Approaches in Molecular Modeling Engineering, July 24, 2007 (Poster).
- A Numerical Study of the Regularized Poisson-Boltzmann Equation on Structured Grids, Urbana, IL, UIUC CSE Symposium, April 10, 2007 (Presentation).
- A Comparison of Maximum Likelihood and Weighted Residual Approximations to the Potential of Mean Force, Costa Mesa, CA, SIAM CSE, February 2007 (Presentation).
Software Projects
I have at some point contributed to the following software projects, although, they have certainly evolved far beyond my contributions. Here they are for reference
- CAEFF FEM Software: Collaborated with E. Duffy and J.B. von Oehsen in the Spring and summer of 2003 on (very) early software design of the FEM portion of the code. It seems to have grown a lot since I left!
- Surfpack: In the summer of 2002 while an intern under the guidance of A. Giunta at SNL-ABQ, I participated in the initial development of this software use for surface fitting methods. In 2006 the software was presented at a conference along with a paper.
Last updated December 12, 2008