Bayesian Uncertainty Quantification for Particle-Based Simulation of Lipid Bilayer Membranes
A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to Bayesian uncertainty quantification using transitional Markov chain Monte Carlo (TMCMC) is extremely parallelizable and has opened the door to a variety of applications which were previously too computationally intensive to be practical. In this chapter, we first explore the machinery required to understand and implement Bayesian uncertainty quantification using TMCMC. We then describe dissipative particle dynamics, a computational particle simulation method which is suitable for modeling biological structures on the subcellular level, and develop an example simulation of a lipid membrane in fluid. Finally, we apply the algorithm to a basic model of uncertainty in our lipid simulation, effectively recovering a target set of parameters (along with distributions corresponding to the uncertainty) and demonstrating the practicality of Bayesian uncertainty quantification for complex particle simulations.
Part of this research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University. CB was partially supported by the NSF through grant DMS-1148284. AR was supported in part by the Simons Foundation under Collaboration Grant 359575. DS acknowledges support from NSF under awards 1409577 and 1505878. KL and AM were partially supported by the NSF through grants DMS-1521266 and DMS-1552903. The authors gratefully acknowledge discussions with Petros Koumoutsakos and his group during the preparation of this chapter. AM thanks the Computational Science and Engineering Laboratory at ETH Zürich for their warm hospitality during a sabbatical semester.
- 4.D. Barber, Bayesian Reasoning and Machine Learning. (Cambridge University Press, 2012)Google Scholar
- 6.Z. Chen, K. Larson, C. Bowman, P. Hadjidoukas, C. Papadimitriou, P. Koumoutsakos, and A. Matzavinos: Data-driven prediction and origin identification of epidemics in population networks. Submitted. (2018)Google Scholar
- 7.B. Efron and T. Hastie, Computer Age Statistical Inference: Algorithms, Evidence, and Data Science. (Cambridge University Press, 2016)Google Scholar
- 18.G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation. (Springer, New York, 2005)Google Scholar
- 21.O.P. Le Maître and O.M. Knio, Spectral Methods for Uncertainty Quantification. (Springer, New York, 2010)Google Scholar
- 30.P. Salamon, P. Sibani, and R. Frost, Facts, Conjectures, and Improvements for Simulated Annealing. (SIAM, 2002)Google Scholar
- 32.R. Smith, Uncertainty Quantification: Theory, Implementation, and Applications. (Society for Industrial and Applied Mathematics, Philadelphia, 2014)Google Scholar
- 34.D. Stroock, An Introduction to Markov Processes, 2nd edn. (Springer, 2014)Google Scholar
- 36.A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation. (Society for Industrial and Applied Mathematics, Philadelphia, 2005)Google Scholar
- 37.K.-V. Yuen,Bayesian Methods for Structural Dynamics and Civil Engineering. (Wiley Verlag, 2010)Google Scholar
- 41.D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach. (Princeton University Press, 2010)Google Scholar