Novel Algorithm Adds Reality to Problem Solving
While modern computers allow numerical models to routinely simulate physical system behaviors in scientific domains ranging from climate to chemistry and materials to biology, parametric uncertainty, a notable error source in modeling physical systems stemming from incomplete knowledge about the systems being simulated, means many of those models deviate from reality. In the paper, “An Adaptive Importance sampling Algorithm for Bayesian Inversion with Multimodal Distributions,” authors Weixuan Li, from Pacific Northwest National Laboratory, and Guang Lin, from Purdue University, tackle the problem of parametric uncertainty using an adaptive importance sampling algorithm that provides an effective means to infer model parameters from any direct and/or indirect measurement data through uncertainty quantification while also improving computational efficiency.
Their method employs two key techniques: 1) a Gaussian mixture model adaptively constructed to capture the distribution of uncertain parameters and 2) a mixture of polynomial chaos expansions built as a surrogate model to alleviate the computational burden caused by forward model evaluations. These techniques afford the algorithm great flexibility to handle complex multimodal distributions and strongly nonlinear models while keeping the computational costs at a minimum level.
Ultimately, the algorithm has potential applications that are especially relevant to the U.S. Department of Energy. For example, it can be used to estimate the unknown location of an underground contaminant source and to improve the accuracy of the model that predicts how groundwater is affected by this source (see related PNNL highlight).
This material is based on work conducted under the Multifaceted Mathematics for Complex Energy Systems (M2ACS) and Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) projects supported by the DOE’s Office of Advanced Scientific Computing Research Applied Mathematics program.
Reference: Li W and G Lin. 2015. “An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions.” Journal of Computational Physics 294:173-190. DOI: 10.1016/j.jcp.2015.03.047.
Bochev Honored with 2014 Ernest Orlando Lawrence Award
In May, U.S. Energy Secretary Ernest Moniz announced nine exceptional U.S. scientists and engineers who received the 2014 Ernest Orlando Lawrence Award for their contributions to Department of Energy science. Among those, Dr. Pavel Bochev, a co-Principal Investigator and Concurrent Coupling task lead on the CM4 project, was honored for his “pioneering theoretical and practical advances in numerical methods for partial differential equations.”
Along with the other recipients, Bochev, who is a computational mathematician at Sandia National Laboratories, will be honored at a ceremony in Washington D.C. later this year, where he will receive a medal and a $20,000 honorarium.
George Karniadakis Awarded 2015 Ralph E. Kleinman Prize
George Em Karniadakis, a joint appointee with PNNL and Brown University, was awarded the Ralph E. Kleinman Prize, sponsored by the Society for Industrial and Applied Mathematics to recognize individual achievement for outstanding research or contributions that bridge the gap between mathematics and applications. Karniadakis will receive the Kleinman Prize during an award ceremony at the International Congress on Industrial and Applied Mathematics being held in Beijing, August 10-14, 2015.
Shape Up: New Study Examines How Membrane Structure Affects Protein Mobility in Lipids
Published in the April 2014 issue of the Proceedings of the National Academy of Sciences of the United States of America, “Shape Matters in Protein Mobility within Membranes” is co-authored by Dr. Paul J. Atzberger, a co-principal investigator with the CM4 project from the University of California, Santa Barbara. The work takes a closer look at the long-held theory, introduced by the Saffman–Delbrück formula in 1975, that lateral Brownian mobility of proteins within cell membranes depends on their size and the viscosity of both the membrane and its surrounding medium. Instead, by comparing the mobility of two transmembrane proteins that bend the membrane differently—aquaporin 0 (AQP0) and voltage-gated potassium channel (KvAP)—and using single-particle tracking (SPT), Atzberger and his collaborators showed KvAP undergoes a significant increase in mobility under tension, while AQP0 is unresponsive amid that same tension. The featured experiment, simulations and analysis showed that, beyond the Saffman–Delbrück formula, Brownian motion of a shaping-membrane protein is influenced by the lateral extension of the deformed membrane patch, which depends on tension.
To show how membrane protein mobility depends on local membrane deformation that self-generates around the protein, the scientists reconstituted AQP0 and KvAP in giant unilamellar (single-layer) vesicles and labeled a small portion of the protein with quantum dots. They controlled the tension with micropipette aspiration and used epifluorescence microscopy to record protein lateral mobility in the fluctuating membrane. They were able to analyze the diffusion coefficients against the applied tension to show the connection between membrane shaping and mobility. The models explored mechanisms that take into account dissipation both internal (in the bilayer) and external (in the surrounding medium). As part of the work, the corresponding numerical simulations, which employed stochastic dynamic equations and a Monte Carlo approach (among other techniques), were used to generate energy minimizing shape profiles and stochastic protein dynamics.
The research was supported by the Agence Nationale de la Recherche, La Fondation Pierre-Gilles de Gennes, and a France Parkinson Fellowship (all based in France); the Chinese Academy of Sciences’ Project of Knowledge Innovation Program; and the National Science Foundation, as well as the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) sponsored by the Department of Energy’s Office of Advanced Scientific Computing Research.
- Protein diffusion subject to small membrane tension [side view]
- Protein diffusion subject to small membrane tension [top view]
- Protein diffusion subject to large membrane tension [side view]
- Protein diffusion subject to large membrane tension [top view]
Reference: Quemeneur F, JK Sigurdsson, M Renner, PJ Atzberger, P Bassereau, and D Lacoste. 2014. “Shape matters in protein mobility within membranes.” Proceedings of the National Academy of Sciences of the United States of America 111(14):5083-5087. DOI: 10.1073/pnas.1321054111.
Surpassing Boundaries in Fluid Dynamics Using the Smoothed Particle Hydrodynamics–Continuous Boundary Force Method
In the paper, “Smoothed Particle Hydrodynamics Continuous Boundary Force Method for Navier-Stokes Equations Subject to a Robin Boundary Condition,” published in the Journal of Computational Physics, lead author Wenxiao Pan, the CM4 project task leader for Scalable Algorithms and Applications (from Pacific Northwest National Laboratory), and her co-authors introduce and evaluate a new method—smoothed particle hydrodynamics-continuous boundary force (SPH-CBF)—to analyze and model physical phenomena associated with fluid flows and the forces that affect them at various scales and boundary conditions. The SPH-CBF formulation has several advantages for solving Navier-Stokes equations. Most notably, the SPH discretization of the equations and boundary condition that results from the CBF method offer a computationally efficient way to model boundary conditions ranging from no slip to full slip.
To examine its accuracy, the SPH-CBF method was tested with two- and three-dimensional plane shear flow, as well as a periodic lattice of cylinders. The results then were compared with those obtained using finite difference or finite element method (FEM) approaches. Even in a domain with complex boundaries, comparisons of SPH-CBF velocity profiles closely agreed with those from the FEM solutions, demonstrating the method’s capability for modeling flows with different slip lengths.
In addition to advancing existing SPH theory, the method uses SPH strengths in modeling diverse physics problems, such as those involving atmospheric systems, energy materials and processes, subsurface flow and transport, and high-strength materials, which are highly relevant to important U.S. Department of Energy mission objectives (see related highlight).
The research was conducted through the CM4 project supported by DOE’s Office of Advanced Scientific Computing Research Applied Mathematics program.Reference: Pan W, J Bao, and AM Tartakovsky. 2014. “Smoothed Particle Hydrodynamics Continuous Boundary Force Method for Navier-Stokes Equations Subject to a Robin Boundary Condition.” Journal of Computational Physics 259:242-259. DOI: 10.1016/j.jcp.2013.12.014.
A New Way to get the Temperature Right: The Fluctuating Hydrodynamics Thermostat
Recently published in Physical Review E, "Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: Fluctuating hydrodynamics thermostat," is co-authored by Paul J. Atzberger, a co-principal investigator with the CM4 project from the University of California, Santa Barbara. The work introduces a momentum-conserving fluctuating hydrodynamics thermostat for dynamic simulations of implicit-solvent coarse-grained models, which addresses important correlations and dynamic contributions that standard implicit-solvent models and Langevin dynamics approaches can overlook.
The fluctuating hydrodynamics thermostat couples coarse-grained degrees of freedom to a stochastic continuum field that accounts for both the solvent hydrodynamics and thermal fluctuations. In their work, the scientists investigated the diffusivity of lipids within the bilayer and their spatial correlations. Their results revealed lipid motions exhibit interesting collective correlations, resembling a vortex-like flow structure similar to those observed in other explicit solvent bilayer simulations. Thus, the fluctuating hydrodynamics thermostat captures important solvent-mediated effects not accounted for in conventional Langevin dynamics. The results also indicate that introduced fluctuating hydrodynamics methods provides a promising set of approaches for extending implicit-solvent lipid models for studies of dynamical phenomena within lipid bilayer membranes.
The research was supported by several grants from the National Science Foundation, as well as the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) sponsored by the Department of Energy's Office of Advanced Scientific Computing Research.
Reference: Wang Y, JK Sigurdsson, E Brandt, and PJ Atzberger. 2013. "Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: Fluctuating hydrodynamics thermostat." Physical Review E 88(2):023301. DOI: 10.1103/PhysRevE.88.023301
Mesoscale Simulations See into Sickle Cells
The research of Dr. George Karniadakis, a joint appointee at PNNL and Brown University and principal investigator of the CM4 project, was recently referenced in The Telegraph (U.K.) in an article about how computer programs are being used to create lifelike models of the human body (http://bit.ly/1bSFmdC). Dr. Karniadakis' research involved using a systematic, dissipative particle dynamics-based (a stochastic simulation technique for complex fluids) simulation study of individual sickle red blood cells in shear flow to analyze the biophysical characteristics surrounding vasoocclusion crisis, vascular blockage that occurs when sickle-shaped cells obstruct circulation.
The research was supported by the National Institutes of Health and the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) sponsored by the Department of Energy's Office of Advanced Scientific Computing Research. Computations were made possible via an ASCR Innovative & Novel Computational Impact on Theory and Experiment (INCITE) award.
Reference: Lei H and GE Karniadakis. 2013. "Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations." Proceedings of the National Academy of Sciences (PNAS) 110(28):11326-11330. DOI: 10.1073/pnas.1221297110.