Panagiotis Angelikopoulos

Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework

We present a Bayesian probabilistic framework for quantifying and propagating the uncertainties in the parameters of force fields employed in molecular dynamics (MD) simulations. We propose a highly parallel implementation of the transitional Markov chain Monte Carlo for populating the posterior probability distribution of the MD force-field parameters. Efficient scheduling algorithms are proposed to handle the MD model runs and to distribute the computations in clusters with heterogeneous architectures. Furthermore, adaptive surrogate models are proposed in order to reduce the computational cost associated with the large number of MD model runs. The effectiveness and computational efficiency of the proposed Bayesian framework is demonstrated in MD simulations of liquid and gaseous argon.

Kapitza Resistance between Few-Layer Graphene and Water: Liquid Layering Effects

The Kapitza resistance (RK) between few-layer graphene (FLG) and water was studied using molecular dynamics simulations. The RK was found to depend on the number of the layers in the FLG though, surprisingly, not on the water block thickness. This distinct size dependence is attributed to the large difference in the phonon mean free path between the FLG and water. Remarkably, RK is strongly dependent on the layering of water adjacent to the FLG, exhibiting an inverse proportionality relationship to the peak density of the first water layer, which is consistent with better acoustic phonon matching between FLG and water. These findings suggest novel ways to engineer the thermal transport properties of solid-liquid interfaces by controlling and regulating the liquid layering at the interface.

π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

We present ?4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

Homogeneous Hydrophobic-Hydrophilic Surface Patterns Enhance Permeation of Nanoparticles through Lipid Membranes.

We employ coarse-grained molecular dynamics simulations to understand why certain interaction patterns on the surface of a nanoparticle promote its translocation through a lipid membrane. We demonstrate that switching from a random, heterogeneous distribution of hydrophobic and hydrophilic areas on the surface of a nanoparticle to even, homogeneous patterns substantially flattens the translocation free-energy profile and dramatically enhances permeation. We then proceed to construct a more detailed coarse-grained model of a nanoparticle with flexible hydrophobic and hydrophilic ligands arranged into striped domains. Molecular dynamics simulations of these nanoparticles show that the terminal groups of the ligands tend to arrange themselves into homogeneous patterns, despite the underlying striped domains. These observations are linked to recent experimental studies.

Membrane Partitioning of Anionic, Ligand-Coated Nanoparticles Is Accompanied by Ligand Snorkeling, Local Disordering, and Cholesterol Depletion

Intracellular uptake of nanoparticles (NPs) may induce phase transitions, restructuring, stretching, or even complete disruption of the cell membrane. Therefore, NP cytotoxicity assessment requires a thorough understanding of the mechanisms by which these engineered nanostructures interact with the cell membrane. In this study, extensive Coarse-Grained Molecular Dynamics (MD) simulations are performed to investigate the partitioning of an anionic, ligand-decorated NP in model membranes containing dipalmitoylphosphatidylcholine (DPPC) phospholipids and different concentrations of cholesterol. Spontaneous fusion and translocation of the anionic NP is not observed in any of the 10-µs unbiased MD simulations, indicating that longer timescales may be required for such phenomena to occur. This picture is supported by the free energy analysis, revealing a considerable free energy barrier for NP translocation across the lipid bilayer. 5-µs unbiased MD simulations with the NP inserted in the bilayer core reveal that the hydrophobic and hydrophilic ligands of the NP surface rearrange to form optimal contacts with the lipid bilayer, leading to the so-called snorkeling effect. Inside cholesterol-containing bilayers, the NP induces rearrangement of the structure of the lipid bilayer in its vicinity from the liquid-ordered to the liquid phase spanning a distance almost twice its core radius (8–10 nm). Based on the physical insights obtained in this study, we propose a mechanism of cellular anionic NPpartitioning, which requires structural rearrangements of both the NP and the bilayer, and conclude that the translocation of anionic NPs through cholesterol-rich membranes must be accompanied by formation of cholesterol-lean regions in the proximity of NPs.

A hierarchical Bayesian framework for force field selection in molecular dynamics simulations

We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.

Pharmacokinetics of Anti‐VEGF Agent Aflibercept in Cancer Predicted by Data‐Driven, Molecular‐Detailed Model

Mathematical models can support the drug development process by predicting the pharmacokinetic (PK) properties of the drug and optimal dosing regimens. We have developed a pharmacokinetic model that includes a biochemical molecular interaction network linked to a whole‐body compartment model. We applied the model to study the PK of the anti‐vascular endothelial growth factor (VEGF) cancer therapeutic agent, aflibercept. Clinical data is used to infer model parameters using a Bayesian approach, enabling a quantitative estimation of the contributions of specific transport processes and molecular interactions of the drug that cannot be examined in other PK modeling, and insight into the mechanisms of aflibercepts antiangiogenic action. Additionally, we predict the plasma and tissue concentrations of unbound and VEGF‐bound aflibercept. Thus, we present a computational framework that can serve as a valuable tool for drug development efforts.

Bayesian Hierarchical Models for Uncertainty Quantification in Structural Dynamics

The Bayesian framework for hierarchical modeling is applied to quantify uncertainties, arising mainly due to manufacturing variability, for a group of identical structural components. Parameterized Gaussian models of uncertainties in structural model parameters are introduced that depend on a set of hyperparameters. Laplace methods of asymptotic approximation and more accurate stochastic simulation algorithms are used for estimating posterior joint and marginal distributions of structural model parameters and hyper-parameters. The posterior distribution of the hyperparameters is formulated as the product of as many multi-dimensional integrals as the number of structural components tested, with the dimension in each integral equal to the number of physical uncertain model parameters. Novel analytical approximations of these integrals are proposed that are shown to be computationally efficient, accurate and highly parallelized. A parallelized blocked Gibbs sampler is also proposed to efficiently generate samples simultaneously along the different uncertain parameter subspaces associated with the different number of structural component tested. Theoretical and computational developments are illustrated using simulated data for modal frequencies obtained from a number of identical bar structures.

NDL-v2.0: A new version of the numerical differentiation library for parallel architectures

We present a new version of the numerical differentiation library (NDL) used for the numerical estimation of first and second order partial derivatives of a function by finite differencing. In this version we have restructured the serial implementation of the code so as to achieve optimal task-based parallelization. The pure shared-memory parallelization of the library has been based on the lightweight OpenMP tasking model allowing for the full extraction of the available parallelism and efficient scheduling of multiple concurrent library calls. On multicore clusters, parallelism is exploited by means of TORC, an MPI-based multi-threaded tasking library. The new MPI implementation of NDL provides optimal performance in terms of function calls and, furthermore, supports asynchronous execution of multiple library calls within legacy MPI programs. In addition, a Python interface has been implemented for all cases, exporting the functionality of our library to sequential Python codes. New version program summary Program title: NDL-v2.0 Catalog identifier: AEDG_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDG_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 63036 No. of bytes in distributed program, including test data, etc.: 801872 Distribution format: tar.gz Programming language: ANSI Fortran-77, ANSI C, Python. Computer: Distributed systems (clusters), shared memory systems. Operating system: Linux, Unix. Has the code been vectorized or parallelized?: Yes. RAM: The library uses O(N)O(N) internal storage, NN being the dimension of the problem. It can use up to O(N2)O(N2) internal storage for Hessian calculations, if a task throttling factor has not been set by the user. Classification: 4.9, 4.14, 6.5. Catalog identifier of previous version: AEDG_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180(2009)1404 Does the new version supersede the previous version?: Yes Nature of problem: The numerical estimation of derivatives at several accuracy levels is a common requirement in many computational tasks, such as optimization, solution of nonlinear systems, and sensitivity analysis. For a large number of scientific and engineering applications, the underlying functions correspond to simulation codes for which analytical estimation of derivatives is difficult or almost impossible. A parallel implementation that exploits systems with multiple CPUs is very important for large scale and computationally expensive problems. Solution method: Finite differencing is used with a carefully chosen step that minimizes the sum of the truncation and round-off errors. The parallel versions employ both OpenMP and MPI libraries. Reasons for new version: The updated version was motivated by our endeavors to extend a parallel Bayesian uncertainty quantification framework [1], by incorporating higher order derivative information as in most state-of-the-art stochastic simulation methods such as Stochastic Newton MCMC [2] and Riemannian Manifold Hamiltonian MC [3]. The function evaluations are simulations with significant time-to-solution, which also varies with the input parameters such as in [1, 4]. The runtime of the NN-body-type of problem changes considerably with the introduction of a longer cut-off between the bodies. In the first version of the library, the OpenMP-parallel subroutines spawn a new team of threads and distribute the function evaluations with a PARALLEL DO directive. This limits the functionality of the library as multiple concurrent calls require nested parallelism support from the OpenMP environment. Therefore, either their function evaluations will be serialized or processor oversubscription is likely to occur due to the increased number of OpenMP threads. In addition, the Hessian calculations include two explicit parallel regions that compute first the diagonal and then the off-diagonal elements of the array. Due to the barrier between the two regions, the parallelism of the calculations is not fully exploited. These issues have been addressed in the new version by first restructuring the serial code and then running the function evaluations in parallel using OpenMP tasks. Although the MPI-parallel implementation of the first version is capable of fully exploiting the task parallelism of the PNDL routines, it does not utilize the caching mechanism of the serial code and, therefore, performs some redundant function evaluations in the Hessian and Jacobian calculations. This can lead to: (a) higher execution times if the number of available processors is lower than the total number of tasks, and (b) significant energy consumption due to wasted processor cycles. Overcoming these drawbacks, which become critical as the time of a single function evaluation increases, was the primary goal of this new version. Due to the code restructure, the MPI-parallel implementation (and the OpenMP-parallel in accordance) avoids redundant calls, providing optimal performance in terms of the number of function evaluations. Another limitation of the library was that the library subroutines were collective and synchronous calls. In the new version, each MPI process can issue any number of subroutines for asynchronous execution. We introduce two library calls that provide global and local task synchronizations, similarly to the BARRIER and TASKWAIT directives of OpenMP. The new MPI-implementation is based on TORC, a new tasking library for multicore clusters [5–7]. TORC improves the portability of the software, as it relies exclusively on the POSIX-Threads and MPI programming interfaces. It allows MPI processes to utilize multiple worker threads, offering a hybrid programming and execution environment similar to MPI+OpenMP, in a completely transparent way. Finally, to further improve the usability of our software, a Python interface has been implemented on top of both the OpenMP and MPI versions of the library. This allows sequential Python codes to exploit shared and distributed memory systems. Summary of revisions: The revised code improves the performance of both parallel (OpenMP and MPI) implementations. The functionality and the user-interface of the MPI-parallel version have been extended to support the asynchronous execution of multiple PNDL calls, issued by one or multiple MPI processes. A new underlying tasking library increases portability and allows MPI processes to have multiple worker threads. For both implementations, an interface to the Python programming language has been added. Restrictions: The library uses only double precision arithmetic. The MPI implementation assumes the homogeneity of the execution environment provided by the operating system. Specifically, the processes of a single MPI application must have identical address space and a user function resides at the same virtual address. In addition, address space layout randomization should not be used for the application. Unusual features: The software takes into account bound constraints, in the sense that only feasible points are used to evaluate the derivatives, and given the level of the desired accuracy, the proper formula is automatically employed. Running time: Running time depends on the function’s complexity. The test run took 23 ms for the serial distribution, 25 ms for the OpenMP with 2 threads, 53 ms and 1.01 s for the MPI parallel distribution using 2 threads and 2 processes respectively and yield-time for idle workers equal to 10 ms. References: [1] P. Angelikopoulos, C. Paradimitriou, P. Koumoutsakos, Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework, J. Chem. Phys 137 (14). [2] H.P. Flath, L.C. Wilcox, V. Akcelik, J. Hill, B. van Bloemen Waanders, O. Ghattas, Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations, SIAM J. Sci. Comput. 33 (1) (2011) 407–432. [3] M. Girolami, B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 73 (2) (2011) 123–214. [4] P. Angelikopoulos, C. Paradimitriou, P. Koumoutsakos, Data driven, predictive molecular dynamics for nanoscale flow simulations under uncertainty, J. Phys. Chem. B 117 (47) (2013) 14808–14816. [5] P.E. Hadjidoukas, E. Lappas, V.V. Dimakopoulos, A runtime library for platform-independent task parallelism, in: PDP, IEEE, 2012, pp. 229–236. [6] C. Voglis, P.E. Hadjidoukas, D.G. Papageorgiou, I. Lagaris, A parallel hybrid optimization algorithm for fitting interatomic potentials, Appl. Soft Comput. 13 (12) (2013) 4481–4492. [7] P.E. Hadjidoukas, C. Voglis, V.V. Dimakopoulos, I. Lagaris, D.G. Papageorgiou, Supporting adaptive and irregular parallelism for non-linear numerical optimization, Appl. Math. Comput. 231 (2014) 544–559.

Bayesian Annealed Sequential Importance Sampling: An Unbiased Version of Transitional Markov Chain Monte Carlo

The transitional Markov chain Monte Carlo (TMCMC) is one of the efficient algorithms for performing Markov chain Monte Carlo (MCMC) in the context of Bayesian uncertainty quantification in parallel...