Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes

When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large matrix. Moreover, in a MLMC framework, the white noise samples must be coupled between subsequent levels. We show how our technique can be used to enforce this coupling even in the case of non-nested mesh hierarchies. We demonstrate the efficacy of our method with numerical experiments. We observe optimal convergence rates for the finite element solution of the elliptic SPDEs of interest in 2D and 3D and we show convergence of the sampled field covariances. In a MLMC setting, a good coupling is enforced and the telescoping sum is respected.Comment: 28 pages, 10 figure

PROSESS: a protein structure evaluation suite and server

PROSESS (PROtein Structure Evaluation Suite and Server) is a web server designed to evaluate and validate protein structures generated by X-ray crystallography, NMR spectroscopy or computational modeling. While many structure evaluation packages have been developed over the past 20 years, PROSESS is unique in its comprehensiveness, its capacity to evaluate X-ray, NMR and predicted structures as well as its ability to evaluate a variety of experimental NMR data. PROSESS integrates a variety of previously developed, well-known and thoroughly tested methods to evaluate both global and residue specific: (i) covalent and geometric quality; (ii) non-bonded/packing quality; (iii) torsion angle quality; (iv) chemical shift quality and (v) NOE quality. In particular, PROSESS uses VADAR for coordinate, packing, H-bond, secondary structure and geometric analysis, GeNMR for calculating folding, threading and solvent energetics, ShiftX for calculating chemical shift correlations, RCI for correlating structure mobility to chemical shift and PREDITOR for calculating torsion angle-chemical shifts agreement. PROSESS also incorporates several other programs including MolProbity to assess atomic clashes, Xplor-NIH to identify and quantify NOE restraint violations and NAMD to assess structure energetics. PROSESS produces detailed tables, explanations, structural images and graphs that summarize the results and compare them to values observed in high-quality or high-resolution protein structures. Using a simplified red–amber–green coloring scheme PROSESS also alerts users about both general and residue-specific structural problems. PROSESS is intended to serve as a tool that can be used by structure biologists as well as database curators to assess and validate newly determined protein structures. PROSESS is freely available at http://www.prosess.ca

Fault tolerance of MPI applications in exascale systems: The ULFM solution

[Abstract] The growth in the number of computational resources used by high-performance computing (HPC) systems leads to an increase in failure rates. Fault-tolerant techniques will become essential for long-running applications executing in future exascale systems, not only to ensure the completion of their execution in these systems but also to improve their energy consumption. Although the Message Passing Interface (MPI) is the most popular programming model for distributed-memory HPC systems, as of now, it does not provide any fault-tolerant construct for users to handle failures. Thus, the recovery procedure is postponed until the application is aborted and re-spawned. The proposal of the User Level Failure Mitigation (ULFM) interface in the MPI forum provides new opportunities in this field, enabling the implementation of resilient MPI applications, system runtimes, and programming language constructs able to detect and react to failures without aborting their execution. This paper presents a global overview of the resilience interfaces provided by the ULFM specification, covers archetypal usage patterns and building blocks, and surveys the wide variety of application-driven solutions that have exploited them in recent years. The large and varied number of approaches in the literature proves that ULFM provides the necessary flexibility to implement efficient fault-tolerant MPI applications. All the proposed solutions are based on application-driven recovery mechanisms, which allows reducing the overhead and obtaining the required level of efficiency needed in the future exascale platforms.Ministerio de Economía y Competitividad and FEDER; TIN2016-75845-PXunta de Galicia; ED431C 2017/04National Science Foundation of the United States; NSF-SI2 #1664142Exascale Computing Project; 17-SC-20-SCHoneywell International, Inc.; DE-NA000352