Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

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Scalable Molecular Dynamics with NAMD

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

During the 70's and 80's, considerable effort was devoted to developing efficient and reliable time stepping procedures for transient structural analysis Mathematically, the equations governing this type of problems are generally stiff, ie, they exhibit a wide spectrum in the linear range The algorithms best suited to this type of applications are those which accurately integrate the low frequency content of the response without necessitating the resolution of the high frequency modes This means that the algorithms must be unconditionally stable, which in turn rules out explicit integration The most exciting possibility in the algorithms development area in recent years has been the advent of parallel computers with multiprocessing capabilities So, this work is mainly concerned with the development of parallel algorithms in the area of structural dynamics A primary objective is to devise unconditionally stable and accurate time stepping procedures which lend themselves to an efficient implementation in concurrent machines Some features of the new computer architecture are summarized A brief survey of current efforts in the area is presented A new class of concurrent procedures, or Group Implicit algorithms is introduced and analyzed The numerical simulation shows that GI algorithms hold considerable promise for application in coarse grain as well as medium grain parallel computers

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Group implicit concurrent algorithms in nonlinear structural dynamics

The development of new materials and structures for extreme conditions including impact remains a continuing challenge despite steady advances. Design is currently accomplished using a sequential approach: an optimal material is first developed using the process-structure-properties paradigm, where performance is measured against a blended measure. Then, the structure is optimized while holding the material properties fixed. In this paper, we propose an alternative concurrent and goal-oriented optimization approach where both the material properties and the structure are optimized simultaneously against an overall system-wide performance measure. We develop a non-intrusive, high-performance computational framework based on DAKOTA and GMSH and use it to study the ballistic impact of a double-layer plate of strong AZ31B magnesium alloy and soft polyurea. We show that the proposed concurrent and goal-oriented optimization strategy can provide significant advantage over the traditional sequential optimization approach.

Concurrent goal-oriented materials-by-design

We model numerically the mechanical effects of UV induced photo-polymerization in elastomeric artificial lens. The elastomer is originated upon cross-linking of a silicone matrix. UV irradiation of one side of the lens polymerizes selectively a photosensitive macromer, causing local variations of its concentration. The subsequent diffusion of macromers from high concentration to low concentration zones modifies the shape of the lens and thus its dioptric power. In vitro experiments on artificial lens showed that the power change is dependent on UV exposure time, irradiation intensity and light pattern. With the aim to define a numerical tool able to predict the dioptric power adjustment as a function of the UV irradiation parameters, we setup a purely mechanic finite element model of the lens, adopting a hyperelastic material model embedded with eigen-deformations. Numerical simulations of axis-symmetric irradiation closely reproduced the experimental results, in terms of both lens geometry and dioptric power, for positive, negative and lock-in corrections.

A numerical model of light adjustable lens

Understanding the transport of hydrogen within metals is crucial for the advancement of energy storage and the mitigation of hydrogen embrittlement. Using nanosized palladium particles as a model, recent experimental studies have revealed several highly nonlinear phenomena that occur over a long period of time. The time scale of these phenomena is beyond the capability of established atomistic models. In this work, we present the application of a new model, referred to as diffusive molecular dynamics (DMD), to simulating long-term diffusive mass transport at atomistic length scale. Specifically, we validate the model for the long-term dynamics of a single hydrogen atom on palladium lattice. We show that the DMD result is in satisfactory agreement with the result of the classical random walk model. Then, we apply the DMD model to simulate the absorption of hydrogen by a palladium nanocube with an edge length of 16 nm. We show that the absorption process is dominated by the propagation of a sharp, coherent α/β hydride phase boundary. We also characterize the local lattice deformation near the dynamic phase boundary using the mean positions of the palladium and hydrogen atoms.

Michael Ortiz

Papers

Group implicit concurrent algorithms in nonlinear structural dynamics

Concurrent goal-oriented materials-by-design

A numerical model of light adjustable lens

Atomistic Simulation of Hydrogen Diffusion in Palladium Nanoparticles Using a Diffusive Molecular Dynamics Method

Model-Free and Prior-Free Data-Driven Inference in Mechanics