2
Applied and Computational Mathematics Division
INTRODUCTION
The Applied and Computational Mathematics Division (ACMD) of the Information Technology Laboratory (ITL) “provides leadership within NIST in the use of applied and computational mathematics to solve science and engineering problems arising in measurement science and related applications.”1 The staff accomplishes this through research on analytical and numerical methods; high-performance computing and visualization; peer-to-peer collaborations to apply these to NIST problems; providing stewardship of mathematical reference data; and developing standards and tests for scientific computation. The division is organized into four groups of about equal size: Mathematical Analysis and Modeling, Mathematical Software, Computing and Communication Theory, and High-Performance Computing and Visualization.
QUALITY OF THE RESEARCH
The technical projects in mathematics of metrology, high-performance computing and visualization, and materials modeling and simulation involve modeling in the applied physical sciences. This requires a combination of mathematical analysis and simulation. These involve collaborations between the ACMD and other laboratories within NIST, as well as collaborations with universities and other government agencies, including funding from the latter. These are areas in which the ACMD is strong and successful in performing high-impact work. Highlights include the use of computer simulation in the development of a standard reference mortar to replace expensive oils in concrete rheometers, the design of standard reference artifacts for calibrating magnetic resonance imagers (MRIs), and the deployment of community software for computing the physical properties of complex microstructures in solids from image data in three dimensions. A distinctive feature of ACMD’s work in these areas is the integration of analytical methods with simulation to solve problems, as opposed to the use of simulation alone. This combined approach is a key feature of ACMD’s success.
The work in quantum information science is focused on the investigation of fundamental mathematical questions in quantum computing and communications related to areas such as communications, cryptography, cybersecurity, randomness, clocks, and sensors. Some of this work is conducted through the NIST/University of Maryland Joint Center for Quantum Information and Computer Science, which is a multidisciplinary collaboration involving computer scientists and physicists at both institutions. A notable accomplishment in this area was development of an efficient method for generation of uniformly distributed random bitstrings from a quantum source, with applications in secure communications.
___________________
1 National Institute of Standards and Technology (NIST), 2017, Applied and Computational Mathematics Division: Summary of Activities for Fiscal Year 2017, NISTIR 8208, NIST, Gaithersburg, Md., p. 3.
The work in foundations of measurement science for information systems includes a variety of topics in computer science and discrete mathematics. The topics include graph analysis, combinatorics, network security and reliability, and software testing, as well as interdisciplinary work in the Internet of Things (IoT).
The mathematical knowledge management area includes the Digital Library of Mathematical Functions, a highly successful project to update the National Bureau of Standards’ Handbook of Mathematical Functions. The digital library uses Internet and graphical technologies to facilitate access to the information. This has led to the development of a widely used new version of the handbook as well as a heavily used website providing novel three-dimensional (3D) interactive graphical and visualization methods for displaying the properties of these functions. The website also provides links to software for evaluating special functions.
The complexity of simulations of physical systems is rapidly increasing. There is a need for higher model fidelity, such as replacing lower-dimensional models with fully 3D ones, representing more realistic complex geometries, and representing multiphysics and multiscale phenomena. In addition, the processor architecture of computers used in simulation and modeling is becoming vastly more complex, with deep memory hierarchies and heterogeneous compute engines with high degrees of parallelism on a single node. It is difficult to get even modest performance on such systems with existing programming tools, yet the need for higher fidelity representations will require it. There is a serious risk that the existing approach in the ACMD of having a small number of people, or even a single staff member, implement complete simulation capabilities starting from scratch will no longer be feasible.
RECOMMENDATION: The ACMD should evaluate simulation software development practices in light of the disruptive changes in high-performance computing technology.
SCIENTIFIC EXPERTISE
The ACMD has an excellent group of career staff members. Their core expertise is in applied analysis and numerical methods that arise in the physical sciences, and mathematical techniques associated with theoretical computer science, particularly in problems related to quantum computing. A number of them have received professional recognition, including 2 NIST fellows (out of a total of 40 for all of NIST) and 8 fellows in various professional societies. The ACMD has a robust presence in leadership positions in the community, including membership on standards committees (6), journal editorial positions (14), and conference organizing committees (37). Another indicator of the technical strength of the organization is the large number of successful collaborations between ACMD staff and scientists from other disciplines that have led to many coauthored publications. The ACMD has also been successful in recruiting excellent postdoctoral researchers.
The demographics in the ACMD are shifting, and therefore anticipating multiple retirements is warranted. Losing talent will cause disruptions in various ACMD ongoing projects. However, adding professional staff could provide a clear opportunity to refresh, accelerate, or pivot in new directions or to add different ranges of expertise. The challenge of staff renewal is made more complicated by the inability to hire noncitizens as federal employees, thus reducing the pool of potential candidates for staff positions and for National Research Council (NRC) postdoctoral researchers. There are also far fewer graduate students involved in research activities than would be expected in an organization with the size and scientific visibility of the ACMD, a need that was specifically noted by ACMD staff.
ADEQUACY OF FACILITIES, EQUIPMENT, AND HUMAN RESOURCES
The ACMD is funded at a level of around $15.8 million per year (fiscal year 2018, estimated); one staff full-time equivalent (FTE) costs about $250,000 to $300,000 per year. Most of this is core
funding (i.e., stable and noncompeted), with around $1.6 million per year awarded competitively either across the ITL or across NIST. This level of funding has been nearly flat over the last 5 years.
There are six technical project areas in ACMD: mathematics of metrology (to which 15 percent of the division’s funds are allocated), high-performance computing and visualization (16 percent), materials modeling and simulation (16 percent), quantum information science (19 percent), foundations of measurement science for information systems (16 percent), and mathematical knowledge management (10 percent); the remaining 8 percent is division overhead funds or not yet allocated.
The computing landscape is changing radically due to disruptive changes in hardware and software, combined with the requirement for increasing fidelity of computer models. These changes have the potential of making infeasible the approach used in the ACMD of having small teams, or even single investigators, writing applications simulation codes from scratch.
The ACMD is experiencing large stresses that may have an impact on its ability to meet its goal of providing comprehensive mathematical expertise for NIST. There is more demand for such expertise than can be met by the current ACMD staffing, both in their core areas of expertise, and in new areas that require mathematical support, such as biomedical applications, machine learning, and the IoT. Simultaneously, there is an anticipation of substantial turnover due to the potential retirement of a significant fraction of staff in the near future, and difficulty recruiting new staff due to salary constraints and the requirement for U.S. citizenship. Responding to these stresses may require a more top-down level of strategic planning and deployment of resources than is currently employed by the ACMD.
One of the key facilities issues for the ACMD is access to evolving computing resources. Current requirements are met by a combination of compute servers and a visualization laboratory at the division level, NIST shared resources, and ad hoc access to external resources through the National Science Foundation (NSF) XSEDE and Department of Energy INCITE programs. This combination currently appears to provide adequate access to compute capabilities.
DISSEMINATION OF OUTPUTS
The ACMD has a diverse set of activities in support of disseminating its work. ACMD staff members publish extensively in high-visibility refereed journals and conference proceedings. They also distribute software in a number of areas, including micromagnetic modeling, tools for combinatorial testing of software, and the aforementioned Digital Library for Mathematical Functions website and book. Through their participation in the standards setting for metrology, ACMD staff members contribute to the publication of those standards in NIST reports. They have also authored 46 journal publications and 34 conference publications, which have appeared in the last 18 months. More generally, their scientific enterprise is built on a culture of collaboration with other scientific disciplines, which leads to a broad dissemination of research ideas from the ACMD, resulting in high scientific impact.
As a research organization, the ACMD is very successful, considering several factors: executing high-quality research in applied and computational mathematics; meeting the needs of collaborators in diverse scientific disciplines; fulfilling the institutional missions of NIST in metrology; and disseminating its work to broader communities. Especially noteworthy is its strength in mathematical analysis, particularly when used in tandem with simulation, which provides a high degree of scientific insight and is a distinctive strength of the ACMD.
