# DOE Applied Math Summit

**DOE Applied Math Summit (Washington, D.C.)**

March 7, 2012 from 8:30 a.m. to 5 p.m.

American Geophysical Union (AGU), 2000 Florida Ave, N.W. Washington, D.C. 20009

**A New Paradigm for DOE Applied Mathematics:**

The Applied Mathematics program has traditionally funded long-term basic research projects focused on a specific mathematical aspect or application. Projects range from single PIs to smaller teams, on the order of 3 researchers plus post-docs/GRAs, to a couple of larger teams, 5+ researchers plus post-docs/GRAs. Since 2008, new thrust areas in applied mathematics were introduced in multiscale mathematics and optimization of complex systems, mathematics for complex distributed systems, uncertainty quantification, mathematics for analysis of petascale data, and joint applied math /computer science institutes. In the current project paradigm, foundational and computational mathematics research impacts the DOE mission by developing numerical libraries and software, e.g. PETSc, TAO, etc., developing methods and algorithms that are adopted by SciDAC Institutes and Partnerships, e.g. adaptive mesh generation. In several projects, applied mathematics researchers are directly interacting with DOE application scientists and have transitioned research capabilities under the applied mathematics program to full applications, for example, stochastic optimization for the electric grid and numerical formulations and robust, scalable solvers for extended magneto-hydrodynamics.

While the current paradigm has worked well, the challenges of solving complex problems within DOE’s mission areas of energy, environment and security, problems that involve coupled models from multiple scientific disciplines for complex continuous and discrete phenomena with both stochastic and deterministic elements, that require integration of simulation and data, and are characterized by pervasive uncertainties, may require a new paradigm for DOE’s applied mathematics program. These problems pose grand challenges in applied mathematics. In addition to the mission challenges, disruptive changes with computer architectures and computing environments are expected in the next 5-10 years. The expected explosion in the amount of data and complexity of data will make data-driven science a new key facet of applied mathematics. These problems suggest a new mode of operation for applied mathematicians; a mode that crosscuts the boundaries of traditional developments of methods and tools. To contribute towards solving problems of major importance to DOE, the applied mathematics program must not only consider new research directions but new modes of research and collaboration. We believe that the vision for the future includes a new paradigm to holistically address mathematics for increasingly complex DOE-relevant systems for scientific discovery, design, optimization and risk assessment.

We are proposing funding mathematics centers that address the multifaceted capabilities that will enable DOE applications developers to push beyond the current computational boundaries. The *Mathematical Multifaceted Integrated Capability Centers* (MMICCs) will enable applied mathematics researchers to work together in large, collaborative teams to more effectively address application mathematical problems earlier in the problem solving process. The MMICCs allow one to take a broader view of the problem as a whole, and devise solution strategies that attack the problem in “its entirety” by building fundamental, multidisciplinary mathematical capabilities and tools. The centers would have the flexibility and technical expertise to simultaneously consider all aspects of the problem-solving process ranging from the mathematical formulation to the development of appropriate models to the implementation of prototype capabilities. These centers may also consider architectural and computer science challenges such as the resiliency, efficiency and evolving programming models. To make this work effectively will require the assembly of teams of scientists and applied mathematics researchers. This is not an easy job by any means; however, the national laboratories can play a central role, by taking long-term ownership of the problem.

These new mathematics centers and this integrated approach will be balanced and supplemented by the traditional single-PI and teams of researchers working on foundational and computational mathematics. These new centers will help serve as entry points for researchers to more readily understand DOE-relevant problems and have access to DOE scientists and mathematicians. Figure 1 illustrates this new paradigm. Again, the goal of this new paradigm is to holistically address mathematics for increasingly complex DOE-relevant systems.

We envision standing up several of these new mathematics centers over time. At the same time, many projects focused on specific applied mathematics research, e.g. optimization, stochastic, multi-scale mathematics, analysis, will continue to be supported as well as initiating several smaller high-risk, high payoff projects. The high-risk, high-payoff projects may address a unique niche or a specialized aspect of a mathematical problem that has the potential of contributing to DOE mission objectives. Collectively these projects will interact at many levels; some may be independent, there may be loose interactions, or there may be tight interactions. All levels are acceptable. One of the goals is that these new mathematics centers will have buy-in from DOE application domains at some level.

**Summit Discussion:**

- What are the pro’s and con’s of this new paradigm? Are there examples of other centers that we can learn from?

- What should the mathematics centers focus on, e.g. themes?

- How close to, or removed from, an application should the center be?

- Can a center focus on foundational and computational mathematics effectively for multiple domain applications?

- How might they change over time?

- How will this be received within the applied mathematics community? How should this be socialized?

- How do you measure success of a center?

- After this meeting what should be the next step in accomplishing this paradigm shift.

**Of Note:**

- This not an attempt to turn the applied mathematicians into computer scientists

- We have not explored a funding distribution model for the three areas: MMICC, Computational Mathematics and Exploratory Applied Mathematics Projects

- The MMICCs will not support efforts for specific applications

The public is welcome to participate in this informal conversation about the DOE Applied Mathematics. However, space at the AGU is limited and on-site registration will be used to accommodate as many participants as possible. To register in advance, please email christine.chalk@science.doe.gov