### Questions on Future Research Directions

We solicit short whitepapers that address one or more questions (see below) on potential high-impact future research directions for the DOE Applied Mathematics program. Whitepapers on other topics will not be considered. The goal of whitepapers is to brainstorm broadly about new areas of work needed to meet DOE mission needs. The organizing committee will consider whitepaper submissions in order to determine panelists to spearhead discussions during the meeting. Also, attendees will vote during the meeting on whitepaper topics for several short presentations. There is no limit on the number of whitepapers that attendees may submit.

1. Multiscale, multiphysics, multifidelity modeling research

1aSignificant advances in coupling scales and physics have occurred during the past several decades. What research gaps and/or clearly superior/unifying methods are emerging from these diverse approaches?

1bHow can we truly advance beyond interpretive simulation to predictive simulation, optimization, and design for complex physical systems? What obstacles remain, and what will characterize the models, algorithms, and computational horsepower necessary to overcome them?

2. Convergence of data- and model-driven discovery

2aAs related to the development of new mathematical theory and proof, what is needed to advance simulation (scale and resolution) and data analytics (size and complexity) so that they can be used to automate and accelerate theoretical development?

2bHow can machine learning, artificial intelligence, and applied statistics contribute to our research space and/or open up new areas of research? Since these topics cross the divide of computer science and mathematics, on what aspects should the DOE Applied Mathematics portfolio focus?

3. Sustaining applied mathematics workforce and products

3aWhat new skills and training processes do future and existing applied mathematics researchers need in order to meet emerging and future research needs? How can the DOE national labs and academia initiate and collaborate to improve current practices?

3bWhat is the appropriate role of software development in ASCR applied math research, and what are funding models that would support that role? Should we have a software management and sustainability plan similar to the required data management plans?

4. Applied mathematics for future computing directions

4aWhat kinds of new complexity models are needed in order to better reflect the true costs of computation (e.g., data motion, not flops)? How should such models be used insitu to adapt computational/mathematical methodologies to architecture and machine state?

4bWhat applied mathematics research is needed for the era of supercomputing beyond the scaling limits of Moore's law? What existing elements in the DOE applied mathematics portfolio can be leveraged?