in computational science, as illustrated by the development and maintenance of robust academic codes. This stems in part from the broad training in mathematics and physical sciences received by scientists in those fields and the strong reward system (career positions in academia, government, and industry) that allows theory and computational science to thrive within the fields. Evolutionary biology has successfully collaborated with statisticians, physicists, and computer scientists, but only since the 1990s, to address the inevitable computational issues surrounding an explosion of genomic-scale data. This has pushed evolutionary biology into quantitative directions as never before, through new training grants and genuinely interdisciplinary programs in computational biology.

These early successes also show that the four fields examined here are developing at different paces toward the solution of their HECC-dependent major challenges. Evolutionary biology is increasingly moving to quantitative models that organize and query a flood of information on species, in varying formats such as flat files of DNA sequences to complex visual imagery data. To approach these problems in the future, students will need stronger foundations in discrete mathematics and statistics, familiarity with tree-search and combinatorial optimization algorithms, and better understanding of the data mining, warehousing, and visualization techniques that have developed in computer science and information technology. Evolutionary biology is currently limited by the artificial separation of the biological sciences from quantitative preparation in mathematics and physics that are standard in the so-called “hard” sciences and in engineering disciplines. Thus, the key change that must take place in evolutionary biology is greater reliance on HECC for overcoming the major challenges.

Advances in chemical separations rely heavily on compute-bound algorithms of electronic structure theory solved by advanced linear algebra techniques, as well as on advanced sampling methods founded on statistical mechanics, to do large particle simulations of materials at relevant thermodynamic state points. Chemistry and chemical engineering departments at universities traditionally employ theoretical/ computational scientists who focus broadly on materials science applications but less on chemical separations problems, which are more strongly centered in the industrial sector. Moreover, these academic departments have emphasized coursework on chemical fundamentals and analytic models, and they need to better integrate numerical approaches to solving chemically complex problems into their undergraduate and graduate curricula. The chemical separations industry should consider sponsoring workshops, internships, and master’s degree programs in computational science to support R&D in this economically important field.

Astrophysics and the atmospheric sciences are the most HECC-ready of the four fields, evidenced in part by their consensus on many models and algorithms. In the case of the atmospheric sciences, the community has even evolved standardized community codes. However, the chemistry and physics knowledge in these fields continues to increase in complexity, and algorithms to incorporate all of that complexity are either unknown or limited by software deployment on advanced hardware architectures. Even though these disciplines have a strong tradition as consumers of HECC hardware resources, preparation in basic computational science practices (algorithms, software, hardware) is not specifically addressed in the graduate curriculum.

Astrophysics, chemical separations, evolutionary biology, and—to a lesser extent—the atmospheric sciences typify the academic model for the development of a large-scale and complex software project in which Ph.D. students integrate a new physics model or algorithm into a larger existing software infrastructure. The emphasis in the science disciplinary approach is a proof-of-principle piece of software, with less emphasis on “hardening” the software or making it extensible to larger problems or to alternative computing architectures. This is a practical outcome of two factors: (1) limitations in training in computational science and engineering and (2) the finite time of a Ph.D. track. While computer time at the large supercomputing resource centers is readily available and no great effort is needed to

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