CSE is at the intersection of mathematics and statistics, computer science, and core disciplines from the sciences and engineering. This combination gives rise to a new field whose character is different from its original constituents. Image credit: .
Over the past two decades, computational science and engineering (CSE) has become an increasingly important part of research in academia, industry, and laboratories. Mathematics-based advanced computing is now a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society, and the CSE community is at the core of this transformation. SIAM has been a driving force in this development by hosting the Activity Group on Computational Science and Engineering (SIAG/CSE), organizing the biennial flagship SIAM Conference on CSE, and publishing the SIAM Journal on Scientific Computing
– one of the top journals in the field. A 2001 report, Graduate Education in Computational Science and Engineering
by the SIAM Working Group on CSE Education , has helped to define the role and scope of CSE during the past two decades. However, a combination of disruptive developments—including the architectural complexity of extreme-scale computing, the planet’s ongoing data revolution, and the penetration of mathematically-based CSE methodology into more and more fields—is currently redefining CSE’s reach.
The CSE pipeline, from physical problem to model and algorithms to efficient implementation in simulation software, with verification and validation driven by data. The pipeline is actually a loop that requires multiple feedbacks. Image credit: 
While CSE is rooted in the mathematical and statistical sciences, computer science, the physical sciences, and engineering, today it increasingly pursues its own unique research agenda. The field is now widely recognized as an essential cornerstone that drives scientific and technological progress in conjunction with theory and experiment. Scientific experimentation and theory, the classical paradigms of the scientific method, both strive to describe the physical world. However, high-fidelity predictive capabilities can often be realized only by numerical computation. CSE’s overarching goal of achieving truly predictive scientific capabilities is its distinguishing factor. It accomplishes this through advances that combine modeling, numerical analysis, algorithms, simulation, big data analytics, high performance computing, and scientific software. The development of predictive capabilities lies at the core of CSE as a new discipline in its own right and has already impacted a number of disciplines, including but not limited to simulation-based design in the automotive industry, simulation-based decisions in computational medicine, and simulation-based predictions of global climate. It is also set to catalyze fundamental changes in many more areas of technical, economic, societal, and political decision processes.
This image, featured on the cover of the 2016 Research and Education in Computational Science and Engineering report, illustrates Earth mantle convection, the planet-wide creeping flow of the Earth’s mantle on time scales of millions of years. The computational mesh is generated from an icosahedron that is hierarchically refined 12 times to reach a global resolution of one km, resulting in a finite-element mesh with more than one trillion (1012) degrees of freedom. Petascale class machines and highly efficient, parallel multigrid methods are required to solve the resulting equations in a timestepping procedure. The image first appeared in the 2014 DFG mathematics calendar and is an outcome of the DFG project TerraNeo (led by Hans-Peter Bunge, Ulrich Rüde, and Barbara Wohlmuth) in the Priority Programme 1648 Software for Exascale Computing.
A new report, titled Research and Education in Computational Science and Engineering
, analyzes the current status of CSE and the aforementioned new developments. The report, available in preprint form
and on the SIAG/CSE wiki page
, summarizes the status of CSE as an emerging discipline and presents the field’s trends and challenges in research and education for the next decade. The report is based on the outcomes of a 2014 workshop sponsored by SIAM and the European Exascale Software Initiative, a minisymposium and a panel discussion held during the 2015 SIAM Conference on CSE, as well as feedback from the CSE community collected over the past two years. Despite CSE’s fundamental importance, the report finds that many current institutional structures do not adequately reflect the needs of the discipline. Examples of barriers preventing CSE advancement include a dearth of appropriate interdisciplinary structures at universities and funding institutions, lack of recognition for the important role of scientific software, and institutional challenges in creating suitable educational programs. The new report elaborates on these arguments in detail and reveals the following central findings:
- CSE has matured to a discipline in its own right.
- Computational algorithms lie at the core of CSE progress, and scientific software, which codifies and organizes algorithmic models of reality, is the primary means of encapsulating CSE research to enable advances in scientific and engineering understanding.
- CSE methods and techniques are essential to capitalize on the rapidly-growing ubiquitous availability of scientific and technological data.
The report also highlights a number of specific CSE “success stories” – application examples in which CSE research is significantly impacting the real world. These accounts emphasize both the long-term payoff of investment in fundamental CSE research and the criticality of sustaining that investment to leverage current and future opportunities—as articulated in the report’s recommendations—for CSE research and education over the next decade.
 Rüde, U., Willcox, K., McInnes, L.C., De Sterck, H., Biros, G., Bungartz, H., Corones, J., Cramer, E., Crowley, J., Ghattas, O., Gunzburger, M., Hanke, M., Harrison, R., Heroux, M., Hesthaven, J., Jimack, P., Johnson, C., Jordan, K.E., Keyes, D.E., Krause, R., Kumar, V., Mayer, S., Meza, J., Mørken, K.M., Oden, J.T., Petzold, L., Raghavan, P., Shontz, S.M., Trefethen, A., Turner, P., Voevodin, V., Wohlmuth, B., & Woodward, C.S. (2016). Research and Education in Computational Science and Engineering. Preprint, arXiv.org. https://arxiv.org/abs/1610.02608.
 SIAM Working Group on CSE Education. (2001). Graduate Education in Computational Science and Engineering. SIAM Review, 43(1), 163-177. http://dx.doi.org/10.1137/S0036144500379745.