What is Computational Science?

Computational science comprises a wide variety of research areas where the development and the use of simulation tools play an important role. Such research areas are found in both the basic sciences and in applied research. Examples are reservoir simulation, seismic analysis, molecular dynamics, materials research, computational mechanics, bioinformatics, medical diagnostics, and climate modelling. A common feature of all these activities is a strong interdisciplinary character: physical modelling, mathematical analysis, numerical analysis and algorithm development, computationally intensive problems, software development, and visualization. The working group has looked at the future opportunities and challenges in this field, in particular, based on expected progress in mathematical, statistical and numerical methods for solving scientific and technological problems, as well as the availability of significantly more powerful computational resources and tools for exploiting these.

Outline of this document

Since the application areas are driving much of the development of computational science, we start by discussing the future of a few selected areas. We then discuss some issues related to advances in mathematical and computational methods, and in computational infrastructure. Finally, we reflect on the impact computational science will have on future education.

1. Computational mechanics

As an introduction, consider first the classical example of direct numerical simulation of turbulent flows involving a single fluid phase with homogeneous material properties [1]. The governing equations are known from a continuum description, and provide an excellent mathematical model at a macroscopic level. However, current numerical methods and available computational resources only allow these equations to be solved for relatively simple cases (simple geometries and at fairly low Reynolds numbers). For most industrial problems, including marine applications, a direct numerical solution of the governing equations is out of reach. Even with a continued progress in algorithm development and computational power, it is expected that such a direct computational approach will not be possible even in 2020 for many problems of engineering interest. The main reason for this is the large range of temporal and spatial scales necessary to resolve. Note that an increase in resolution by a modest factor of 2 in each spatial direction and in the time direction will give a 16-fold increase in the number of degrees-of-freedom, implying at least an order of magnitude (perhaps two orders of magnitude) increase in the necessary computational resources. And much more resolution is needed...

Despite the limitations mentioned above, simulation of turbulent phenomena are being performed today with the help of turbulence models; such approximate models make it possible to reduce the number of unknowns to a level which is compatible with current computational resources. The trend is therefore to complement (or replace) expensive laboratory experiments with simulations, also for difficult problems like combustion.

Computational mechanics has had a tremendous impact upon science and engineering in the past [2]. Current knowledge allows us to simulate complex systems comprising structures and fluids, and also the coupling of such systems. The need for computational mechanics in science and engineering will continue in an expanded set of applications:

Medical technology

Medical technology following from advances in computational mechanics offers promising possibilities. Current use of medical technology is often of a diagnostic nature (x-rays, ultrasound, NMR etc). New application of computational mechanics promises new tools for predictive surgery [3]. Computational methods can be used to simulate blood flow and vessel dynamics, test hypotheses of disease formation, evaluate devices that have not yet been built and treatments that have not yet been implemented.

Nanotechnology

Nanotechnology is an important new area in materials research. The syntesis of nanoscale materials promises lower energy usage, lower environmental pollution, structural perfection, small size, high stiffness, high strength and excellent electronic properties. Nanoscale materials may be used in material reinforcement, as sensors, and as medical diagnostic and delivery systems [4]. Nanotechnology is expected to have a profound impact on the basic research being performed in medicine, electronics, and materials science in the coming years. Engineering software which incorporates multiscale modelling and computation will be needed; see a discussion of this approach later in this document.

Inverse problems

Inverse problems refer to problems where the objective is to infer system characteristics from measurements. Examples include seismic analysis, medical tomography (ultrasound, NMR, etc), meteorology, and satellite remote sensing. Such problems can also be regarded as optimization problems, and are computationally very demanding. It is expected that improved mathematical and computational methods will make such problems much more tractable. One promising approach is based on a probabilistic framework denoted as Bayesian inversion.

Reservoir simulation

Reservoir simulation will continue to be an important tool for determining the best way to manage our oil and gas reserves. In the coming years, it may be feasible to use high-resolution geomodels, for example, based on a multiscale approach [5]. This will allow details at the microscopic level to be better accounted for on the macroscopic level. Together with improved measurement techniques, this will allow a much better system description. Such detailed models can also be used to develop and validate low-dimensional (reduced) models, which in turn can be used in the context of real time reservoir management.

Climate modelling

Climate modelling will become an increasingly important tool in order to predict and control the effect of human activities on Earth. For global climate simulation, many submodels are of interest: atmosphere, ocean, land surface, cryosphere and biosphere. The spatial resolution of these submodels will increase significantly in the future (down to about 10 km), and new submodels will be added, e.g., atmospheric chemistry [6]. The incorporation of local effects will also be better accounted for, perhaps using multiscale modelling. Climate models will provide individual nations and the international community with increasingly important predictive tools that can possibly also be used for educational purposes.

Systems biology

Systems biology is used as a general term for the systematic analysis of complex relationships in living organisms, in particular, at a macromolecular level. The current trend indicates that system biology will become very important in the years ahead. Computational demands will most likely come in the area of simulating cellular and (macro)molecular systems, and in particular in combined, multilevel simulations, where different levels of complexity (and resolution with respect to amount of detail in model and theory) are combined in a single, integrated system. In the future, the ability to better predict and understand complex biological systems is expected to lead to advances in drug design, disease diagnosis, biologically inspired computers, and environmental health [7].

Summary

The current trend indicates that much more complex systems will be simulated, involving the modelling and simulation of multiscale and multiphysics phenomena. Computational science will increasingly complement theory and experiments. However, we predict that the need to obtain good measurements will become more important, and not less; mediocre experiments will replaced by computerized analyses and thus become superfluous.

2. Mathematical and computational methods

In addition to developing improved models in any specific application area, it will be equally important to continuously analyze and understand the underlying mathematical and statistical properties. This is important in order to have a firm and rigorous framework to build computational methods from. The numerical methods themselves need to be both efficient and accurate. The availability of scalable algorithms will become even more important in the quest to solve ever larger problems [8]. Algorithms that may otherwise be attractive will be subject to a selection process where only algorithms that prove to be both accurate and scalable will survive as practical tools for the simulation of very complex systems. It will become crucially important to develop methods that can be used to ensure fidelity in the computational results (error estimation).

As one example, let us consider one promising computational framework in more detail.

Multiscale methods

Consider materials constructed at the nanoscale. Such materials cannot be described with standard continuum models. Some of the critical phenomena need to be described at the atomistic and molecular level. However, nanoscale materials may interact with other components that are larger and have longer response times. There is therefore a need to simulate systems over an enormous range of time and length scales, ranging over many orders of magnitude. This will necessitate a coupling of atomistic, molecular and continuum models. The mathematical and computational challenges will be to link these models together and to make the simulation of fully coupled systems feasible. To this end, the emerging field of multiscale analysis and multiscale methods promises great research opportunities. Some key issues are how to separate the various scales as much as possible and at the same time ensure the correct coupling of one model level with the next one [4,5].

This approach may also prove useful for the direct simulation of turbulent phenomena.

3. Software development

Software, together with hardware, represents the engine of computational science. Despite tremendous progress over the past decades, software development for scientific and engineering problems still represents a huge investment of human resources; reliability and functionality have a very high cost. The introduction of parallel processing has certainly not made matters easier. In the past, scientific software has typically been developed by researchers and engineers with background from specific application areas. This is starting to change now, and the trend is to put more emphasis on creating reusable software, and to use more modern programming techniques. Nonetheless, software development is still an obstacle for many research groups. The availability (or non-availability) of software will influence decisions regarding research tools for doctoral students. The reality today is that the turnover time for a doctoral student is about 3-4 years, the life time of research software may be 1-15 years, the hardware (and enabling tools) changes every 4 years or so, and the active life time of a researcher is about 30 years. There is obviously a strong incentive to make software development easier, more robust, and less human resource intensive. Perhaps some of today’s efforts in this direction will be successful [9]. It is a fact that advanced mathematical ideas are more likely to be used by scientists and engineers if they are embodied in software [10]. However, such software must be created, and this requires time and interdisciplinary skills.

Hardware development

Twenty years ago, single process systems were dominant for scientific computation. In recent years, large-scale parallel processing has been the norm for challenging problems. The current trend suggests that distributed computing and storage of large data sets will also involve many computational sites. Grid computing has certainly the potential to change the way scientists and engineers work, however, it also introduces additional challenges in terms of software development, education etc. For many research groups, it may be beneficial to wait for new enabling technology to reach a certain level of maturity before investing heavily into it.

Visualization

Methods for extracting and present useful information from large data sets will be important.

4. Education

Computational science and engineering (CSE) offers a computational approach to solve problems in science and engineering which complements a pure theoretical and experimental approach. The emergence of CSE is due to the rapid advance of computational methods and computational infrastructure. The field naturally combines skills from many different fields. This interdisciplinary nature will also impact future education. We already see the emergence of specific CSE-programs within universities, at least at a graduate level, perhaps not so much at the undergraduate level. The introduction of "Computational X" classes is fairly common. How to best incorporate CSE in education is currently being discussed, and some experiences have already been documented [11]. What seems clear is that the strict borders between different departments are starting to become blurred. As an example, we mention a new PhD program in Computational Systems Biology at MIT which starts this year [7]. However, it is also clear that many current university programs are not sensitive enough to this development; it is not always easy for today’s students to mix classes from different departments in order to gain a sufficiently broad set of interdisciplinary skills.

One thing is certain: computational science is here to stay.

Finally: It is utmost important for the future credibility of computational science to educate students with a critical mindset towards the use of modelling and computation.

References

• [1] P. Moin and J. Kim , "Tackling Turbulence with Supercomputers", Scientific American, 276(1), 1997, pp. 62-68.
• [2] J.T. Oden, T. Belytschko, I. Babuska and T.J.R. Hughes , "Research Directions in Computational Mechanics," Computer Methods in Applied Mechanics and Engineering, 192, 2003, pp. 913-922.
• [3] C.A. Taylor and M.T. Draney, "Experimental and computational methods in cardiovascular fluid mechanics," Annual Review of Fluid Mechanics, 35, 2004, pp. 197-231.
• [4] W.K. Liu, E.G. Karpov, S. Zhang, and H.S. Park, "An introduction to computational nanomechanics and materials," Computer Methods in Applied Mechanics and Engineering, 2004 (in press).
• [5] W.E and B. Engquist, "Multiscale modelling and computation," Notices Amer. Math. Soc., 50(9), 2003, pp 1062-1070.
• [6] Houghton, J. T., Ding, Y., Griggs, D. J., Noguer, M., der Linden, P. J. V., Dai, X., Maskell, K. and Johnson, C. A., eds. 2001: "Climate Change 2001: The Scientific Basis: Contribution of Working Group I to the Third Assesment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, New York. http://www.grida.no/climate/ipcc_tar/wg1/index.htm
• [7] Computational and Systems Biology Initiative (CSBi): http://csbi.mit.edu/ Conference on systems biology: http://web.mit.edu/newsoffice/nr/2003/csbi2.html
• [8] ScaLeS - Science Case for Large-scale Simulation. http://www.pnl.gov/scales/
• [9] Technology Review, MIT’s Magazine for Innovation, 106(9), November 2003. Special focus on "Extreme software."
• [10] M. Wright and A. Chorin, "Mathematics and Science," Division of Mathematical Sciences, National Science Foundation, April 5, 1999. http://www.nsf.gov/pubsys/ods/getpub.cfm?mps0001
• [11] O. Yasar and R.H. Landau, "Elements of computational science and engineering education," SIAM Reviw, 45(4), 2003, pp. 787-805