# Computational science

**Computational science**, also known as

**scientific computing**or

**scientific computation**, is a rapidly growing field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core, it involves the development of models and simulations to understand natural systems.

- Algorithms : mathematical models, computational models, and computer simulations developed to solve science, engineering, and humanities problems
- Computer hardware that develops and optimizes the advanced system hardware, firmware, networking, and data management components needed to solve computationally demanding problems
- The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science

## The computational scientist

The term computational scientist is used to describe someone skilled in scientific computing. This person is usually a scientist, an engineer or an applied mathematician who applies high-performance computing in different ways to advance the state-of-the-art in their respective applied disciplines in physics, chemistry or engineering.Computational science is now commonly considered a third mode of science, complementing and adding to experimentation/observation and theory. Here, we define a system as a potential source of data, an experiment as a process of extracting data from a system by exerting it through its inputs and a model for a system and an experiment as anything to which E can be applied in order to answer questions about S. A computational scientist should be capable of:

- recognizing
**complex problems** - adequately
**conceptualise**the system containing these problems - design a framework of algorithms suitable for studying this system: the
**simulation** - choose a suitable
**computing infrastructure** - hereby, maximising the
**computational power**of the simulation - assessing to what level the output of the simulation resembles the systems: the model is
**validated** - adjust the conceptualisation of the system accordingly
- repeat cycle until a suitable level of validation is obtained: the computational scientists trusts that the simulation generates adequately realistic results for the system, under the studied conditions

Philosophers of science addressed the question to what degree computational science qualifies as science, among them Humphreys and Gelfert. They address the general question of epistemology: how do we gain insight from such computational science approaches. Tolk uses these insights to show the epistemological constraints of computer-based simulation research. As computational science uses mathematical models representing the underlying theory in executable form, in essence, they apply modeling and simulation. While simulation and computational science are our most sophisticated way to express our knowledge and understanding, they also come with all constraints and limits already known for computational solutions.

## Applications of computational science

Problem domains for computational science/scientific computing include:### Urban complex systems

In 2015, over half the world's population live in cities. By the middle of the 21st century, it is estimated that 75% of the world's population will be urban. This urban growth is focused in the urban populations of developing countries where city dwellers will more than double, increasing from 2.5 billion in 2009 to almost 5.2 billion in 2050. Cities are massive complex systems created by humans, made up of humans and governed by humans. Trying to predict, understand and somehow shape the development of cities in the future requires complex thinking, and requires computational models and simulations to help mitigate challenges and possible disasters. The focus of research in urban complex systems is, through modeling and simulation, to build a greater understanding of city dynamics and help prepare for the coming urbanisation.### Computational finance

In today's financial markets huge volumes of interdependent assets are traded by a large number of interacting market participants in different locations and time zones. Their behavior is of unprecedented complexity and the characterization and measurement of the risk inherent to these highly diverse set of instruments is typically based on complicated mathematical and computational models. Solving these models exactly in closed form, even at a single instrument level, is typically not possible, and therefore we have to look for efficient numerical algorithms. This has become even more urgent and complex recently, as the credit crisis has clearly demonstrated the role of cascading effects going from single instruments through portfolios of single institutions to even the interconnected trading network. Understanding this requires a multi-scale and holistic approach where interdependent risk factors such as market, credit and liquidity risk are modelled simultaneously and at different interconnected scales.### Computational biology

Exciting new developments in biotechnology are now revolutionizing biology and biomedical research. Examples of these techniques are high-throughput sequencing, high-throughput quantitative PCR, intra-cellular imaging, in-situ hybridization of gene expression, three-dimensional imaging techniques like Light Sheet Fluorescence Microscopy and Optical Projection, -Computer Tomography. Given the massive amounts of complicated data that is generated by these techniques, their meaningful interpretation, and even their storage, form major challenges calling for new approaches. Going beyond current bioinformatics approaches, computational biology needs to develop new methods to discover meaningful patterns in these large data sets. Model-based reconstruction of gene networks can be used to organize the gene expression data in a systematic way and to guide future data collection. A major challenge here is to understand how gene regulation is controlling fundamental biological processes like biomineralisation and embryogenesis. The sub-processes like gene regulation, organic molecules interacting with the mineral deposition process, cellular processes, physiology and other processes at the tissue and environmental levels are linked. Rather than being directed by a central control mechanism, biomineralisation and embryogenesis can be viewed as an emergent behavior resulting from a complex system in which several sub-processes on very different temporal and spatial scales are connected into a multi-scale system. One of the few available options to understand such systems is by developing a multi-scale model of the system.### Complex systems theory

Using information theory, non-equilibrium dynamics and explicit simulations computational systems theory tries to uncover the true nature of complex adaptive systems.### Computational science in engineering

Computational science and engineering is a relatively new discipline that deals with the development and application of computational models and simulations, often coupled with high-performance computing, to solve complex physical problems arising in engineering analysis and design as well as natural phenomena. CSE has been described as the "third mode of discovery". In many fields, computer simulation is integral and therefore essential to business and research. Computer simulation provides the capability to enter fields that are either inaccessible to traditional experimentation or where carrying out traditional empirical inquiries is prohibitively expensive. CSE should neither be confused with pure computer science, nor with computer engineering, although a wide domain in the former is used in CSE and some problems in the latter can be modeled and solved with CSE methods.## Methods and algorithms

Algorithms and mathematical methods used in computational science are varied. Commonly applied methods include:- Computer algebra, including symbolic computation in fields such as statistics, equation solving, algebra, calculus, geometry, linear algebra, tensor analysis, optimization
- Numerical analysis, including Computing derivatives by finite differences
- * Application of Taylor series as convergent and asymptotic series
- * Computing derivatives by Automatic differentiation
- * Finite element method for solving PDEs
- * High order difference approximations via Taylor series and Richardson extrapolation
- * Methods of integration on a uniform mesh: rectangle rule, trapezoid rule, Simpson's rule
- * Runge–Kutta methods for solving ordinary differential equations
- * Newton's method
- Discrete Fourier transform
- Monte Carlo methods
- Numerical linear algebra, including decompositions and eigenvalue algorithms
- Linear programming
- Branch and cut
- Branch and bound
- Molecular dynamics, Car–Parrinello molecular dynamics
- Space mapping
- Time stepping methods for dynamical systems

Computational science application programs often model real-world changing conditions, such as weather, airflow around a plane, automobile body distortions in a crash, the motion of stars in a galaxy, an explosive device, etc. Such programs might create a 'logical mesh' in computer memory where each item corresponds to an area in space and contains information about that space relevant to the model. For example, in weather models, each item might be a square kilometer; with land elevation, current wind direction, humidity, temperature, pressure, etc. The program would calculate the likely next state based on the current state, in simulated time steps, solving equations that describe how the system operates; and then repeat the process to calculate the next state.

## Conferences and journals

In the year 2001, the was first organised. Since then it has been organised yearly. ICCS is an**A-rank**conference in CORE classification.

The international published its first issue in May 2010. A new initiative was launched in 2012, the

*Journal of Open Research Software.*

In 2015, ReScience dedicated to the replication of computational results has been started on GitHub.

## Education

At some institutions, a specialization in scientific computation can be earned as a "minor" within another program. However, there are increasingly many bachelor's, master's and doctoral programs in computational science. The joint degree programme at the University of Amsterdam and the Vrije Universiteit in computational science was first offered in 2004. In this programme, students:- learn to build computational models from real-life observations;
- develop skills in turning these models into computational structures and in performing large-scale simulations;
- learn theory that will give a firm basis for the analysis of complex systems;
- learn to analyse the results of simulations in a virtual laboratory using advanced numerical algorithms.

School of Computational and Integrative Sciences, Jawaharlal Nehru University also offers a vibrant master's science program for computational science with two specialities namely- Computational Biology and Complex Systems.

## Related fields

- Bioinformatics
- Car–Parrinello molecular dynamics
- Cheminformatics
- Chemometrics
- Computational archaeology
- Computational biology
- Computational chemistry
- Computational materials science
- Computational economics
- Computational electromagnetics
- Computational engineering
- Computational finance
- Computational fluid dynamics
- Computational forensics
- Computational geophysics
- Computational history
- Computational informatics
- Computational intelligence
- Computational law
- Computational linguistics
- Computational mathematics
- Computational mechanics
- Computational neuroscience
- Computational particle physics
- Computational physics
- Computational sociology
- Computational statistics
- Computational sustainability
- Computer algebra
- Computer simulation
- Financial modeling
- Geographic information system
- High-performance computing
- Machine learning
- Network analysis
- Neuroinformatics
- Numerical linear algebra
- Numerical weather prediction
- Pattern recognition
- Scientific visualization
- Simulation
## Additional sources

- E. Gallopoulos and A. Sameh, "CSE: Content and Product". IEEE Computational Science and Engineering Magazine, 4:39–43
- G. Hager and G. Wellein, Introduction to High Performance Computing for Scientists and Engineers, Chapman and Hall
- A.K. Hartmann, , World Scientific
- Journal , Polish Academy of Sciences
- Journal , Institute of Physics
- R.H. Landau, C.C. Bordeianu, and M. Jose Paez, , Princeton University Press