“Mathematics is the alphabet with which God has written the universe.”
- Galileo Galilei
It has long been said by scientists that everything in the world can be explained through mathematics. Eugene Wigner, in his 1960 article, talks about the “unreasonable effectiveness of mathematics in the natural sciences.”
Any physical process or system that we see, can be reduced into numbers. Some go as far as to say mathematics doesn’t simply describe our universe, but that in some way, mathematics is what the universe is made up of.
Computational Science is a branch of study that deals with using computing systems to apply mathematical models, with the purpose of describing and solving natural systems and ultimately finding answers to scientific problems.
As mentioned above, mathematical models have the capability to describe any natural system. With computers, understanding, processing, and simulating these behaviours using mathematical models become easier than by human capability alone. The increasing and ever-advancing capabilities of today’s computers are what makes computational science possible and practical.
Computation is a relatively new addition to the long-existing other two branches of science. Any behaviour, process, or system, can be described and studied by Theory, Experimentation, and Computation.
They feed into each other and validate each other, ultimately forming a complete understanding of any system. Computational science can also be used where it becomes impossible or impractical to apply experimental methods.
Computational science is often thought of as an integration of three disciplines- Mathematics, Computer Science, and Science. Here the word science describes both the theoretical and experimental part of science- in most cases a particular branch of science.
The elements of Science and the elements of Computational Science
In practice, computational science brings together disciplines like applied mathematics, data science, engineering, and computing, along with whatever branch of science the model intends to study- be it biology, finance, or anything else.
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Complex systems can be described by a mathematical model. Algorithms are formulated using these models. A computing environment is used to run these models and simulations, to describe and solve the behavior of a physical system.
Basically, the high processing capabilities of computing software and hardware enables running a lot of what-if statements simultaneously, to arrive at results. The enormous data processing capabilities also allow for analyzing the amount of data generated by these simulations or analyses.
How Computational Scientific Thinking works. (Source)
The computational scientific approach to a problem has a general series of steps-
Theory: A scientific theory, or the problem statement, is used as the basis of a model.
Model: A mathematical model of the system is devised. Algorithms can be formulated to perform analyses based on the model. The rules that drive a simulation are set.
Analysis/ Simulation: Numerical analysis or simulations can be run based on algorithms. The procedure is implemented using programs and toolsets with the required capabilities.
Assessment: The data from simulation results, as well as experimental results in certain cases, are used for refining further iterations. The process is repeated until the model is solved, or a conclusion reached.
Computational science can be applied to any natural phenomenon, process, or system. This means it works together with several other branches of science to find answers to scientific problems.
Computational physics is the intersection of computer science, applied mathematics, and physics, computational chemistry is computer science, applied mathematics, and theoretical chemistry, and so on.
Here are some of the distinct disciplines formed by the application of computational science.
Computational Biology studies biological systems- including anatomical, ecological, evolutionary, behavioural, and social systems.
Here are some of the many specific subcategories to computational biology-
Computational methods have been used for gene sequencing, and computational science is partly responsible for our current understanding of genomes. Applications of computational genomics include comparative genomics, analyzing gene expression, studying gene evolution, mining biosynthetic gene clusters, and so on.
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Computational Biology has several applications in medicine, as it helps predict the behavior of human systems.
For example, using computational oncology and analyzing patterns in the growth and progression of tumors can help in better understanding the disease. It can also be used to analyze the effects of medicines, like predicting drug responses in cancer cells using computational methods. Computational immunology, which helps understand the immune system, can also help in understanding diseases and their effects.
Biological systems, including the human body, can be modeled using computational biology, from the cellular level to modeling an entire organism. Everything from brain activity to protein structures can be modeled and used for research.
With the growth of technology, studying the structure and chemistry of biomolecules becomes simpler, and there are several advancements in biomolecular modeling in recent times.
Ecological models can also be created, which gives us insight into the relationships within ecosystems. Studying and analyzing behavioral patterns of flora and fauna can help better understand changes to the environment. For example, studying changes in migratory patterns of birds can give insights into the progress of global warming and how it’s affecting them.
Computational chemistry means using computers to solve chemical problems- to study and predict chemical reactions and understand molecular structures and properties. Computational chemistry works with chemistry and quantum mechanics. Most of the algorithms in computational chemistry are based on the Schrodinger equation.
There are different methods used in computational chemistry- Ab initio methods, density functional methods, empirical methods, molecular mechanics, etc. These different methods find application in different ways.
Computational modeling allows for quicker analysis of x-ray diffraction data to understand molecular structures. This helps in better understanding and predicting exact molecular structures. Relationships between molecular properties and structures can also be drawn using computational chemistry.
One of the most important and well-known applications of figuring out molecular interactions using computational chemistry is in pharmaceuticals. Computational modeling can be used in the development of drugs. The effects caused by altering a drug molecule can be predicted using simulations. This along with biomodelling of disease progression makes drug design quicker and more efficient.
Computational physics deals with the study and analysis of physical problems through computation and modeling. The applications in physics are vast, and computational models are used in almost all branches of physics. These are some of them.
CFD is a branch of fluid mechanics that utilizes computational models to analyze fluid flow. Although different approaches are used in CFD, the fundamental methodology remains the same. A CAD model of the system is formed, a mesh is created and boundary conditions are defined, and then the simulation is solved through iteration.
Large scale astronomical events cannot be accurately studied or predicted using theoretical methods, and experimental methods are out of the question. A supernova couldn’t be possibly studied through experimental methods. Computational physics allows for the understanding of the formation and lives of stars by solving computational models of supernovae.
Nature Computational Science published an article recently that talked about new views of black holes made possible from computational imaging.
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This is the study of using computational models to find out how electromagnetism interacts with physical entities in an environment.
Computational finance has gained much popularity in recent times and permeates every aspect of finance. Making the best investments is what so often what those specializing in computational finance helps do.
Computational science is greatly suited to solve optimization problems, which requires trial through numerous different iterations. Portfolio optimization, asset pricing, and risk analysis, for instance, can be done in a fast and efficient way with computing.
Trading is a precise business with variables like time, price, and volume that need to be accounted for before making decisions. Algorithmic trading is an automation of this process, giving the reins over to computational models and predictive analysis. High-Frequency Trading is also a similar automated trading system based on algorithms.
Computational social science focuses on solving social problems- including behavioral patterns of human society, progression of culture, relationships, economics, etc.
Modelling of social interactions on small and large scales can be done through computational science. Computational models can effectively create predictive models of behavior within human society.
Big data, data mining, and social data analysis contribute much to this area nowadays. Vast amounts of data can be obtained through social media and the internet, and human behavior can be studied through mining this data, organizing it, and creating simulations based on the data.
Computational science, with social modeling, has applications in marketing as well.
Different from computational finance, this branch focuses on predictive economic models. The economic growth and trends of a society can be predicted to some degree of accuracy with computational analysis.
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Computational science has been instrumental in the fight against the ongoing COVID-19 pandemic in a variety of ways. Computational models can, and have been, providing insight into the working of the virus, mapping disease progression, helping predict public response, make decisions, and aiding in vaccine and drug development.
Furthermore, the recognition of biomolecular simulation in particular as a useful tool has resulted in a rapid wave of broader adoption and sharing of this technology. This can be expected to have lasting effects, even beyond the pandemic.
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