Computational science: the most powerful tool to understand the world

To understand it from its name, computational science is a way to study the world with computational methods. In other word, everything should be stored with “1” or “0” and manipulated by computer algorithms. Basically, this process consists of two parts, constructing mathematical modeling and quantitative analysis.

People might suspect about the accuracy of the computational model, since it is discrete while the real world objects are mostly continuous without gaps. This is correct because computational models are fundamentally only consist two discrete statuses, such as “0” and “1”. However, it is also this discrete model that provides computational methods high efficiency when solving problems modeled in this way. Fortunately, computational scientists have developed various digitalization methods to provide a solution with trade-off between accuracy and efficiency. Considering the difference between the normal screen and the retina screen of iPad, you might think that the later retina screen will represent the image more accurate than the older one. However both of them are using huge numbers of discrete points to model the picture. The only difference is that the retina screen will use much more points than the normal ones. The more accurate model we construct, the bigger amount of data we will use and the more complex problem we should solve. Besides the digitalization, a good mathematical modeling will need to consider lots of other issues, such as boundary conditions, the outliers and the structure of the model which is similar to the real problems, etc. Some parametric models will need model fitting to determine the value of parameters.

Ref: Biocomputation Research, http://simbios.stanford.edu/BioAlg.htm

With a good computational model, we can perform quantitative analysis for solving a given question. For example, given a network model of an integrated circuit and the timing model of each gate in the circuit, we can perform quantitative analysis to calculate the longest delay of the whole circuit under some environment temperature. This technique will be very useful to chip design companies since they need not to determine whether the chip will function well until post-manufacture. To realize this simulation process, we need to develop a suitable algorithm to traverse the whole network graph and on each node, we need to perform numerical integration to solve the non-linear functions with variables such as current and voltage. The similar process will be used to simulate biology system such as metabolism system. As soon as we obtained an accurate enough model, we can perform simulation with little cost and at any speed. With less than an hour, we can obtain the behavior of circuits after thirty years or know the evolutionary status of a living organism.  In this way, computational science provides us an unprecedented tool to study the unknown world and I can’t wait to see more amazing achievements in these fields.