Experiment is the engine of many branches of science. We are accustomed to full-scale, laboratory experiments. But what is a computational experiment? In this article, we suggest that you deal with this phenomenon, its stages, and distinctive features.
What is it?
To begin with, we give the definitions of a computational experiment that are relevant to the scientific world:
- A specific research organization in which the properties of phenomena and objects are studied on the basis of mathematical models. The behavior of objects is played under various conditions, on the basis of which scientists choose the optimal mode for them (A. Samarsky).
- The transition from the study of any real subject to the study of its mathematical model. The last one or more equations appear.
- A technology for studying mathematical models based on their construction and subsequent analysis using computing electronic devices.
- Imitation of some reality.
The use of computational experiments is associated with the study of such processes, laboratory or full-scale study of which was difficult or completely impossible. For example, in the 40-50s of the last century, the Soviet academician M. Keldysh developed a mathematical description of space flights.
Distinctive characteristics of the method
The basis of the computational experiment is mathematical modeling. Its theoretical basis is applied mathematics, and the technological basis is modern powerful computers. In addition, such studies require extensive knowledge in many areas of mechanics, mathematics, physics, ecology, chemistry and economics.
A computational experiment is working with three models:
- System, real object.
- Simulation model of a real object.
- Information Computer System.
Computational experiments make it possible to find out what is not subject to classical (laboratory and field) methods:
- Internal interactions of various subsystems, elements, the impact on their activities of environmental changes.
- To discover important features of the functioning of the system, to develop a plan for its improvement.
- To gain new knowledge, even having incomplete information about the system.
- Work out various methods of action and strategies.
Laboratory and field experiments
Models of a computational experiment are the "younger brothers" of other studies that have existed from time immemorial: full-scale and laboratory. Once upon a time, scientists did only with these methods to test their hypotheses, scientific ideas, technical solutions, new designs and devices.
How are they different from modeling, a computational experiment? The difference can be recognized by reading the definitions:
- Field experiment - various tests to which new devices and apparatuses were subjected. The goal was to establish their characteristics, verify the capabilities and declared properties. Such studies are most characteristic of the technical sphere.
- Laboratory experiment - the creation of experimental facilities, the development of measuring devices, as well as methods for conducting the experiment. Similar studies are characteristic of chemistry and physics.
Key benefits of the method
We list the main advantages of a computational experiment over other methods:
- An object of interest can be investigated without creating a real model of the apparatus, installation.
- The ability to study each of the factors separately, while they act simultaneously in reality.
- The ability to study those processes and phenomena that cannot exist in the real world.
Experiment Methods
We list the main methods of a computational experiment:
- Distributed and parallel programming.
- Creation of relativistic plasma and electron clots, subsequent control of their movement.
- The method of particles in a cell (for three-dimensional and two-dimensional plasma processes).
- Electromagnetic one-dimensional modeling.
- Modeling of one-dimensional electromagnetic processes.
- Modeling of plasma one-dimensional systems.
- Plasma models constructed according to the Vlasov equation.
- Modeling of physical systems that consist of a large number of interacting particles.
Stages
“Conduct a computational experiment" - this task means that the researcher in his work must go through several stages:
- Qualitative comprehensive analysis of the subject of interest. The construction of his mathematical model.
- Development of computational algorithms.
- Creating a program capable of implementing the created computational algorithm.
- Carrying out the necessary calculations on electronic computers.
- Processing of the results, analysis of the study, the formation of conclusions.
Carrying out a computational experiment, like any other study, begins with setting goals for subsequent work:
- Working hypotheses in need of verification.
- Questions needing answers.
- Management actions in need of answers.
And now we offer you to analyze in detail each of the stages of the study.
First step
Here, the scientist's first main task is to choose from the whole variety of properties of the object of study those that really need to be studied during the experiment.
Further, for the process under study, a computational (mathematical) model is necessarily built. It is created in such a way that it is able to separate all factors influencing the object of the experiment into two groups:
- The main ones. Necessarily taken into account.
- Minor Those that can be dropped.
Then it is imperative to form a framework for the applicability of the model to which the results are considered fair.
Second phase
At the next stage of the computational experiment, a method for calculating the mathematical problem formed by the researcher is developed. In this case, a computational algorithm. In fact, it will be a certain combination of algebraic formulas (they will be used for calculations) and logical conditions (they will help establish the necessary sequence for applying the formulas).
Third stage
At this step of the computer experiment, a program is created that allows you to implement the compiled algorithm. This is a programming step for electronic computing devices.
In fact, a project for the preparation of code compiled in a high-level language is being created here. It will be the implementation of an algorithm for numerical problem solving.
Here before scientists the following problematic questions arise:
- Justification of the complexity of the computational model. Such mathematical models are desirable that could give the most complete idea of the functioning of the system, but at the same time would not require complex calculations, programming.
- The duration of the calculations on the computer. The experiment should take a reasonable amount of time.
- Adequacy of the created model of simulation reality. How valuable is the compiled model? How useful is a simulation experiment?
Fourth stage
At this stage, calculations are carried out directly on the computer. I must say, this stage is largely reminiscent of the implementation of a laboratory experiment. The difference is only one: if in the laboratory, scientists using a specially designed installation ask their questions to nature, then here, using computers, questions are already asked to the mathematical model.
Fifth stage
So we have come to the end of the computational experiment. It is important to get the calculation results presented by some digital information that needs further decoding.
Scientists are moving to calculations and analysis of the results. This requires not only significant intellectual efforts, but also sufficient skills to present, process and rethink the available conclusions:
- Is the studied factor controlled?
- Are its values observable?
- Is factor influence a subject to study?
- Are factor levels inherently qualitative or quantitative?
- Is the identified factor random or fixed?
This concludes our acquaintance with the latest type of experiment - computational. Its main difference from the full-scale and laboratory ones is that the scientists here are studying not reality itself, but its mathematical model, imitation. This experiment also has its own methods, a specific research algorithm in five main steps. Perhaps in the future he will find a more innovative successor.