Scientific modelling

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Example scientific modelling. A schematic of chemical and transport processes related to atmospheric composition. Atmosphere composition diagram-en.svg
Example scientific modelling. A schematic of chemical and transport processes related to atmospheric composition.

Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject.

Contents

Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. [1] [2] The following was said by John von Neumann. [3]

... the sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area.

There is also an increasing attention to scientific modelling [4] in fields such as science education, [5] philosophy of science, systems theory, and knowledge visualization. There is a growing collection of methods, techniques and meta-theory about all kinds of specialized scientific modelling.

Overview

MathModel.svg

A scientific model seeks to represent empirical objects, phenomena, and physical processes in a logical and objective way. All models are in simulacra, that is, simplified reflections of reality that, despite being approximations, can be extremely useful. [6] Building and disputing models is fundamental to the scientific enterprise. Complete and true representation may be impossible, but scientific debate often concerns which is the better model for a given task, e.g., which is the more accurate climate model for seasonal forecasting. [7]

Attempts to formalize the principles of the empirical sciences use an interpretation to model reality, in the same way logicians axiomatize the principles of logic. The aim of these attempts is to construct a formal system that will not produce theoretical consequences that are contrary to what is found in reality. Predictions or other statements drawn from such a formal system mirror or map the real world only insofar as these scientific models are true. [8] [9]

For the scientist, a model is also a way in which the human thought processes can be amplified. [10] For instance, models that are rendered in software allow scientists to leverage computational power to simulate, visualize, manipulate and gain intuition about the entity, phenomenon, or process being represented. Such computer models are in silico. Other types of scientific models are in vivo (living models, such as laboratory rats) and in vitro (in glassware, such as tissue culture). [11]

Basics

Modelling as a substitute for direct measurement and experimentation

Models are typically used when it is either impossible or impractical to create experimental conditions in which scientists can directly measure outcomes. Direct measurement of outcomes under controlled conditions (see Scientific method) will always be more reliable than modeled estimates of outcomes.

Within modeling and simulation, a model is a task-driven, purposeful simplification and abstraction of a perception of reality, shaped by physical, legal, and cognitive constraints. [12] It is task-driven because a model is captured with a certain question or task in mind. Simplifications leave all the known and observed entities and their relation out that are not important for the task. Abstraction aggregates information that is important but not needed in the same detail as the object of interest. Both activities, simplification, and abstraction, are done purposefully. However, they are done based on a perception of reality. This perception is already a model in itself, as it comes with a physical constraint. There are also constraints on what we are able to legally observe with our current tools and methods, and cognitive constraints that limit what we are able to explain with our current theories. This model comprises the concepts, their behavior, and their relations informal form and is often referred to as a conceptual model. In order to execute the model, it needs to be implemented as a computer simulation. This requires more choices, such as numerical approximations or the use of heuristics. [13] Despite all these epistemological and computational constraints, simulation has been recognized as the third pillar of scientific methods: theory building, simulation, and experimentation. [14]

Simulation

A simulation is a way to implement the model, often employed when the model is too complex for the analytical solution. A steady-state simulation provides information about the system at a specific instant in time (usually at equilibrium, if such a state exists). A dynamic simulation provides information over time. A simulation shows how a particular object or phenomenon will behave. Such a simulation can be useful for testing, analysis, or training in those cases where real-world systems or concepts can be represented by models. [15]

Structure

Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art. [16]

Systems

A system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. In general, a system is a construct or collection of different elements that together can produce results not obtainable by the elements alone. [17] The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and form relationships between an element of the set and elements not a part of the relational regime. There are two types of system models: 1) discrete in which the variables change instantaneously at separate points in time and, 2) continuous where the state variables change continuously with respect to time. [18]

Generating a model

Modelling is the process of generating a model as a conceptual representation of some phenomenon. Typically a model will deal with only some aspects of the phenomenon in question, and two models of the same phenomenon may be essentially different—that is to say, that the differences between them comprise more than just a simple renaming of components.

Such differences may be due to differing requirements of the model's end users, or to conceptual or aesthetic differences among the modelers and to contingent decisions made during the modelling process. Considerations that may influence the structure of a model might be the modeler's preference for a reduced ontology, preferences regarding statistical models versus deterministic models, discrete versus continuous time, etc. In any case, users of a model need to understand the assumptions made that are pertinent to its validity for a given use.

Building a model requires abstraction. Assumptions are used in modelling in order to specify the domain of application of the model. For example, the special theory of relativity assumes an inertial frame of reference. This assumption was contextualized and further explained by the general theory of relativity. A model makes accurate predictions when its assumptions are valid, and might well not make accurate predictions when its assumptions do not hold. Such assumptions are often the point with which older theories are succeeded by new ones (the general theory of relativity works in non-inertial reference frames as well).

Evaluating a model

A model is evaluated first and foremost by its consistency to empirical data; any model inconsistent with reproducible observations must be modified or rejected. One way to modify the model is by restricting the domain over which it is credited with having high validity. A case in point is Newtonian physics, which is highly useful except for the very small, the very fast, and the very massive phenomena of the universe. However, a fit to empirical data alone is not sufficient for a model to be accepted as valid. Factors important in evaluating a model include:[ citation needed ]

People may attempt to quantify the evaluation of a model using a utility function.

Visualization

Visualization is any technique for creating images, diagrams, or animations to communicate a message. Visualization through visual imagery has been an effective way to communicate both abstract and concrete ideas since the dawn of man. Examples from history include cave paintings, Egyptian hieroglyphs, Greek geometry, and Leonardo da Vinci's revolutionary methods of technical drawing for engineering and scientific purposes.

Space mapping

Space mapping refers to a methodology that employs a "quasi-global" modelling formulation to link companion "coarse" (ideal or low-fidelity) with "fine" (practical or high-fidelity) models of different complexities. In engineering optimization, space mapping aligns (maps) a very fast coarse model with its related expensive-to-compute fine model so as to avoid direct expensive optimization of the fine model. The alignment process iteratively refines a "mapped" coarse model (surrogate model).

Types

Applications

Modelling and simulation

One application of scientific modelling is the field of modelling and simulation, generally referred to as "M&S". M&S has a spectrum of applications which range from concept development and analysis, through experimentation, measurement, and verification, to disposal analysis. Projects and programs may use hundreds of different simulations, simulators and model analysis tools.

Example of the integrated use of Modelling and Simulation in Defence life cycle management. The modelling and simulation in this image is represented in the center of the image with the three containers. Modeling and Simulation Integrated Use.jpg
Example of the integrated use of Modelling and Simulation in Defence life cycle management. The modelling and simulation in this image is represented in the center of the image with the three containers.

The figure shows how modelling and simulation is used as a central part of an integrated program in a defence capability development process. [15]

See also

Related Research Articles

Abstraction is a process wherein general rules and concepts are derived from the usage and classification of specific examples, literal signifiers, first principles, or other methods.

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences and engineering disciplines, as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right.

A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultimate purpose of science. This discipline overlaps with metaphysics, ontology, and epistemology, for example, when it explores the relationship between science and truth. Philosophy of science focuses on metaphysical, epistemic and semantic aspects of science. Ethical issues such as bioethics and scientific misconduct are often considered ethics or science studies rather than the philosophy of science.

<span class="mw-page-title-main">Computational physics</span> Numerical simulations of physical problems via computers

Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics — an area of study which supplements both theory and experiment.

A scientific theory is an explanation of an aspect of the natural world and universe that can be repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, some theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.

<span class="mw-page-title-main">Model</span> Informative representation of an entity

A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, a measure.

<span class="mw-page-title-main">Computer simulation</span> Process of mathematical modelling, performed on a computer

Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics, astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.

Social simulation is a research field that applies computational methods to study issues in the social sciences. The issues explored include problems in computational law, psychology, organizational behavior, sociology, political science, economics, anthropology, geography, engineering, archaeology and linguistics.

<span class="mw-page-title-main">Operationalization</span> Part of the process of research design

In research design, especially in psychology, social sciences, life sciences and physics, operationalization or operationalisation is a process of defining the measurement of a phenomenon which is not directly measurable, though its existence is inferred from other phenomena. Operationalization thus defines a fuzzy concept so as to make it clearly distinguishable, measurable, and understandable by empirical observation. In a broader sense, it defines the extension of a concept—describing what is and is not an instance of that concept. For example, in medicine, the phenomenon of health might be operationalized by one or more indicators like body mass index or tobacco smoking. As another example, in visual processing the presence of a certain object in the environment could be inferred by measuring specific features of the light it reflects. In these examples, the phenomena are difficult to directly observe and measure because they are general/abstract or they are latent. Operationalization helps infer the existence, and some elements of the extension, of the phenomena of interest by means of some observable and measurable effects they have.

<span class="mw-page-title-main">Social complexity</span> Conceptual framework

In sociology, social complexity is a conceptual framework used in the analysis of society. In the sciences, contemporary definitions of complexity are found in systems theory, wherein the phenomenon being studied has many parts and many possible arrangements of the parts; simultaneously, what is complex and what is simple are relative and change in time.

An artificial society is an agent-based computational model for computer simulation in social analysis. It is mostly connected to the themes of complex systems, emergence, the Monte Carlo method, computational sociology, multi-agent systems, and evolutionary programming. While the concept was simple, actually realizing this conceptual point took a while. Complex mathematical models have been, and are, common; deceivingly simple models only have their roots in the late forties, and took the advent of the microcomputer to really get up to speed.

Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes

In philosophy of science, idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve. That is, it is determined whether the phenomenon approximates an "ideal case," then the model is applied to make a prediction based on that ideal case.

The term conceptual model refers to any model that is formed after a conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience.

Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.

<span class="mw-page-title-main">Computational engineering</span>

Computational Engineering is an emerging discipline that deals with the development and application of computational models for engineering, known as Computational Engineering Models or CEM. Computational engineering uses computers to solve engineering design problems important to a variety of industries. At this time, various different approaches are summarized under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven approach In Computational Engineering, algorithms solve mathematical and logical models that describe engineering challenges, sometimes coupled with some aspect of AI, specifically Reinforcement Learning.

The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups:

<span class="mw-page-title-main">Theoretical physics</span> Branch of physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.

<span class="mw-page-title-main">Hypothesis</span> Proposed explanation for an observation, phenomenon, or scientific problem

A hypothesis is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis proposed for further research in a process beginning with an educated guess or thought.

References

  1. Cartwright, Nancy. 1983. How the Laws of Physics Lie . Oxford University Press
  2. Hacking, Ian. 1983. Representing and Intervening. Introductory Topics in the Philosophy of Natural Science. Cambridge University Press
  3. von Neumann, J. (1995), "Method in the physical sciences", in Bródy F., Vámos, T. (editors), The Neumann Compendium, World Scientific, p. 628; previously published in The Unity of Knowledge, edited by L. Leary (1955), pp. 157-164, and also in John von Neumann Collected Works, edited by A. Taub, Volume VI, pp. 491-498.
  4. Frigg and Hartmann (2009) state: "Philosophers are acknowledging the importance of models with increasing attention and are probing the assorted roles that models play in scientific practice". Source: Frigg, Roman and Hartmann, Stephan, "Models in Science", The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.), (source)
  5. Namdar, Bahadir; Shen, Ji (2015-02-18). "Modelling-Oriented Assessment in K-12 Science Education: A synthesis of research from 1980 to 2013 and new directions". International Journal of Science Education. 37 (7): 993–1023. Bibcode:2015IJSEd..37..993N. doi:10.1080/09500693.2015.1012185. ISSN   0950-0693. S2CID   143865553.
  6. Box, George E.P. & Draper, N.R. (1987). [Empirical Model-Building and Response Surfaces.] Wiley. p. 424
  7. Hagedorn, R. et al. (2005) http://www.ecmwf.int/staff/paco_doblas/abstr/tellus05_1.pdf [ permanent dead link ]Tellus 57A:219–33
  8. Leo Apostel (1961). "Formal study of models". In: The Concept and the Role of the Model in Mathematics and Natural and Social. Edited by Hans Freudenthal. Springer. pp. 8–9 (Source)],
  9. Ritchey, T. (2012) Outline for a Morphology of Modelling Methods: Contribution to a General Theory of Modelling
  10. C. West Churchman, The Systems Approach, New York: Dell Publishing, 1968, p. 61
  11. Griffiths, E. C. (2010) What is a model?
  12. Tolk, A. (2015). Learning something right from models that are wrong – Epistemology of Simulation. In Yilmaz, L. (Ed.) Concepts and Methodologies in Modelling and Simulation. Springer–Verlag. pp. 87–106
  13. Oberkampf, W. L., DeLand, S. M., Rutherford, B. M., Diegert, K. V., & Alvin, K. F. (2002). Error and uncertainty in modelling and simulation. Reliability Engineering & System Safety 75(3): 333–57.
  14. Ihrig, M. (2012). A New Research Architecture For The Simulation Era. In European Council on Modelling and Simulation. pp. 715–20).
  15. 1 2 3 Systems Engineering Fundamentals. Archived 2007-09-27 at the Wayback Machine Defense Acquisition University Press, 2003.
  16. Pullan, Wendy (2000). Structure. Cambridge: Cambridge University Press. ISBN   0-521-78258-9.
  17. Fishwick PA. (1995). Simulation Model Design and Execution: Building Digital Worlds. Upper Saddle River, NJ: Prentice-Hall.
  18. Sokolowski, J.A., Banks, C.M.(2009). Principles of Modelling and Simulation. Hoboken, NJ: John Wiley and Sons.

Further reading

Nowadays there are some 40 magazines about scientific modelling which offer all kinds of international forums. Since the 1960s there is a strongly growing number of books and magazines about specific forms of scientific modelling. There is also a lot of discussion about scientific modelling in the philosophy-of-science literature. A selection: