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Overview
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 [31]. 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 [43].
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 [47, 55].
For the scientist, a model is also a way in which the human thought
processes can be amplified [32]. 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) [41].
Basics of scientific modelling
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
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(see Scientific method) will always be more reliable than modelled
estimates of outcomes.
Within modelling and simulation, a model is a task-driven,
purposeful simplification and abstraction of a perception of reality, shaped
by physical, legal, and cognitive constraints [62]. 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 which limit what we are able to explain with our
current theories. This model comprises the concepts, their behavior, and
their relations in formal 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 [53]. Despite all these epistemological and
computational constraints, simulation has been recognized as the third pillar
of scientific methods: theory building, simulation, and experimentation
[44].
Simulation
A simulation is the implementation of a model. 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 brings a model to life and
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 [61].
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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 [54].
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 [38]. 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
from 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 [58].
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 modellers
and to contingent decisions made during the modelling process.
Considerations that may influence the structure of a model might be the
modeller's preference for a reduced ontology, preferences regarding
statistical models versus deterministic models, discrete versus continuous
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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).
The term "assumption" is actually broader than its standard use,
etymologically speaking. The Oxford English Dictionary (OED) and online
Wiktionary indicate its Latin source as assumere ("accept, to take to
oneself, adopt, usurp"), which is a conjunction of ad- ("to, towards, at") and
sumere (to take). The root survives, with shifted meanings, in the Italian
sumere and Spanish sumir. In the OED, "assume" has the senses of (i)
“investing oneself with (an attribute), ” (ii) “to undertake” (especially in
Law), (iii) “to take to oneself in appearance only, to pretend to possess,”
and (iv) “to suppose a thing to be.” Thus, "assumption" connotes other
associations than the contemporary standard sense of “that which is
assumed or taken for granted; a supposition, postulate,” and deserves a
broader analysis in the philosophy of science.
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.
Other factors important in evaluating a model include:
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Ability to explain past observations
Ability to predict future observations
Cost of use, especially in combination with other models
Refutability, enabling estimation of the degree of confidence in the
model
Simplicity, or even aesthetic appeal
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 "quasiglobal" modeling formulation to link companion "coarse" (ideal or lowfidelity) 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).
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Types of scientific modelling
Analogical modelling
Assembly modelling
Catastrophe modelling
Choice Modelling
Climate model
Continuous modelling
Data modelling
Discrete modeling
Document modelling
Economic model
Ecosystem model
Empirical modelling
Enterprise modelling
Futures studies
Geologic modelling
Goal Modelling
Homology modelling
Hydrogeology
Hydrography
Hydrologic modelling
Idealized modelling
Informative Modelling
Macroscale modelling
Mathematical modelling
Metabolic network modelling
Microscale modelling
Modeling biological systems
Modelling in Epidemiology
Molecular modelling
Multiscale modelling
NLP modelling
Phenomenological modelling
Predictive intake modelling
Predictive modelling
Scale modeling
Simulation
Software modelling
Solid modelling
Space mapping
Statistics
Stochastic modelling
(insurance)
Surrogate model
System architecture
System dynamics
Systems modelling
Water quality modelling
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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.
Figure 3. Example of the integrated use of Modelling and Simulation in
Defence life cycle management.
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The modelling and simulation in this image is represented in the
center of the image with the three containers [61].
The figure shows how Modelling and Simulation is used as a central
part of an integrated program in a Defence capability development process
[61].
Model-based learning in education
Figure 4. Model-based learning in education.
Model-based learning in education, particularly in relation to learning
science involves students creating models for scientific concepts in order to
[45]:
Gain insight of the scientific idea(s)
Acquire deeper understanding of the subject through visualization
of the model
Improve student engagement in the course
Different types of model based learning techniques include [45]:
Physical macrocosms
Representational systems
Syntactic models
Emergent models
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Model–making in education is an iterative exercise with students
refining, developing and evaluating their models over time. This shifts
learning from the rigidity and monotony of traditional curriculum to an
exercise of students' creativity and curiosity. This approach utilizes the
constructive strategy of social collaboration and learning scaffold theory.
Model based learning includes cognitive reasoning skills where existing
models can be improved upon by construction of newer models using the
old models as a basis [52].
"Model–based learning entails determining target models and a
learning pathway that provide realistic chances of understanding." [35]
Model making can also incorporate blended learning strategies by using
web based tools and simulators, thereby allowing students to:
Familiarize themselves with on-line or digital resources
Create different models with various virtual materials at little or no
cost
Practice model making activity any time and any place
Refine existing models
"A well-designed simulation simplifies a real world system while
heightening awareness of the complexity of the system. Students can
participate in the simplified system and learn how the real system operates
without spending days, weeks or years it would take to undergo this
experience in the real world." [30]
The teacher's role in the overall teaching and learning process is
primarily that of a facilitator and arranger of the learning experience. He or
she would assign the students, a model making activity for a particular
concept and provide relevant information or support for the activity. For
virtual model making activities, the teacher can also provide information on
the usage of the digital tool and render troubleshooting support in case of
glitches while using the same. The teacher can also arrange the group
discussion activity between the students and provide the platform necessary
for students to share their observations and knowledge extracted from the
model making activity.
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Model–based learning evaluation could include the use of rubrics that
assess the ingenuity and creativity of the student in the model construction
and also the overall classroom participation of the student vis-a-vis the
knowledge constructed through the activity.
It is important, however, to give due consideration to the following
for successful model–based learning to occur:
Use of the right tool at the right time for a particular concept
Provision within the educational setup for model–making activity:
e.g., computer room with internet facility or software installed to
access simulator or digital tool1.
1
При подготовке данной главы использовались материалы
открытого Интернет-ресурса Wikipedia
(https://en.wikipedia.org/wiki/Conceptual_model
https://en.wikipedia.org/wiki/Model)
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