Computational Model

A Computational Model is a mathematical model that executes on computing systems to simulate and analyze complex systems (enabling system simulation tasks through computational resource utilization and system capability exploitation).

• AKA: Computer-based Model, Digital Model.
• Context:
  • It can typically process Input Data.
  • It can typically generate Output Data.
  • It can (often) execute Simulation Processes through computational methods.
  • It can (often) validate Model Results through computational validation.
  • It can (often) require specific Hardware Resources through computing system selection.
  • It can (often) leverage System Capabilitys via hardware acceleration and specialized processors.
  • ...
  • It can range from being a Hardware-Independent Model to being a Hardware-Specific Model, depending on its system requirements.
  • It can range from being a Resource-Light Model to being a Resource-Intensive Model, depending on its computational demands.
  • It can range from being a Simple Simulation Model to being a Complex Simulation Model, depending on its system complexity.
  • It can range from being a Static Representation Model to being a Dynamic Representation Model, depending on its temporal adaptation capability.
  • It can range from being a Single Domain Model to being a Cross Domain Model, depending on its application scope.
  • It can range from being a Real-time Computational Model to being an Offline Computational Model, depending on its processing timeline.
  • It can range from being a Single Component Computational Model to being a Multi-component Computational Model, depending on its system scope.
  • It can range from being a Low-fidelity Computational Model to being a High-fidelity Computational Model, depending on its model accuracy.
  • It can range from being a General Purpose Computational Model to being a Domain Specific Computational Model, depending on its application scope.
  • It can range from being an Human-Performed Computational Model to being an Automated Computational Model, depending on its human interaction.
  • It can range from being a Single Scale Model to being a Multi Scale Model, depending on its scale coverage.
  • It can range from being a Fixed Parameter Model to being a Learning Based Model, depending on its parameter adaptation.
  • It can range from being a Standalone Computational Model to being a Cloud Based Computational Model, depending on its deployment architecture.
  • It can range from being a Theoretical Computational Model to being a Deployed Computational Model, depending on its implementation status.
  • It can range from being a Design Phase Model to being a Production Phase Model, depending on its operational maturity.
  • ...
• Examples:
  • AI Models and Machine Learning Models, such as:
    • Neural Network Models, such as:
      • Convolutional Neural Network Model for image recognition.
      • Recurrent Neural Network Model for sequence data processing.
    • Symbolic AI Models, such as:
      • Expert System Model for diagnostic reasoning.
      • Knowledge Graph Reasoning Model for semantic inference.
    • Probabilistic Graphical Models, such as:
      • Bayesian Network Model for medical decision support.
      • Hidden Markov Model for speech recognition.
  • Computational Engineering Models and Robotics Models, such as:
    • Finite Element Models, such as:
      • Structural Analysis Model for bridge safety testing.
      • Thermal Analysis Model for heat transfer optimization.
    • Control System Models, such as:
      • PID Control Model for motor control.
      • Model Predictive Control Model for industrial automation.
    • Robotic Path-Planning Models, such as:
      • Graph-based Search Model for autonomous navigation.
      • Sensor Fusion Model for obstacle avoidance.
  • Computational Physical Science Models, such as:
    • Climate Simulation Models, such as:
      • Global Circulation Model for climate change research.
      • Mesoscale Meteorological Model for regional weather prediction.
    • Computational Fluid Dynamics (CFD) Models, such as:
      • Aerodynamic Simulation Model for aircraft design.
      • Multiphase Flow Model for industrial process optimization.
  • Computational Life Science Models, such as:
    • Computational Epidemiology Models, such as:
      • SIR-based Disease Spread Model for pandemic forecasting.
      • Agent-based Infection Model for population-level intervention studies.
    • Computational Protein Folding Models, such as:
      • Molecular Dynamics Model for protein structure prediction.
      • Quantum Chemical Model for reaction mechanism analysis.
  • Computational Social Science Models, such as:
    • Agent-based Social Simulation Models, such as:
      • Crowd Behavior Model for evacuation planning.
      • Artificial Society Model for policy impact studies.
    • Computational Network Analysis Models, such as:
      • Social Network Growth Model for community detection.
      • Influence Propagation Model for viral marketing research.
  • Computational Finance and Economic Models, such as:
    • Algorithmic Trading Models, such as:
      • High-frequency Trading Model for real-time market execution.
      • Reinforcement Learning Trading Model for automated strategy development.
    • Risk Assessment Models, such as:
      • Value-at-Risk (VaR) Model for portfolio management.
      • Credit Scoring Model for loan risk evaluation.
  • Computational Data Analysis Models, such as:
    • Predictive Analytics Models, such as:
      • Regression-based Forecasting Model for trend analysis.
      • Time-series Prediction Model for economic indicators.
    • Unsupervised Learning Models, such as:
      • Clustering Model for customer segmentation.
      • Dimensionality Reduction Model for feature extraction.
  • System-Optimized Models, such as:
    • GPU-Accelerated Models, such as:
      • Deep Learning Model for parallel computation.
      • Graphics Rendering Model for visual simulation.
    • Distributed Models, such as:
      • Cloud-Native Model for scalable processing.
      • Grid Computing Model for distributed simulation.
    • Embedded Models, such as:
      • Real-time Control Model for device operation.
      • Edge Computing Model for local processing.
  • ...
• Counter-Examples:
  • Analytical Model, which uses mathematical equations without requiring computational resources.
  • Physical Model, which represents system models through physical representations rather than computational simulations.
  • Conceptual Model, which describes system models through abstract concepts without computational formulations.
• See: Computer Simulation, Artificial Intelligent Entity, Computational Technology, Model Transformation, Learning-based Programming Paradigm, Neural Network, Mathematical Model, Computational Science, Computational Resource, Complex System, Computer Simulation, Nonlinear System, Analytical Solution, Weather Forecasting, Earth Simulator, Flight Simulator, Protein Folding.

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References

2024-12-21

• Perplexity.ai
  • Question: What is a Computational Model System and how does it differ from mathematical models? Please explain their key components, applications, and types. Include information about their implementation approaches and practical considerations.
  • Answer: A computational model is a mathematical representation of a dynamical system that uses computer programs to simulate and study complex systems through algorithmic or mechanistic approaches. These models are designed to analyze systems where simple analytical solutions are not readily available, particularly in cases involving complex nonlinear systems.
    • Core Components:
      • Variables and Parameters:
        • The model contains numerous variables that characterize the system being studied.
        • Allows researchers to adjust parameters and observe different outcomes through computational experiments.
      • Execution Methods:
        • Running simulations to study system behavior.
        • Adjusting variables individually or in combination.
        • Analyzing experimental outcomes to derive operational theories.
    • Applications:
      • Scientific Research:
        • Weather forecasting and climate prediction.
        • Molecular protein folding analysis.
        • Flight simulation and aircraft design.
        • Earthquake behavior prediction.
      • Healthcare and Medicine:
        • Tracking infectious diseases.
        • Supporting clinical decisions.
        • Predicting drug side effects.
        • Studying biological systems at multiple scales.
    • Model Types:
      • Deterministic Models:
        • Produce unique dynamics for each initial state.
      • Probabilistic/Stochastic Models:
        • Generate different dynamics from the same initial state.
    • Core Differences:
      • Fundamental Approach:
        • Mathematical models rely on equations and functions with pre-set parameters.
        • Computational models use algorithms and specifications to simulate complex systems.
    • Characteristics:
      • Mathematical Models:
        • Use statistical regression, algebraic equations, and differential equations.
        • Work well with smaller, manageable datasets.
        • Provide simpler, more interpretable solutions.
        • Have fixed formulas and limited application range.
      • Computational Models:
        • Employ algorithms and specifications rather than pure equations.
        • Handle large-scale data processing.
        • Allow for modular composition of different components.
        • Can represent more complex relationships and interactions.
  • Citations:

[1] https://en.wikipedia.org/wiki/Computational_model
[2] https://library.fiveable.me/applications-of-scientific-computing/unit-3
[3] https://www1.grc.nasa.gov/space/human-research-program/computational-modeling/
[4] https://www.nibib.nih.gov/sites/default/files/2022-05/Fact-Sheet-Computational-Modeling.pdf
[5] https://www.vaia.com/en-us/explanations/media-studies/digital-and-social-media/computational-models/
[6] https://pages.di.unipi.it/milazzo/teaching/AA1920-CMCS/slides/01-Introduction.pdf
[7] https://www.nibib.nih.gov/science-education/science-topics/computational-modeling
[8] https://pmc.ncbi.nlm.nih.gov/articles/PMC10921860/
[9] https://hal.science/hal-04148865/document
[10] https://www.reddit.com/r/learnmachinelearning/comments/108ybl2/what_is_the_difference_between_a_mathematical/
[11] https://cs.stackexchange.com/questions/48218/what-is-the-difference-between-computational-model-model-of-computation-and-a-c
[12] https://pmc.ncbi.nlm.nih.gov/articles/PMC2704205/
[13] https://www.researchgate.net/publication/5239107_Dichotomies_between_computational_and_mathematical_models

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Computational_model Retrieved:2023-10-13.
  • A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, Operation theories of the model can be derived/deduced from these computational experiments. Examples of common computational models are weather forecasting models, earth simulator models, flight simulator models, molecular protein folding models, Computational Engineering Models (CEM), and neural network models.

2018a

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Computational_model Retrieved:2018-9-2.
  • A computational model is a mathematical model in computational science that requires extensive computational resources to study the behavior of a complex system by computer simulation.

    The system under study is often a complex nonlinear system for which simple, intuitive analytical solutions are not readily available. Rather than deriving a mathematical analytical solution to the problem, experimentation with the model is done by adjusting the parameters of the system in the computer, and studying the differences in the outcome of the experiments. Operation theories of the model can be derived/deduced from these computational experiments.

    Examples of common computational models are weather forecasting models, earth simulator models, flight simulator models, molecular protein folding models, and neural network models.

2018b

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Computer_simulation#Simulation_versus_model Retrieved:2018-9-2.
  • A computer model is the algorithms and equations used to capture the behavior of the system being modeled. By contrast, computer simulation is the actual running of the program that contains these equations or algorithms. Simulation, therefore, is the process of running a model. Thus one would not "build a simulation"; instead, one would "build a model", and then either "run the model" or equivalently "run a simulation".

2018c

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Mathematical_model#Training_and_tuning Retrieved:2018-9-2.
  • Any model which is not pure white-box contains some parameters that can be used to fit the model to the system it is intended to describe. If the modeling is done by an artificial neural network or other machine learning, the optimization of parameters is called training, while the optimization of model hyperparameters is called tuning and often uses cross-validation. In more conventional modeling through explicitly given mathematical functions, parameters are often determined by curve fitting.

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