Introduction to dynamical system modelling
Introduction to dynamical system modelling
Shan He
School for Computational ScienceUniversity of Birmingham
Module 06-23836: Computational Modelling with MATLAB
Introduction to dynamical system modelling
Outline
Outline of Topics
Dynamical systems
Concepts about modelling
How to model?
How to use models for scientific research
Introduction to dynamical system modelling
Dynamical systems
What is a system?
A System: consisting of interconnected components, built orevolved with a desired purpose.Examples:
I Toilet tank.
I Car engine.
I Brain.
I Bird flock.
I Climatesystem.
Introduction to dynamical system modelling
Dynamical systems
What is a system?
A System: consisting of interconnected components, built orevolved with a desired purpose.Examples:
I Toilet tank.
I Car engine.
I Brain.
I Bird flock.
I Climatesystem.
Introduction to dynamical system modelling
Dynamical systems
What is a system?
A System: consisting of interconnected components, built orevolved with a desired purpose.Examples:
I Toilet tank.
I Car engine.
I Brain.
I Bird flock.
I Climatesystem.
Introduction to dynamical system modelling
Dynamical systems
What is a system?
A System: consisting of interconnected components, built orevolved with a desired purpose.Examples:
I Toilet tank.
I Car engine.
I Brain.
I Bird flock.
I Climatesystem.
Introduction to dynamical system modelling
Dynamical systems
What is a system?
A System: consisting of interconnected components, built orevolved with a desired purpose.Examples:
I Toilet tank.
I Car engine.
I Brain.
I Bird flock.
I Climatesystem.
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Static vs. Dynamical.
I Static system: current inputs =⇒ outputs.
Static systemInputs xt Outputs y
I Dynamical system: history + current inputs =⇒ outputs.
Dynamical system
Memory
Inputs xt Outputs y
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Static vs. Dynamical.
I Static system: current inputs =⇒ outputs.
Static systemInputs xt Outputs y
I Dynamical system: history + current inputs =⇒ outputs.
Dynamical system
Memory
Inputs xt Outputs y
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Static vs. Dynamical.
I Static system: current inputs =⇒ outputs.
Static systemInputs xt Outputs y
I Dynamical system: history + current inputs =⇒ outputs.
Dynamical system
Memory
Inputs xt Outputs y
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Outputs depend on the present and past values of the inputs.
I Changes over time.
I Sometimes called dynamic systems or sequential systems.
I Mathematically described with differential or differenceequations.
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Outputs depend on the present and past values of the inputs.
I Changes over time.
I Sometimes called dynamic systems or sequential systems.
I Mathematically described with differential or differenceequations.
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Outputs depend on the present and past values of the inputs.
I Changes over time.
I Sometimes called dynamic systems or sequential systems.
I Mathematically described with differential or differenceequations.
Introduction to dynamical system modelling
Dynamical systems
What is a dynamical system?
I Outputs depend on the present and past values of the inputs.
I Changes over time.
I Sometimes called dynamic systems or sequential systems.
I Mathematically described with differential or differenceequations.
Introduction to dynamical system modelling
Dynamical systems
Which one is a dynamical system?
Which one is a dynamical system?
I Toilet tank.
I Car engine.
I Brian.
I Bird flock.
I Climate system.
I X
I X
I X
I X
I X
Introduction to dynamical system modelling
Dynamical systems
Which one is a dynamical system?
Which one is a dynamical system?
I Toilet tank.
I Car engine.
I Brian.
I Bird flock.
I Climate system.
I X
I X
I X
I X
I X
Introduction to dynamical system modelling
Dynamical systems
Which one is a dynamical system?
Which one is a dynamical system?
I Toilet tank.
I Car engine.
I Brian.
I Bird flock.
I Climate system.
I X
I X
I X
I X
I X
Introduction to dynamical system modelling
Dynamical systems
Which one is a dynamical system?
Which one is a dynamical system?
I Toilet tank.
I Car engine.
I Brian.
I Bird flock.
I Climate system.
I X
I X
I X
I X
I X
Introduction to dynamical system modelling
Dynamical systems
Which one is a dynamical system?
Which one is a dynamical system?
I Toilet tank.
I Car engine.
I Brian.
I Bird flock.
I Climate system.
I X
I X
I X
I X
I X
Introduction to dynamical system modelling
Dynamical systems
Which one is a dynamical system?
Which one is a dynamical system?
I Toilet tank.
I Car engine.
I Brian.
I Bird flock.
I Climate system.
I X
I X
I X
I X
I X
Introduction to dynamical system modelling
Dynamical systems
Biological systems
I Outputs depend on the present and past values of the inputs.
I Biological systems change over time.
I Biological systems are dynamical systems.
I Biological systems are complex: emergence.
I Reductionism might not work well
I System point of view on biological systems is new - SystemsBiology.
Introduction to dynamical system modelling
Dynamical systems
Biological systems
I Outputs depend on the present and past values of the inputs.
I Biological systems change over time.
I Biological systems are dynamical systems.
I Biological systems are complex: emergence.
I Reductionism might not work well
I System point of view on biological systems is new - SystemsBiology.
Introduction to dynamical system modelling
Dynamical systems
Biological systems
I Outputs depend on the present and past values of the inputs.
I Biological systems change over time.
I Biological systems are dynamical systems.
I Biological systems are complex: emergence.
I Reductionism might not work well
I System point of view on biological systems is new - SystemsBiology.
Introduction to dynamical system modelling
Dynamical systems
Biological systems
I Outputs depend on the present and past values of the inputs.
I Biological systems change over time.
I Biological systems are dynamical systems.
I Biological systems are complex: emergence.
I Reductionism might not work well
I System point of view on biological systems is new - SystemsBiology.
Introduction to dynamical system modelling
Dynamical systems
Biological systems
I Outputs depend on the present and past values of the inputs.
I Biological systems change over time.
I Biological systems are dynamical systems.
I Biological systems are complex: emergence.
I Reductionism might not work well
I System point of view on biological systems is new - SystemsBiology.
Introduction to dynamical system modelling
Concepts about modelling
What are models?
When we say models, we usually mean computational/mathmeticalmodels.
I Model: a description of a system usingmathematical/computational concepts and language.
I Mathematical model: a set of variables and a set ofequations that establish relationships between the variables.
I Computational model: a computer program thatimplements computational techniques, e.g., rules, automata,petri nets or artificial neural networks to describe a system.
I Can be hybrid: Mathematical models + Computationalmodels.
Introduction to dynamical system modelling
Concepts about modelling
What are models?
When we say models, we usually mean computational/mathmeticalmodels.
I Model: a description of a system usingmathematical/computational concepts and language.
I Mathematical model: a set of variables and a set ofequations that establish relationships between the variables.
I Computational model: a computer program thatimplements computational techniques, e.g., rules, automata,petri nets or artificial neural networks to describe a system.
I Can be hybrid: Mathematical models + Computationalmodels.
Introduction to dynamical system modelling
Concepts about modelling
What are models?
When we say models, we usually mean computational/mathmeticalmodels.
I Model: a description of a system usingmathematical/computational concepts and language.
I Mathematical model: a set of variables and a set ofequations that establish relationships between the variables.
I Computational model: a computer program thatimplements computational techniques, e.g., rules, automata,petri nets or artificial neural networks to describe a system.
I Can be hybrid: Mathematical models + Computationalmodels.
Introduction to dynamical system modelling
Concepts about modelling
What are models?
When we say models, we usually mean computational/mathmeticalmodels.
I Model: a description of a system usingmathematical/computational concepts and language.
I Mathematical model: a set of variables and a set ofequations that establish relationships between the variables.
I Computational model: a computer program thatimplements computational techniques, e.g., rules, automata,petri nets or artificial neural networks to describe a system.
I Can be hybrid: Mathematical models + Computationalmodels.
Introduction to dynamical system modelling
Concepts about modelling
Why use models?
We use model to describe phenomena and understand phenomena.More specifically:
I Predict: Make testable prediction
I Explain: Reveal underlying mechanisms or rule out particularexplanations
I Discover: Propose new questions
I Guide: Data collection or experiments design
Introduction to dynamical system modelling
Concepts about modelling
Why use models?
We use model to describe phenomena and understand phenomena.More specifically:
I Predict: Make testable prediction
I Explain: Reveal underlying mechanisms or rule out particularexplanations
I Discover: Propose new questions
I Guide: Data collection or experiments design
Introduction to dynamical system modelling
Concepts about modelling
Why use models?
We use model to describe phenomena and understand phenomena.More specifically:
I Predict: Make testable prediction
I Explain: Reveal underlying mechanisms or rule out particularexplanations
I Discover: Propose new questions
I Guide: Data collection or experiments design
Introduction to dynamical system modelling
Concepts about modelling
Why use models?
We use model to describe phenomena and understand phenomena.More specifically:
I Predict: Make testable prediction
I Explain: Reveal underlying mechanisms or rule out particularexplanations
I Discover: Propose new questions
I Guide: Data collection or experiments design
Introduction to dynamical system modelling
Concepts about modelling
Example: Climate models
By building climate models, we can:
I Predict: How temperature changes in the next few days?
I Explain: How the global atmosphere is operating?
I Discover: How the carbon dioxide affects our climate?
I Guide: Collect climate data.
Introduction to dynamical system modelling
Concepts about modelling
Example: Climate models
By building climate models, we can:
I Predict: How temperature changes in the next few days?
I Explain: How the global atmosphere is operating?
I Discover: How the carbon dioxide affects our climate?
I Guide: Collect climate data.
Introduction to dynamical system modelling
Concepts about modelling
Example: Climate models
By building climate models, we can:
I Predict: How temperature changes in the next few days?
I Explain: How the global atmosphere is operating?
I Discover: How the carbon dioxide affects our climate?
I Guide: Collect climate data.
Introduction to dynamical system modelling
Concepts about modelling
Example: Climate models
By building climate models, we can:
I Predict: How temperature changes in the next few days?
I Explain: How the global atmosphere is operating?
I Discover: How the carbon dioxide affects our climate?
I Guide: Collect climate data.
Introduction to dynamical system modelling
How to model?
Modelling methods
I Equation based methods:
I Differential equation: Ordinary Differential Equation, Partialdifferential equation.
I Statistical methods: linear regression, multilevel model andStructural equation model.
I Game theoretic methods.
I Agent-based methods.
I Other methods: data driven methods.
Introduction to dynamical system modelling
How to model?
Modelling methods
I Equation based methods:I Differential equation: Ordinary Differential Equation, Partial
differential equation.
I Statistical methods: linear regression, multilevel model andStructural equation model.
I Game theoretic methods.
I Agent-based methods.
I Other methods: data driven methods.
Introduction to dynamical system modelling
How to model?
Modelling methods
I Equation based methods:I Differential equation: Ordinary Differential Equation, Partial
differential equation.I Statistical methods: linear regression, multilevel model and
Structural equation model.
I Game theoretic methods.
I Agent-based methods.
I Other methods: data driven methods.
Introduction to dynamical system modelling
How to model?
Modelling methods
I Equation based methods:I Differential equation: Ordinary Differential Equation, Partial
differential equation.I Statistical methods: linear regression, multilevel model and
Structural equation model.I Game theoretic methods.
I Agent-based methods.
I Other methods: data driven methods.
Introduction to dynamical system modelling
How to model?
Modelling methods
I Equation based methods:I Differential equation: Ordinary Differential Equation, Partial
differential equation.I Statistical methods: linear regression, multilevel model and
Structural equation model.I Game theoretic methods.
I Agent-based methods.
I Other methods: data driven methods.
Introduction to dynamical system modelling
How to model?
Modelling methods
I Equation based methods:I Differential equation: Ordinary Differential Equation, Partial
differential equation.I Statistical methods: linear regression, multilevel model and
Structural equation model.I Game theoretic methods.
I Agent-based methods.
I Other methods: data driven methods.
Introduction to dynamical system modelling
How to model?
Modelling principles
I Question: How to build the best model to model a system?
I No answer, even no a single definition to ‘the best model’.I One good attempt is Minimum Description Length principle,
or Occam’s razor.
I “The best model is the one that is the smallest.”
I Einstein’s razor’ (Better!):
I The model should be made as simple as possible, but nosimpler.
Introduction to dynamical system modelling
How to model?
Modelling principles
I Question: How to build the best model to model a system?
I No answer, even no a single definition to ‘the best model’.
I One good attempt is Minimum Description Length principle,or Occam’s razor.
I “The best model is the one that is the smallest.”
I Einstein’s razor’ (Better!):
I The model should be made as simple as possible, but nosimpler.
Introduction to dynamical system modelling
How to model?
Modelling principles
I Question: How to build the best model to model a system?
I No answer, even no a single definition to ‘the best model’.I One good attempt is Minimum Description Length principle,
or Occam’s razor.
I “The best model is the one that is the smallest.”
I Einstein’s razor’ (Better!):
I The model should be made as simple as possible, but nosimpler.
Introduction to dynamical system modelling
How to model?
Modelling principles
I Question: How to build the best model to model a system?
I No answer, even no a single definition to ‘the best model’.I One good attempt is Minimum Description Length principle,
or Occam’s razor.I “The best model is the one that is the smallest.”
I Einstein’s razor’ (Better!):
I The model should be made as simple as possible, but nosimpler.
Introduction to dynamical system modelling
How to model?
Modelling principles
I Question: How to build the best model to model a system?
I No answer, even no a single definition to ‘the best model’.I One good attempt is Minimum Description Length principle,
or Occam’s razor.I “The best model is the one that is the smallest.”
I Einstein’s razor’ (Better!):
I The model should be made as simple as possible, but nosimpler.
Introduction to dynamical system modelling
How to model?
Modelling principles
I Question: How to build the best model to model a system?
I No answer, even no a single definition to ‘the best model’.I One good attempt is Minimum Description Length principle,
or Occam’s razor.I “The best model is the one that is the smallest.”
I Einstein’s razor’ (Better!):I The model should be made as simple as possible, but no
simpler.
Introduction to dynamical system modelling
How to model?
How to put into practice?
I found this paper very useful: 5 Simple principles of modelling byProfessor Mike Pidd. Here are the 5 principles:
I Model simple, think complicated.
I Be parsimonious, start small and add.
I Divide and conquer, avoid mega models.
I Don’t fall in love with data.
I Model building may feel like muddling through.
Introduction to dynamical system modelling
How to model?
How to put into practice?
I found this paper very useful: 5 Simple principles of modelling byProfessor Mike Pidd. Here are the 5 principles:
I Model simple, think complicated.
I Be parsimonious, start small and add.
I Divide and conquer, avoid mega models.
I Don’t fall in love with data.
I Model building may feel like muddling through.
Introduction to dynamical system modelling
How to model?
How to put into practice?
I found this paper very useful: 5 Simple principles of modelling byProfessor Mike Pidd. Here are the 5 principles:
I Model simple, think complicated.
I Be parsimonious, start small and add.
I Divide and conquer, avoid mega models.
I Don’t fall in love with data.
I Model building may feel like muddling through.
Introduction to dynamical system modelling
How to model?
How to put into practice?
I found this paper very useful: 5 Simple principles of modelling byProfessor Mike Pidd. Here are the 5 principles:
I Model simple, think complicated.
I Be parsimonious, start small and add.
I Divide and conquer, avoid mega models.
I Don’t fall in love with data.
I Model building may feel like muddling through.
Introduction to dynamical system modelling
How to model?
How to put into practice?
I found this paper very useful: 5 Simple principles of modelling byProfessor Mike Pidd. Here are the 5 principles:
I Model simple, think complicated.
I Be parsimonious, start small and add.
I Divide and conquer, avoid mega models.
I Don’t fall in love with data.
I Model building may feel like muddling through.
Introduction to dynamical system modelling
How to model?
Modelling process
SimulationDefinitionIdentification
ValidationAnalysis Satisfied?
No
Yes
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)
I Gene regulatory networks.I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:
I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.
I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:
I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.I Cellular signalling networks.
I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:
I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:
I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).
I For example, if we model prey-predator interaction, we wish toanswer:
I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:
I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:I How predators affect prey populations, and vice-versa?
I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Identification
I Identify the system to model (What)I Gene regulatory networks.I Cellular signalling networks.I Prey-predator interaction.
I Or more importantly, identify the problems to answer (Why).I For example, if we model prey-predator interaction, we wish to
answer:I How predators affect prey populations, and vice-versa?I Whether a prey-predator system is stable or collapse?
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
SimulationDefinitionIdentification
ValidationAnalysis Satisfied?
No
Yes
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.
I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.
I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?
I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?
I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Definition
The most important step. General suggestions are:I Draw a detailed picture:
I Defines all components.I Defines the relations between components.
I Define the parameters and variables to be used in the model.I Check literature:
I Any descriptions about the components?I Any relations reported?I What parameters and variables used in similar studies?
I You might need to simplify your assumptions.
Introduction to dynamical system modelling
How to model?
Modelling process: Simulation
SimulationDefinitionIdentification
ValidationAnalysis Satisfied?
No
Yes
Introduction to dynamical system modelling
How to model?
Modelling process: Simulation
This simply means, in our module, to execute your MATLABprogram ;)
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
SimulationDefinitionIdentification
ValidationAnalysis Satisfied?
No
Yes
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ Analysis
I Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?
I Oversimplified assumptions?I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?
I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?I Missing components?
I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Validation
I This simply means compare the outputs from your MATLABprogram with experimental data.
I Decision time: Do the results match the experimental data?
I Answer: Yes =⇒ AnalysisI Answer: No =⇒ Definition. We need to check:
I Simple typos?I Oversimplified assumptions?I Missing components?I Incorrect parameters?
Introduction to dynamical system modelling
How to model?
Modelling process: Analysis
SimulationDefinitionIdentification
ValidationAnalysis Satisfied?
No
Yes
Introduction to dynamical system modelling
How to model?
Modelling process: Analysis
I By analysing the results, we aim to answer:
I What do the results imply or suggested?I What is new and what did not know?I What prediction can we make?
I If the analysis proposes new questions, we need to go back toidentification.
Introduction to dynamical system modelling
How to model?
Modelling process: Analysis
I By analysing the results, we aim to answer:I What do the results imply or suggested?
I What is new and what did not know?I What prediction can we make?
I If the analysis proposes new questions, we need to go back toidentification.
Introduction to dynamical system modelling
How to model?
Modelling process: Analysis
I By analysing the results, we aim to answer:I What do the results imply or suggested?I What is new and what did not know?
I What prediction can we make?
I If the analysis proposes new questions, we need to go back toidentification.
Introduction to dynamical system modelling
How to model?
Modelling process: Analysis
I By analysing the results, we aim to answer:I What do the results imply or suggested?I What is new and what did not know?I What prediction can we make?
I If the analysis proposes new questions, we need to go back toidentification.
Introduction to dynamical system modelling
How to model?
Modelling process: Analysis
I By analysing the results, we aim to answer:I What do the results imply or suggested?I What is new and what did not know?I What prediction can we make?
I If the analysis proposes new questions, we need to go back toidentification.
Introduction to dynamical system modelling
How to use models for scientific research
Modelling process and scientific method
We should always put modelling into the context of scientificmethod:
1. Make general observations of phenomena
2. Formulate a hypothesis that is consistent with yourobservations.
3. Use the hypothesis to make predictions.
4. Develop experiments to test your hypothesis and modify thehypothesis in the light of your results.
5. Repeat steps 3&4 until there are no discrepancies betweenhypothesis and phenomena.
Introduction to dynamical system modelling
How to use models for scientific research
Modelling process and scientific method
We should always put modelling into the context of scientificmethod:
1. Make general observations of phenomena
2. Formulate a hypothesis that is consistent with yourobservations.
3. Use the hypothesis to make predictions.
4. Develop experiments to test your hypothesis and modify thehypothesis in the light of your results.
5. Repeat steps 3&4 until there are no discrepancies betweenhypothesis and phenomena.
Introduction to dynamical system modelling
How to use models for scientific research
Modelling process and scientific method
We should always put modelling into the context of scientificmethod:
1. Make general observations of phenomena
2. Formulate a hypothesis that is consistent with yourobservations.
3. Use the hypothesis to make predictions.
4. Develop experiments to test your hypothesis and modify thehypothesis in the light of your results.
5. Repeat steps 3&4 until there are no discrepancies betweenhypothesis and phenomena.
Introduction to dynamical system modelling
How to use models for scientific research
Modelling process and scientific method
We should always put modelling into the context of scientificmethod:
1. Make general observations of phenomena
2. Formulate a hypothesis that is consistent with yourobservations.
3. Use the hypothesis to make predictions.
4. Develop experiments to test your hypothesis and modify thehypothesis in the light of your results.
5. Repeat steps 3&4 until there are no discrepancies betweenhypothesis and phenomena.
Introduction to dynamical system modelling
How to use models for scientific research
Modelling process and scientific method
We should always put modelling into the context of scientificmethod:
1. Make general observations of phenomena
2. Formulate a hypothesis that is consistent with yourobservations.
3. Use the hypothesis to make predictions.
4. Develop experiments to test your hypothesis and modify thehypothesis in the light of your results.
5. Repeat steps 3&4 until there are no discrepancies betweenhypothesis and phenomena.
Introduction to dynamical system modelling
How to use models for scientific research
SimulationDefinitionIdentification
ValidationAnalysis Satisfied?
No
Yes
Formulate hypothesis
Develop
experiments
Phenomena
Step 1
Step 2
Step 3
Step 4