Intro to modelling_wur
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Transcript of Intro to modelling_wur
Part of the course:Introduction to biological modeling
1. Intro to modeling
2. Intro to biological modeling (Floor)
3. Modeling oscillators (Rob)
Set the model
• dTw/dt = Rate of change of temperature of the water [°C s-1]
• Tw = Temperature of the water [°C]
• Th = Temperature of the heater [°C]
• Ta = Temperature of the air [°C]
• c1 = Heat transfer coefficient 1 [s-1]
• c2 = Heat transfer coefficent 2 [s-1]
• We will measure Tw
Initial parameter values
• From scientific literature.
• Decide which one(s) will be estimated from the experimental data.
0 50 100 150 200 250 30010
20
30
40
50
60
70
80
inpu
t u
p = [0.00029 0.00023]
0 50 100 150 200 250 30023.5
24
24.5
25
25.5
26
26.5
27
time
outp
ut y
and
z (
--)
0 50 100 150 200 250 30010
20
30
40
50
60
70
80
inpu
t u
p = [0.000137 -0.00102]
0 50 100 150 200 250 30023.5
24
24.5
25
25.5
26
26.5
27
time
outp
ut y
and
z (
--)
0 50 100 150 200 250 30010
20
30
40
50
60
70
80
inpu
t u
p = [0.00015 0.0001]
0 50 100 150 200 250 30023.5
24
24.5
25
25.5
26
26.5
27
time
outp
ut y
and
z (
--) P1 = 1
P2 = 1SS = 350
P1 = 1.1P2 = 3SS = 55
P1 = 1.13P2 = 4SS = 12
Manual estimation of the parameters
How precise are the estimated parameters?
2.42.5
2.62.7
2.82.9
x 10-4 -2.4
-2.35-2.3
-2.25-2.2
-2.15-2.1
-2.05-2
x 10-4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
p2
sum of squares surface
p1
We can look at the sum of squares surface:
Menu
The math behind modeling (45 min)
Break (5 min)
A few words about programming (10 min)
Hands-on tutorial (45 min)
What’s next (5 min)
Types of models
• Deterministic
• Non-deterministic
• Probabilistic
• Discrete
• Continuous
(in time)
(in variable values)
Modeling techniques in biology
• Boolean
• Bayesian
• Differential Equations– Ordinary (ODE)
– Partial (PDE)
– Delay (DDE)
• …
ode45
• ODE solver in MATLAB
• Uses information from the fourth and fifth derivative
• How to use it:
[t,x] = ode45(@function, time, x0, [], *)*You can pass whatever, for example the parameters (p) and/or the inputs (u)
Mandatory. Always put in the same order.
Put it here if more info will be passed.
What do we need to use ode45?
• Model
• Parameter(s) values
• Input(s) values
• Independent variable (time) values = to, tf and Δt
• Initial values of dependant variable(s)
Model
Re-write in state-space form:
2.State variables(x): terms with derivative
3.Parameters(p): constants
4.Input(u): what‘s left
From paper to MATLAB
Identify state variables, parameters, inputs.
Define equations and parameter values.
Define initial values, call functions, plot
results.
0.5p = 0.02
Magic word: Function
20x0 = 30 0
0time = 0.1 0.2 … 1
dxdt =
3x11
t0 t1 t2
x1
x2
x3
t3 … t10
20x0 = 30 0
0time = 0.1 0.2 … 1
IN
OUTdxdt =
11x3
x1 x2 x3
t0
t1
t2
t3
… t10
Summary: model function data
Row vector
Row vector
Matrix
0t = 0.1 0.2 … 1
x =
11x3
x1 x2 x3
t0
t1
t2
t3
… t10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
Summary: script data
20x0 = 30 0
0time = 0.1 0.2 … 1
IN
OUTx =
11x3
x1 x2 x3
t0
t1
t2
t3
… t10
0t = 0.1 0.2 … 1
Row vector
Row vector
Matrix
Row vector
From paper to MATLAB
Identify state variables, parameters, inputs.
Define equations and parameter values.
Define initial values, call functions, plot
results.
A few words about programming
All programs run in a defined ‘vertical’ way.
MATLAB is an interpreted language.Errors can be found at any time.
Read the errors messages.Most errors are in manipulation of row/column
vectors.
A few words about programming
• Shell/command line = type commands interactively
• Scripts (.m) = save commands • Functions (.m) = define a command. Give
same name to the function and the file.• Variables– Any word/letter that stores data– They remain after the program ends
• Semicolon (;)
What’s next
Learn/Teach:Introduction to biological modeling (Floor)Modeling oscillators (Rob)
Reproduce modeling by Danino et al. 2010:MATLAB 7.0Team: Brendan, Floor, Rob, Dorett, Mariana, ...
May 6th presentation