Skip to content

Wclaer-P6-studentnb #76

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
warclaer wants to merge 8 commits into
base: main
Choose a base branch
from
Open

Wclaer-P6-studentnb #76

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
8 commits
Select commit Hold shift + click to select a range
8ae2ddc
Update calib_intro.jl
warclaer Mar 26, 2026
f7186f3
Update calib_fermenter_monod.jl
warclaer Mar 26, 2026
5b715de
0.022 instead of 0.22
warclaer Mar 26, 2026
1bd1a2a
change to 0.022
warclaer Mar 26, 2026
43cb477
Update calib_irrigation.jl
warclaer Mar 26, 2026
7a70d76
updating
warclaer Mar 27, 2026
b44eac6
Update optim_wastewater_treatment.jl
warclaer Mar 27, 2026
8b43ff6
Removing redundant ODE prob
warclaer Mar 27, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion exercises/solved_notebooks/P6_calib/calib_fermenter_monod_sol.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -105,7 +105,7 @@ end
md"""
We have previously used the following parameter values:

- `μmax = 0.40`$\mathrm{h^{-1}}$, `Ks = 0.015`$\mathrm{g/L}$, `Sin = 0.22`$\mathrm{g/L}$
- `μmax = 0.40`$\mathrm{h^{-1}}$, `Ks = 0.015`$\mathrm{g/L}$, `Sin = 0.022`$\mathrm{g/L}$
- `Y = 0.67`, `Q = 2.0`$\mathrm{L/h}$, `V = 40.0`$\mathrm{L}$

Furthermore, suppose that at $t = 0\;h$ no substrate $S$ is present in the reactor but that there is initially some biomass with a concentration of `0.0005`$\mathrm{g/L}$.
Expand Down
111 changes: 38 additions & 73 deletions exercises/student_notebooks/P6_calib/calib_fermenter_monod.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,21 +1,14 @@
### A Pluto.jl notebook ###
# v0.20.4
# v0.20.21

using Markdown
using InteractiveUtils

# ╔═╡ c54dae10-60af-4141-b56d-ed61cb0ced8a
begin
# add this cell if you want the notebook to use the environment from where the Pluto server is launched
using Pkg
Pkg.activate("..")
end
using Pkg; Pkg.activate("..")

# ╔═╡ 245ca9d0-10f9-11ef-0ef6-a73594e96db9
using Markdown

# ╔═╡ 78a25bef-31e5-45ef-b0ba-b9a8c8a9edeb
using InteractiveUtils
using Markdown, InteractiveUtils

# ╔═╡ 16438e07-1b2b-467e-822a-081d19cae92b
using Catalyst, OrdinaryDiffEq
Expand All @@ -33,16 +26,12 @@ md"""

# ╔═╡ 595ea8ee-bc67-4696-9232-982612fb554d
md"""
In one of the previous practicals we were introduced to a fermenter in which biomass $X$ [$g/L$] grows by breaking down substrate $S$ [$g/L$]. The reactor is fed with an inlet flow rate $Q_{in}$ [$L/h$], which consists of a (manipulable) inlet concentration of substrate $S_{in}$ [$g/L$]. This process was modelled using Monod kinetics, resulting in the model below:
In one of the previous practica we were introduced to a fermenter in which biomass $X$ [$\mathrm{g/L}$] grows by breaking down substrate $S$ [$\mathrm{g/L}$]. The reactor is fed with an inlet flow rate $Q_{in}$ [$\mathrm{L/h}$], which consists of a (manipulable) input concentration of substrate $S_{in}$ [$\mathrm{g/L}$]. This process was modelled using Monod kinetics:

$$\begin{eqnarray*}
S + X \xrightarrow[\quad\quad]{k} (1 + Y) \, X \quad\quad\quad\quad \textrm{with} \quad k = \cfrac{\mu_{max}}{S + K_s}
S + X \xrightarrow[\quad\quad]{k} (1 + Y) \, X \quad\quad\quad\quad \textrm{with} \quad k = \cfrac{\mu_{max}}{S + K_s} \, .
\end{eqnarray*}$$
"""
# $$\begin{eqnarray*}
# %S \xrightarrow[\quad\quad]{\beta} Y \, X
# S \xrightarrow[\quad\quad]{r} Y \, X \quad\quad\quad\quad r = \mu \, X \quad \textrm{with} \quad \mu = \mu_{max} \, \cfrac{S}{S + K_s}
# \end{eqnarray*}$$


# ╔═╡ 824db995-7a66-4719-a534-7e0f6dec90b5
Expand All @@ -51,20 +40,16 @@ The *reaction network object* for this model could be set-up as:
"""

# ╔═╡ 245c2636-95da-4c76-8b03-c4d20bbabb48
fermenter_monod = @reaction_network begin
μmax/(S+Ks), S + X --> (1 + Y)*X
# Alternatives:
# X * mm(S, μmax, Ks), S => Y*X
# mm(S, μmax, Ks)*X, S + X => (1 + Y)*X
Q/V, (S, X) --> 0
Q/V*Sin, 0 --> S
end
# fermenter_monod = @reaction_network begin
# @species missing
# @parameters missing
# missing
# missing
# missing
# end

# ╔═╡ 956790e2-6cac-46c9-886e-24d5aceae1c5
convert(ODESystem, fermenter_monod, combinatoric_ratelaws=false)

# ╔═╡ 68f9ecb3-15b0-4a53-8864-5dac13a89e95
parameters(fermenter_monod)
# convert(missing, missing)

# ╔═╡ de8ddc14-8f82-403d-8f42-29673ef2a722
md"""
Expand Down Expand Up @@ -98,7 +83,6 @@ Make a scatter plot of the measured data for both $S$ and $X$. Use the following
"""

# ╔═╡ 918fd524-81fa-4aff-a403-37402e47235b
# Uncomment and complete the instruction
# begin
# missing
# missing
Expand All @@ -108,38 +92,22 @@ Make a scatter plot of the measured data for both $S$ and $X$. Use the following
md"""
We have previously used the following parameter values:

- $\mu_{max} = 0.40\;h^{-1}$, $K_s = 0.015\;g/L$, $S_{in} = 0.022\;g/L$
- $Y = 0.67$, $Q = 2.0\;L/h$, $V = 40.0\;L$
- `μmax = 0.40`$\mathrm{h^{-1}}$, `Ks = 0.015`$\mathrm{g/L}$, `Sin = 0.022`$\mathrm{g/L}$
- `Y = 0.67`, `Q = 2.0`$\mathrm{L/h}$, `V = 40.0`$\mathrm{L}$

Furthermore, suppose that at $t = 0\;h$ no substrate $S$ is present in the reactor but that there is initially some biomass with a concentration of $0.0005\;g/L$.

Calibrate the parameter values for $\mu_{max}$ and $K_s$ using the aforementioned measurement data for $S$ and $X$ in a timespan of $[0, 100]\,h$. Take the values above as initial values for $\mu_{max}$ and $K_s$.
"""
Furthermore, suppose that at $t = 0\;h$ no substrate $S$ is present in the reactor but that there is initially some biomass with a concentration of `0.0005`$\mathrm{g/L}$.

# ╔═╡ 7a227eaf-18d0-44f4-ac4b-f529e81c7471
md"""
Create an `ODEProblem`. Use the aforementioned values as initial values for the problem.
Calibrate the parameter values for $\mu_{max}$ and $K_s$ using the aforementioned measurement data for $S$ and $X$ in a timespan of `[0, 100]`$\mathrm{h}$. Take the values above as initial values for $\mu_{max}$ and $K_s$.
"""

# ╔═╡ 6375478f-1af9-4fd2-b6f3-101a6f796f2d
# u0 = missing # Uncomment and complete the instruction

# ╔═╡ 38fe8304-af61-40a7-ac86-480dfb892185
# tspan = missing # Uncomment and complete the instruction

# ╔═╡ 87482f88-8413-4820-9613-7941f3d61bd7
# params = missing # Uncomment and complete the instruction

# ╔═╡ 94f3bd7b-5c2c-4661-a0ab-2cdaf2cd6743
# oprob = missing # Uncomment and complete the instruction

# ╔═╡ f6a8f134-6db0-4d74-8af5-82826347d8f0
md"""
Declare the Turing model. Use `InverseGamma` for the standard deviations of the measurements and `LogNormal` for `μmax` and `K`.
Declare the Turing model. Assume the following for the priors:
- The measurement error is an unknown positive value, but probably near $0$.
- The parameters `μmax` and `K` are both positive and expected to be in $[0.0, 1.0]$, presumably around $0.1$.
"""

# ╔═╡ 4c28a66a-ee2c-42a2-95c7-ea4ddb6a232d
# Uncomment and complete the instruction
# @model function fermenter_fun(t_meas)
# σ_S ~ missing
# σ_X ~ missing
Expand All @@ -152,40 +120,46 @@ Declare the Turing model. Use `InverseGamma` for the standard deviations of the
# X_s ~ missing
# end

# ╔═╡ 5928a9f3-f33c-4689-a6e5-637447f420d6
md"""
!!! tip
This model can change between being non-stiff and stiff based on the sampled parameter values. You can use an auto-switching solver such as `AutoTsit5(Rosenbrock23())` here to make calibration more stable.
"""

# ╔═╡ 3136b15d-5078-4bcd-954b-e89bcb8aed1b
md"""
Provide the time measurements to the defined function and instantly condition the model with the measurements of $S$ and $X$:
Provide the measurements to the Turing model.
"""

# ╔═╡ 6a508a62-61b9-4273-8e45-b26f594e8da9
# fermenter_cond_mod = missing # Uncomment and complete the instruction
# fermenter_inf = missing

# ╔═╡ 63420055-55f8-4def-8b0e-11ea61483010
md"""
Optimize the priors ($\sigma_S$, $\sigma_X$, $\mu_{max}$ and $K_s$). Do this with `MLE` method and Nelder-Mead. Store the optimization results in `results_mle`. If necessary, run the optimization again if you get any errors.
Optimize the likelihood of the parameters ($\sigma_S$, $\sigma_X$, $\mu_{max}$ and $K_s$) using the NelderMead optimizer. Store the optimization results in `results_mle`.
"""

# ╔═╡ d52c9da8-d8a4-4db0-ac6d-6d16ccf4775c
# results_map = missing # Uncomment and complete the instruction
# results_mle = missing

# ╔═╡ e1b0ee01-f16c-40e9-a0f9-80072d690936
md"""
Visualize a summary of the optimized parameters.
Visualize a summary of the optimized parameters. Beware that this may take a lot of time...
"""

# ╔═╡ f2d7daf8-8218-446d-b1d2-e9e05aeadfd9
# missing # Uncomment and complete the instruction
# missing

# ╔═╡ 23d58bb1-d077-402e-8bee-3866c68e069a
md"""
Get the optimized values and assign them to `μmax_opt` and `Ks_opt`.
"""

# ╔═╡ 7b3a3677-b251-43c1-b125-6d6ff1a11ea3
# μmax_opt = missing # Uncomment and complete the instruction
# μmax_opt = missing

# ╔═╡ fa77bcbe-2ddc-4113-8f6a-4a18d219da9e
# Ks_opt = missing # Uncomment and complete the instruction
# Ks_opt = missing

# ╔═╡ 05d13a48-adc8-4e24-a6e4-be24af2c7a59
md"""
Expand All @@ -198,32 +172,29 @@ Set up parameter values with optimized parameter values:
"""

# ╔═╡ 75cf59ed-af8e-4e8a-8ed2-1f3bf4d386d0
# params_opt = missing # Uncomment and complete the instruction
# params_opt = missing

# ╔═╡ 4e8870dc-2da6-4b80-82d6-26c7ceedad7d
md"""
Create an ODEProblem and solve it. Use `Tsit5()` and `saveat=0.5`.
"""

# ╔═╡ 853c1a92-d50f-4b05-9ed3-d3ee1656665a
# oprob_opt = missing # Uncomment and complete the instruction
# oprob_opt = missing

# ╔═╡ f45e8124-e942-438e-99c5-3032ccc01454
# osol_opt = missing # Uncomment and complete the instruction
# osol_opt = missing

# ╔═╡ 5a39b0e0-1ea1-4854-8e68-66d0d4bbf25c
md"""
Plot $S$ and $X$ simulated with the optimal and initial parameter values together with the measured data. We can do this to compare the found values with the initial ones and detect possible errors.
"""

# ╔═╡ d0156099-ad03-4711-ac0f-94882fb78266
# Uncomment and complete the instruction
# begin
# missing
# missing
# missing
# missing
# missing
# end

# ╔═╡ 257ae1a9-6264-4122-80be-8022b4b7500c
Expand All @@ -245,7 +216,6 @@ md"""

# ╔═╡ Cell order:
# ╠═245ca9d0-10f9-11ef-0ef6-a73594e96db9
# ╠═78a25bef-31e5-45ef-b0ba-b9a8c8a9edeb
# ╠═c54dae10-60af-4141-b56d-ed61cb0ced8a
# ╠═16438e07-1b2b-467e-822a-081d19cae92b
# ╠═295caa68-db27-4c9b-bc34-86ab088fec24
Expand All @@ -255,7 +225,6 @@ md"""
# ╟─824db995-7a66-4719-a534-7e0f6dec90b5
# ╠═245c2636-95da-4c76-8b03-c4d20bbabb48
# ╠═956790e2-6cac-46c9-886e-24d5aceae1c5
# ╠═68f9ecb3-15b0-4a53-8864-5dac13a89e95
# ╟─de8ddc14-8f82-403d-8f42-29673ef2a722
# ╟─b7b7d58f-d406-4596-b834-ced6d8fada83
# ╠═99c6f31a-0968-4804-9980-71fcc1af1f49
Expand All @@ -264,13 +233,9 @@ md"""
# ╟─6c481447-28c6-4530-bf2c-64762121bc71
# ╠═918fd524-81fa-4aff-a403-37402e47235b
# ╟─ef977370-06ee-4a73-85e2-609a744167d3
# ╟─7a227eaf-18d0-44f4-ac4b-f529e81c7471
# ╠═6375478f-1af9-4fd2-b6f3-101a6f796f2d
# ╠═38fe8304-af61-40a7-ac86-480dfb892185
# ╠═87482f88-8413-4820-9613-7941f3d61bd7
# ╠═94f3bd7b-5c2c-4661-a0ab-2cdaf2cd6743
# ╟─f6a8f134-6db0-4d74-8af5-82826347d8f0
# ╠═4c28a66a-ee2c-42a2-95c7-ea4ddb6a232d
# ╟─5928a9f3-f33c-4689-a6e5-637447f420d6
# ╟─3136b15d-5078-4bcd-954b-e89bcb8aed1b
# ╠═6a508a62-61b9-4273-8e45-b26f594e8da9
# ╟─63420055-55f8-4def-8b0e-11ea61483010
Expand Down
Loading
Loading