Exploring the loading guide

[ziolai]

I suggest to proceed as follows:

1/ implement the equation for the top oil temperature (Theoretical Documentation => Model Description) as a first order scalar ordinary differential equation in DifferentialEquations.jl (an alternative for scipy). Implement variant for static load, time-harmonic load and transient load. Complement with pen-and-paper computations whenever possible.

2/ implement a disturbance (source term) that is not captured by the fixed time-step sampling of dt = 15 min (here fixed is important, not the actual value) and that is captured by a variable time step method;

3/ implement the absence of any disturbance to show that fixed a time step is doing more than required (i.e., the opposite of previous scenario);

4/ implement an extension to two coupled scalar equations (e.g. top oil temperature and hot spot temperature) (both physics based instead of by scaling one from the other) to show how easy this can be implemented. Explore models in which top oil and hot spot temperature are no longer directly proportional to each other. Explore whether such models math better with data shown in the pitches of June 13th, 2025.

5/ implement a combination of DifferentialEquations.jl and interval arithmetic to quantify how uncertainty in the input translates to uncertainty in the output. See e.g. https://docs.sciml.ai/SciMLTutorialsOutput/html/type_handling/02-uncertainties.html

6/ implement a combination of DifferentialEquations.jl and least-squares fitting to obtain an estimation of a coefficient in the model input (e.g. oil viscosity) from measured data of the model output (e.g. temperature). See e.g. https://docs.sciml.ai/DiffEqParamEstim/stable/tutorials/ensemble/

6/ Show the machine code that DifferentialEquations.jl generates under the hood to show that not only the code is fast, but explain you why it is fast.

[thijsvanderhoeven301]

Hi Ziolai, thank you for your input! Currently we are discussing the vision we have for TTM and depending on the outcome of this discussion these enhancements might be very interesting. Would you be open to a short meeting over Teams to elaborate a bit on these points?