AndreWeiner / ml-cfd-lecture

Lecture material for machine learning applied to computational fluid mechanics
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Solution to the differential equation in the "Trends not considered in this course: Physics-informed neural networks (PINNs)" in the ml_cfd_intro #34

Closed SoufianeAitlhadj closed 7 months ago

SoufianeAitlhadj commented 9 months ago

I think that the solution of the diffrential equation : $$ \frac{\mathrm{d}x}{\mathrm{d}t} = -kx\quad \text{with}\quad x(t=0)=1\quad \text{and}\quad x\in\left[0, 1\right]. $$ has to be : $$ x(t) = \mathrm{exp}\left(-kt\right). $$ not $$ x(t) = \mathrm{exp}\left(-kx\right). $$ since the solution has to be a function of time t.

AndreWeiner commented 7 months ago

Dear @SoufianeAitlhadj, many thanks for your comment and apologies for the delayed reply. You are correct. Good job spotting this typo. I'll note this change for the next revision. Best, Andre