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TL;DR: We measure variable $x$ every $10$ minutes, solve a differential equation $\frac{\mathrm{d}y}{\mathrm{d}t}$ where $y=f(x)$. We are interested in the time it takes for the cumulative value of $y$ to reach a certain value. Let's call that the output $z$. We can repeat the experiment multiple times to get the $z$ for various sequences of measured $x$. Which type of ML model might be best suited to predict $z$ from an ongoing measurement of $x$ in real-time.


We have a differential equation,

$\frac{\mathrm{d}y}{\mathrm{d}t}$ where $y=f(x)$

(We know the value of $y$ at time $t=0$, $y_{t=0}$.)

Tricky part: $x$ is measured in real-time. We get a measurement of its value every $10$ minutes.

x data:

t (min) x (units)
$0$ $x_{t=0} = 0.1$
$10$ 0.3
$20$ 0.25
' '
' '

Because of this we solve the differential equation at time steps of $10$ minutes and use the value of $y$ at the end of each step as the starting value for the next step.

t (min) Starting value of y Solution of diff. equn
$0-10$ $y_{t=0}$ $y_{t=10}$
$10-20$ $y_{t=10}$ $y_{t=20}$
$20-30$ $y_{t=20}$ $y_{t=30}$
' ' '
' ' '

As a result, we have $y$ vs $t$ corresponding to real-time measurements of $x$.

Next, we calculate values of cumulative $y$ vs $t$, and define $z$ as the value of $t$ at which the value of cumulative $y$ reaches a pre-decided threshold value.

Based on all of that, we have our final data,

t (min) x (units) z (min)
$0$ $0.1$ $180$
$10$ $0.3$
$20$ $0.25$
' '
' '
$180$ '

We can repeat this experiment multiple times and generate values of $z$ for various sequences of $x$.

Question: What ML model do you think would be better suited for such data? Our objective is to be able to predict $z$ for ongoing real-life measurements of $x$.

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  • $\begingroup$ This is quite confusing, have a look at meta.stackexchange.com/questions/66377/what-is-the-xy-problem. $\endgroup$ Mar 15, 2023 at 7:15
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    $\begingroup$ @user2974951 thank you for pointing that out, but I can't figure how else to ask the question. I think it only sounds like an XY problem but isn't one. I've added a tl;dr section which is the only way I think I can make it sound less like an XY problem. $\endgroup$ Mar 15, 2023 at 7:30

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