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# System prepended metadata

title: Untitled
tags: [aiphysim]

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tags: aiphysim
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$x_t$ = high-dim low-level var
$y_t$ = low-dim observable var
$z_t$ = low-dim learned var
$z_t = h(x_t)$
$x$'s dynamics yields $z$'s dynamics
$P(z_{t+1} | z_t)$
$$
\min_\theta (y_t - f(z_t))^2 + (x_t - g(z_t))^2 | x_0
$$
$$
x_0 \rightarrow z_0 \rightarrow z_1 \rightarrow \ldots \rightarrow z_t
$$
low-res dynamics
$P(z_{t+T}|z_t)$
provides a good approximation

Alternatively, $z_t$ is an aggregation over time, e.g.,

$z_s = h(x_{1},\ldots, x_t)$ (e.g. recurrent or convolutional or transformer)
$z_s = h(x_{i \in I \subset \{1 \cdots t\}})$ where $s$ is a coarse index for $t$, e.g., $s=int(t/10)$.

and z-space dynamics is as usual $P(z_{s+1}|z_s)$
