Table 3.

Summary of the network input variables.

	Parameter	Notation	Distribution	Unit
Field	Horizontal permeability field	$k_x$	Heterogeneousa	–
	Material anisotropy ratio	$k_x/k_y$	$\text{X}\sim \mathcal{V}\left[1,,,150\right]$	–
	Porosity	$\varnothing$	$\epsilon \sim \mathcal{N}(0,0.005)$	–
	Reservoir thicknessb	b	$\text{X}\sim \mathcal{V}\left[12.5,,,200\right]$	$m$
	Perforation thicknessc	$b_{\mathit{perf}}$	$\text{X}\sim \mathcal{V}\left[12,,,,\text{b}\right]$	$m$
	Perforation locationc	–	$\text{Randomly placed}$	$-$
Scalar	Injection rate	$Q$	$\text{X}\sim \mathcal{V}\left[0.2,,,2\right]$	$MT/y$
	Initial pressure	$P_{\mathit{init}}$	$\text{X}\sim \mathcal{V}\left[100,,,300\right]$	$\mathit{bar}$
	Iso-thermal reservoir temperature	$T$	$\text{X}\sim \mathcal{V}\left[35,,,170\right]$	$_{}^{\circ }\mathrm{C}$
	Irreducible water saturation	$S_{\mathit{wi}}$	$\text{X}\sim \mathcal{V}\left[0.1,,,0.3\right]$	–
	Van Genuchten scaling factor	$\lambda$	$\text{X}\sim \mathcal{V}\left[0.3,,,0.7\right]$	–

Field inputs are maps on a (96, 200) grid. $\mathcal{V}\left[a,,,b\right]$ means that the value ranges from a to b. Note that the perforation thickness and location are sampled as scalars, they are represented as a binary map and therefore we count them as the fifth field input.

^aPermeability maps are sampled from a heterogeneous ensemble of distributions including Gaussian, von Karman, Discontinuous, and homogeneous.

^bReservoir thickness is not an input parameter, however it is reflected in the masked loss.

^cThese three field variables are combined into one binary map and therefore represent one input field parameter.