Notation and Abbreviations

Math notation:

Symbol	Meaning
$A$	matrix
$\eta$	learning rate or step size
$\Gamma$	boundary of computational domain $\Omega$
$f^{*}$	generic function to be approximated, typically unknown
$f$	approximate version of $f^{*}$
$\Omega$	computational domain
$\mathcal P^*$	continuous/ideal physical model
$\mathcal P$	discretized physical model, PDE
$\theta$	neural network params
$t$	time dimension
$\mathbf{u}$	vector-valued velocity
$x$	neural network input or spatial coordinate
$y$	neural network output
$y^*$	learning targets: ground truth, reference or observation data

Abbreviation	Meaning
BNN	Bayesian neural network
CNN	Convolutional neural network
DL	Deep Learning
GD	(steepest) Gradient Descent
MLP	Multi-Layer Perceptron, a neural network with fully connected layers
NN	Neural network (a generic one, in contrast to, e.g., a CNN or MLP)
PDE	Partial Differential Equation
PBDL	Physics-Based Deep Learning
SGD	Stochastic Gradient Descent