  The ability to accurately infer cardiac electrophysiological (EP) properties
is key to improving arrhythmia diagnosis and treatment. In this work, we
developed a physics-informed neural networks (PINNs) framework to predict how
different myocardial EP parameters are modulated by anti-arrhythmic drugs.
Using $\textit{in vitro}$ optical mapping images and the 3-channel Fenton-Karma
model, we estimated the changes in ionic channel conductance caused by these
drugs.
  Our framework successfully characterised the action of drugs HMR1556,
nifedipine and lidocaine - respectively, blockade of $I_{K}$, $I_{Ca}$, and
$I_{Na}$ currents - by estimating that they decreased the respective channel
conductance by $31.8\pm2.7\%$ $(p=8.2 \times 10^{-5})$, $80.9\pm21.6\%$
$(p=0.02)$, and $8.6\pm0.5\%$ $ (p=0.03)$, leaving the conductance of other
channels unchanged. For carbenoxolone, whose main action is the blockade of
intercellular gap junctions, PINNs also successfully predicted no significant
changes $(p>0.09)$ in all ionic conductances.
  Our results are an important step towards the deployment of PINNs for model
parameter estimation from experimental data, bringing this framework closer to
clinical or laboratory images analysis and for the personalisation of
mathematical models.
