  We present an efficient physics-informed neural networks (PINNs) framework,
termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of
interface problems with discontinuous coefficients and/or interfacial jumps.
This framework is an enhanced version of its predecessor, Interface PINNs or
I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves
domain decomposition and assignment of different predefined activation
functions to the neural networks in each subdomain across a sharp interface,
while keeping all other parameters of the neural networks identical. In
AdaI-PINNs, the activation functions vary solely in their slopes, which are
trained along with the other parameters of the neural networks. This makes the
AdaI-PINNs framework fully automated without requiring preset activation
functions. Comparative studies on one-dimensional, two-dimensional, and
three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs
outperform I-PINNs, reducing computational costs by 2-6 times while producing
similar or better accuracy.
