  Physics-informed neural networks exploit the existing models of the
underlying physical systems to generate higher accuracy results with fewer
data. Such approaches can help drastically reduce the computation time and
generate a good estimate of computationally intensive processes in power
systems, such as dynamic security assessment or optimal power flow. Combined
with the extraction of worst-case guarantees for the neural network
performance, such neural networks can be applied in safety-critical
applications in power systems and build a high level of trust among power
system operators. This paper takes the first step and applies, for the first
time to our knowledge, Physics-Informed Neural Networks with Worst-Case
Guarantees for the DC Optimal Power Flow problem. We look for guarantees
related to (i) maximum constraint violations, (ii) maximum distance between
predicted and optimal decision variables, and (iii) maximum sub-optimality in
the entire input domain. In a range of PGLib-OPF networks, we demonstrate how
physics-informed neural networks can be supplied with worst-case guarantees and
how they can lead to reduced worst-case violations compared with conventional
neural networks.
