  Neural networks (NNs) accelerate simulations of quantum dissipative dynamics.
Ensuring that these simulations adhere to fundamental physical laws is crucial,
but has been largely ignored in the state-of-the-art NN approaches. We show
that this may lead to implausible results measured by violation of the trace
conservation. To recover the correct physical behavior, we develop
physics-informed NNs that mitigate the violations to a good extend. Beyond
that, we introduce an approach enforcing the perfect trace conservation by
design.
