  Neural operators, which can act as implicit solution operators of hidden
governing equations, have recently become popular tools for learning the
responses of complex real-world physical systems. Nevertheless, most neural
operator applications have thus far been data-driven and neglect the intrinsic
preservation of fundamental physical laws in data. In this work, we introduce a
novel integral neural operator architecture called the Peridynamic Neural
Operator (PNO) that learns a nonlocal constitutive law from data. This neural
operator provides a forward model in the form of state-based peridynamics, with
objectivity and momentum balance laws automatically guaranteed. As
applications, we demonstrate the expressivity and efficacy of our model in
learning complex material behaviors from both synthetic and experimental data
sets. We show that, owing to its ability to capture complex responses, our
learned neural operator achieves improved accuracy and efficiency compared to
baseline models that use predefined constitutive laws. Moreover, by preserving
the essential physical laws within the neural network architecture, the PNO is
robust in treating noisy data. The method shows generalizability to different
domain configurations, external loadings, and discretizations.
