Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses
This work addresses the challenge of modeling complex material behaviors for applications in physics and engineering, representing an incremental advancement by integrating physical constraints into neural operators.
The authors tackled the problem of learning complex material responses from data by introducing the Peridynamic Neural Operator (PNO), a novel integral neural operator architecture that preserves fundamental physical laws, resulting in improved accuracy and efficiency compared to baseline models with predefined constitutive laws.
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.