A physics-guided smoothing method for material modeling with digital image correlation (DIC) measurements

In PINNs [11], the governing law is known as a given partial differential equation (PDE), then the solution of the equation is modeled by a deep NN that is designed to minimize the equation loss. This idea was also adopted into image processing pipelines to enhance performance and interpretability [12, 13]. When the governing laws are unknown, NOs are an alternative method, which learns the solution operator as a mapping between infinite-dimensional function spaces [14, 15], enabling accurate and consistent predictions of continuum physical surrogates. However, vanilla NOs cannot provide interpretability of the underlying physics. Constitutive operator learning: In order to provide physical interpretability for systems with unknown governing laws, researchers propose to learn constitutive laws [16-18].