  We present a data-driven workflow to biological tissue modeling, which aims
to predict the displacement field based on digital image correlation (DIC)
measurements under unseen loading scenarios, without postulating a specific
constitutive model form nor possessing knowledges on the material
microstructure. To this end, a material database is constructed from the DIC
displacement tracking measurements of multiple biaxial stretching protocols on
a porcine tricuspid valve anterior leaflet, with which we build a neural
operator learning model. The material response is modeled as a solution
operator from the loading to the resultant displacement field, with the
material microstructure properties learned implicitly from the data and
naturally embedded in the network parameters. Using various combinations of
loading protocols, we compare the predictivity of this framework with finite
element analysis based on the phenomenological Fung-type model. From
in-distribution tests, the predictivity of our approach presents good
generalizability to different loading conditions and outperforms the
conventional constitutive modeling at approximately one order of magnitude.
When tested on out-of-distribution loading ratios, the neural operator learning
approach becomes less effective. To improve the generalizability of our
framework, we propose a physics-guided neural operator learning model via
imposing partial physics knowledge. This method is shown to improve the model's
extrapolative performance in the small-deformation regime. Our results
demonstrate that with sufficient data coverage and/or guidance from partial
physics constraints, the data-driven approach can be a more effective method
for modeling biological materials than the traditional constitutive modeling.
