**A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues**

#### **David González <sup>1</sup> , Alberto García-González <sup>2</sup> , Francisco Chinesta <sup>3</sup> and Elías Cueto 1,\***


Received: 21 April 2020; Accepted: 15 May 2020 ; Published: 18 May 2020

**Abstract:** We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true "shape" of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach.

**Keywords:** machine learning; manifold learning; topological data analysis; GENERIC; soft living tissues; hyperelasticity; computational modeling
