### Overview

Computational modeling of material systems have enabled many advances in various industries, with notable examples including (i) automotive industries: where crashworthiness simulations led to a 20% decrease in car accident deaths (only within the last two decades of the 20th century), and (ii) healthcare industries: where computer-aided design of medical implants have enabled its rapid growth, poised to become a 32bn global market by 2032. To maintain similar contributions in recent and emerging technologies, such as advanced manufacturing or nanotechnology, computational paradigms must become increasingly more precise in predicting outcomes of physical processes across different time and length scales, and not just macro-scales. This, in turn, calls upon computational tools to go beyond conventional material modeling schemes by accounting for, and ultimately harnessing, all microstructure-induced complexities (i.e., nonlinearities, heterogeneities, anisotropies). The emergence of data science and AI, coupled with the abundance of material data -obtained either from measurements or *small* scale calculations-, provide pathways that can be leveraged to address these challenges, and transform design and prediction paradigms from the computer-aided to the *computer-guided*.

In recognition of these challenges and opportunities, our lab strives to develop high-fidelity data-driven computational models to predict and ultimately design the behavior of material systems under various multi-physics loadings across all time and length scales applied at the intersection of mechanics of materials and structures, data science, and applied mathematics. **Below is an example project that showcases our endeavors in this research thrust: **

### Data-Driven viscoelasticity (DDV): An unsupervised learning approach

The prevailing classical computational paradigm has been to calibrate empirical material models using observational data and then use the calibrated material model in calculations. An alternative paradigm is to utilize the data directly in the solution of suitably-formulated boundary-value problems. The main advantage of the this paradigm is that is makes direct use of *the data, all the data, and nothing but the data*.

In this spirit, we have developed the Data-Driven Viscoelasticity (DDV) framework for prediction of wave patterns in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST), and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. We showcased the approach by investigating wave patterns in a 3D soft gel sample characterized by MRE data, and verified its robust convergence properties, both with respect to the solver and the data.