Partial differential equations (PDEs) play a fundamental role in modeling and simulating
problems across a wide range of disciplines. Recent advances in deep learning have shown …

Abstract Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system
discovery that has been shown to successfully recover governing dynamical systems from …

Traditional data-driven deep learning models often struggle with high training costs, error
accumulation, and poor generalizability in complex physical processes. Physics-informed …

We employ physics-informed neural networks (PINNs) to infer properties of biological
materials using synthetic data. In particular, we successfully apply PINNs to extract the …

Data-driven methods are becoming an essential part of computational mechanics due to
their advantages over traditional material modeling. Deep neural networks are able to learn …

Weak form equation learning and surrogate modeling has proven to be computationally
efficient and robust to measurement noise in a wide range of applications including ODE …

Pure data-driven deep learning models suffer from high training costs, error accumulation,
and poor generalizability when predicting complex physical processes. A more promising …

We present a novel, fully three-dimensional approach to soft material characterization and
constitutive modeling with relevance to soft biological tissue. Our approach leverages recent …

We extend the classical SIR model of infectious disease spread to account for time
dependence in the parameters, which also include diffusivities. The temporal dependence …

In this work we study the asymptotic consistency of the weak-form sparse identification of
nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from …