On sparse regression, Lp‐regularization, and automated model discovery

JA McCulloch, SR St. Pierre, K Linka… - International Journal for …, 2024 - Wiley Online Library
Sparse regression and feature extraction are the cornerstones of knowledge discovery from
massive data. Their goal is to discover interpretable and predictive models that provide …

[HTML][HTML] Automated model discovery for human cardiac tissue: Discovering the best model and parameters

D Martonová, M Peirlinck, K Linka, GA Holzapfel… - Computer Methods in …, 2024 - Elsevier
For more than half a century, scientists have developed mathematical models to understand
the behavior of the human heart. Today, we have dozens of heart tissue models to choose …

The Ogden model of rubber mechanics: 50 years of impact on nonlinear elasticity

M Destrade, L Dorfmann… - … Transactions of the …, 2022 - royalsocietypublishing.org
We place the Ogden model of rubber elasticity, published in Proceedings of the Royal
Society 50 years ago, in the wider context of the theory of nonlinear elasticity. We then follow …

[HTML][HTML] Best-in-class modeling: A novel strategy to discover constitutive models for soft matter systems

K Linka, E Kuhl - Extreme Mechanics Letters, 2024 - Elsevier
The ability to automatically discover interpretable mathematical models from data could
forever change how we model soft matter systems. For convex discovery problems with a …

Pattern formation in dense populations studied by inference of nonlinear diffusion‐reaction mechanisms

S Srivastava, K Garikipati - International Journal for Numerical …, 2024 - Wiley Online Library
Reaction‐diffusion systems have been proposed as a model for pattern formation and
morphogenesis. The Fickian diffusion typically employed in these constructions model the …

[HTML][HTML] Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells

PC Kinnunen, S Srivastava, Z Wang, KKY Ho… - ArXiv, 2024 - pmc.ncbi.nlm.nih.gov
Targeting signaling pathways that drive cancer cell migration or proliferation is a common
therapeutic approach. A popular experimental technique, the scratch assay, measures the …

Integrated Approach To Material Parameterization And Inflation Control Of Hyperelastic Membrane For Artificial Left Ventricle Development

AK Singh, D Raj, N Kumar - Journal of Physics: Conference …, 2024 - iopscience.iop.org
In transitioning from conventional mechanical to biomedical applications, the choice of
materials becomes critical. While hard materials like steel offer durability, their compatibility …

Inverse Modeling and System Inference from Data

K Garikipati - Data-driven Modelling and Scientific Machine Learning …, 2024 - Springer
In this chapter we turn to questions of inference, specifically, the identification of partial
differential equations (PDEs), with an emphasis on discerning between competing …

Data-driven Modelling and Scientific Machine Learning in Continuum Physics

K Garikipati - (No Title), 2024 - Springer
This monograph is the product of research into data-driven methods for continuum physics
conducted with many students, post-docs, and collaborators. While written from the …