558 citations · 639 across the 6 of their papers we have counts for
21 papers
`Basic' Generalization Error Bounds for Least Squares Regression with Well-specified Models
Karthik Duraisamy
This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear L…
A formal proof of the Lax equivalence theorem for finite difference schemes
Mohit Tekriwal, Karthik Duraisamy, Jean-Baptiste Jeannin
The behavior of physical systems is typically modeled using differential equations which are too complex to solve analytically. In practical problems, these equations are discretiz…
Generalizable Physics-constrained Modeling using Learning and Inference assisted by Feature Space Engineering
Vishal Srivastava, Karthik Duraisamy
This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable augmentations from sparse data. Building on recent advances in data-d…
Sub-grid scale characterization and asymptotic behavior of multi-dimensional upwind schemes for the vorticity transport equations
Daniel Foti, Karthik Duraisamy
We study the sub-grid scale characteristics of a vorticity-transport-based approach for large-eddy simulations. In particular, we consider a multi-dimensional upwind scheme for the…
Variational Encoders and Autoencoders : Information-theoretic Inference and Closed-form Solutions
Karthik Duraisamy
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-t…
Model Reduction for Multi-Scale Transport Problems using Model-form Preserving Least-Squares Projections with Variable Transformation
Cheng Huang, Christopher R. Wentland, Karthik Duraisamy +1
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but comp…