1.5k citations · 3.4k across the 43 of their papers we have counts for
45 papers
Extracting Koopman Operators for Prediction and Control of Non-linear Dynamics Using Two-stage Learning and Oblique Projections
Daisuke Uchida, Karthik Duraisamy
The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework nat…
Data-driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response
Elnaz Rezaian, Karthik Duraisamy
Rapid prediction of the aeroacoustic response is a key component in the design of aircraft and turbomachinery. While it is possible to achieve accurate predictions using direct sol…
Estimating Global Identifiability Using Conditional Mutual Information in a Bayesian Framework
Sahil Bhola, Karthik Duraisamy
A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual informa…
The Minimal Attached Eddy in Wall Turbulence: Statistical Foundations, Inverse Identification and Influence Kernels
Karthik Duraisamy
Townsend's attached eddy hypothesis models the logarithmic region of high Reynolds number wall turbulence as a random superposition of wall-attached, self-similar eddies whose size…
Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections
Cheng Huang, Karthik Duraisamy
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficien…
Control-aware Learning of Koopman Embedding Models
Daisuke Uchida, Karthik Duraisamy
A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space…
A unified understanding of scale-resolving simulations and near-wall modeling of turbulent flows using optimal finite element projections
Aniruddhe Pradhan, Karthik Duraisamy
The main objective of this work is to develop a unified framework that can be used as a lens to quantitatively assess and augment a wide range of coarse-grained models of turbulenc…
A Non-intrusive Approach for Physics-constrained Learning with Application to Fuel Cell Modeling
Vishal Srivastava, Valentin Sulzer, Peyman Mohtat +2
A data-driven model augmentation framework, referred to as Weakly-coupled Integrated Inference and Machine Learning (IIML), is presented to improve the predictive accuracy of physi…
Entropy-Stable Schemes in the Low-Mach-Number Regime: Flux-Preconditioning, Entropy Breakdowns, and Entropy Transfers
Ayoub Gouasmi, Karthik Duraisamy, Scott M. Murman
Entropy-Stable (ES) schemes, specifically those built from [Tadmor \textit{Math. Comput.} 49 (1987) 91], have been gaining interest over the past decade, especially in the context…
`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…
Non-intrusive Balancing Transformation of Highly Stiff Systems with Lightly-damped Impulse Response
Elnaz Rezaian, Cheng Huang, Karthik Duraisamy
Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address reali…
Disentangling Generative Factors of Physical Fields Using Variational Autoencoders
Christian Jacobsen, Karthik Duraisamy
The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This…
Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representations
James Duvall, Karthik Duraisamy, Shaowu Pan
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale…
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…
Variational Multi-scale Super-resolution : A data-driven approach for reconstruction and predictive modeling of unresolved physics
Aniruddhe Pradhan, Karthik Duraisamy
The variational multiscale (VMS) formulation formally segregates the evolution of the coarse-scales from the fine-scales. VMS modeling requires the approximation of the impact of 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…
Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence
Karthik Duraisamy
This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS) and Large Eddy Simulation…
Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspaces
Shaowu Pan, Nicholas Arnold-Medabalimi, Karthik Duraisamy
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques s…
Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics
Jiayang Xu, Karthik Duraisamy
A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural netwo…
Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow
Cheng Huang, Karthik Duraisamy, Charles L. Merkle
The impact of chemical reactions on the robustness and accuracy of projection-based Reduced-Order Models (ROMs) of fluid flows is investigated. Both Galerkin and Least-Squares Petr…
A minimum entropy principle in the compressible multicomponent Euler equations
Ayoub Gouasmi, Karthik Duraisamy, Scott M. Murman +1
In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on [Harten, \textit{J. Comput. Phys.}, 49 (1),…