210 citations · 517 across the 10 of their papers we have counts for
11 papers
Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networks
Rambod Mojgani, Maciej Balajewicz, Pedram Hassanzadeh
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial condit…
Physics-aware registration based auto-encoder for convection dominated PDEs
Rambod Mojgani, Maciej Balajewicz
We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlin…
Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
Francisco J. Gonzalez, Maciej Balajewicz
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular mode…
Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter dependent shocks
Nirmal J. Nair, Maciej Balajewicz
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientati…
Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows
Rambod Mojgani, Maciej Balajewicz
Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximat…
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
Maciej Balajewicz, Jari Toivanen
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates mo…
Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
Maciej Balajewicz, Irina Tezaur, Earl Dowell
For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes a…
Projection-based model reduction for contact problems
Maciej Balajewicz, David Amsallem, Charbel Farhat
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order redu…
Reduction of Nonlinear Embedded Boundary Models for Problems with Evolving Interfaces
Maciej Balajewicz, Charbel Farhat
Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfa…
Lyapunov stable Galerkin models of post-transient incompressible flows
Maciej Balajewicz
A method for deriving provably stable low-dimensional Galerkin models of post-transient incompressible flows is introduced. The proposed approach involves an iterative procedure fo…
A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number
Maciej Balajewicz, Earl Dowell, Bernd Noack
A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical tu…