49 citations · 49 across the 2 of their papers we have counts for
6 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…