7 papers · 1 filter
High-order Conservative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg-de Vries Equation and the Hirota-Satsuma KdV System
M. Shan Tariq, Yanlai Chen, Bo Dong
We develop new conservative discontinuous Galerkin (DG) methods for nonlinear wave problems, focusing on the generalized Korteweg-de Vries (gKdV) equation and the coupled Hirota-Sa…
Nonlinear Model Order Reduction on Quadratic Manifolds via Greedy Algorithms with Dimension-Dependent Regularization
Lijie Ji, Sabrina Rashid, Yanlai Chen +1
Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov -width of the solu…
Greedy Rational Approximation for Frequency-Domain Model Reduction of Parametric LTI Systems
Filip BÄlÃk, Yanlai Chen, Akil Narayan
We investigate model reduction of parametric linear time-invariant (LTI) dynamical systems. When posed in the frequency domain, this problem can be formulated as seeking a low-orde…
Reduced Basis Methods for Parametric Steady-State Radiative Transfer Equation
Kimberly Matsuda, Yanlai Chen, Yingda Cheng +1
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host m…
Derivative-informed Graph Convolutional Autoencoder with Phase Classification for the Lifshitz-Petrich Model
Yanlai Chen, Yajie Ji, Zhenli Xu
The Lifshitz-Petrich (LP) model is a classical model for describing complex spatial patterns such as quasicrystals and multiphase structures. Solving and classifying the solutions…
EGPT-PINN: Entropy-enhanced Generative Pre-Trained Physics Informed Neural Networks for parameterized nonlinear conservation laws
Yajie Ji, Yanlai Chen, Zhenli Xu
We propose an entropy-enhanced Generative Pre-Trained Physics-Informed Neural Network with a transform layer (EGPT-PINN) for solving parameterized nonlinear conservation laws. The…