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Incremental Tensor-Train Compression from Streaming TT-Formatted Data with Applications to Reduced-Order Modeling of Linear Kinetic Equations
Wei Guo, Shuyuan Shang, Zhichao Peng
To mitigate the computational burden due to the high dimensionality of linear kinetic equations, low-rank solvers and data-driven reduced order models (ROMs) have been developed. L…
Enhancing Future Prediction of Linear and Nonlinear Reduced-Order Models for Transport-Dominated Problems Using Lagrangian Data
Meng Li, Yang Xiang, Zhichao Peng
Designing effective reduced-order models (ROMs) for parametrized transport-dominated problems remains challenging because of the well-known Kolmogorov barrier. Autoencoder-based no…
On-the-Fly ROM-Based Acceleration of SI-DSA for Implicit Time Marching of the Radiative Transfer Equation
Ningxin Liu, Zhichao Peng
In implicit time marching of the radiative transfer equation (RTE), the resulting linear systems are commonly solved using source iteration with diffusion synthetic acceleration (S…
Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation
Wei Guo, Zhichao Peng
Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equat…