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TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
Yanlai Chen, Yajie Ji, Akil Narayan +1
We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated part…
Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models
Ankur, Ram Jiwari, Akil Narayan
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixe…
Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonline…
GP-HMAT: Scalable, Gaussian Process Regression with Hierarchical Low-Rank Matrices
Vahid Keshavarzzadeh, Shandian Zhe, Robert M. Kirby +1
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationshi…