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AAROC: Reduced Over-Collocation Method with Adaptive Time Partitioning and Adaptive Enrichment for Parametric Time-Dependent Equations
Lijie Ji, Zhichao Peng, Yanlai Chen
Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced order model (ROM) that is comparable to the cos…
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…
MCMS-RBM: Multi-Component Multi-State Reduced Basis Method toward Efficient Transition Pathway Identification for Crystals and Quasicrystals
Yajie Ji, Lijie Ji, Yanlai Chen +1
Due to quasicrystals having long-range orientational order but without translational symmetry, traditional numerical methods usually suffer when applied as is. In the past decade,…
GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs
Yanlai Chen, Shawn Koohy
Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the express…
Fast optimal mass transport via reduced basis methods for the Monge-Ampre equation
Shijin Hou, Yanlai Chen, Yinhua Xia
Repeatedly solving the parameterized optimal mass transport (pOMT) problem is a frequent task in applications such as image registration and adaptive grid generation. It is thus cr…