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math.NA2023
An analysis of the derivative-free loss method for solving PDEs
Jihun Han, Yoonsang Lee
This study analyzes the derivative-free loss method to solve a certain class of elliptic PDEs and fluid problems using neural networks. The approach leverages the Feynman-Kac formu…
math.NA2023
A Structurally Informed Data Assimilation Approach for Nonlinear Partial Differential Equations
Tongtong Li, Anne Gelb, Yoonsang Lee
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliabl…