3 papers
math.NA2026
Random-Feature Kalman Filtering for Linear PDE Data Assimilation
Xi'an Li, Jiale Linghu, Yangshuai Wang
Data assimilation for time-dependent partial differential equations (PDEs) requires Bayesian updates of an evolving field from streaming, sparse, and noisy observations, while keep…
math.NA2025
Fourier heuristic PINNs to solve the biharmonic equations based on its coupled scheme
Yujia Huang, Xi'an Li ansd Jinran Wu
Physics-informed neural networks (PINNs) have been widely utilized for solving a range of partial differential equations (PDEs) in various scientific and engineering disciplines. T…
math.NA2024
Augmented physics informed extreme learning machine to solve the biharmonic equations via Fourier expansions
Xi'an Li, Jinran Wu, Yujia Huang +4
To address the sensitivity of parameters and limited precision for physics-informed extreme learning machines (PIELM) with common activation functions, such as sigmoid, tangent, an…