4 papers
An Inverse Scattering Inspired Fourier Neural Operator for Time-Dependent PDE Learning
Rixin Yu
Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon d…
Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution
Rixin Yu, Marco Herbert, Markus Klein +1
Predicting the evolution of complex systems governed by partial differential equations (PDEs) remains challenging, especially for nonlinear, chaotic behaviors. This study introduce…
Learning Flame Evolution Operator under Hybrid Darrieus Landau and Diffusive Thermal Instability
Rixin Yu, Erdzan Hodzic, Karl-Johan Nogenmyr
Recent advancements in the integration of artificial intelligence (AI) and machine learning (ML) with physical sciences have led to significant progress in addressing complex pheno…
Parametric Learning of Time-Advancement Operators for Unstable Flame Evolution
Rixin Yu, Erdzan Hodzic
This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators…