12 papers
Fourier Feature Pyramids for Physics-Informed Neural Networks
Brandon Zhao, Yixuan Wang, Jonathan T. Barron +3
We present an improved neural field architecture for solving partial differential equations (PDEs). Current physics-informed neural networks (PINNs) provide a flexible framework fo…
Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
Yixuan Wang
This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation…
Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study
Spyros Rigas, Dhruv Verma, Georgios Alexandridis +1
Kolmogorov-Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility…
Nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes Equation
Thomas Hou, Yixuan Wang, Changhe Yang
The nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes equations is one of the central open problems in mathematical fluid dynamics. In this pape…
KANO: Kolmogorov-Arnold Neural Operator
Jin Lee, Ziming Liu, Xinling Yu +4
We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretabil…
FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation
Adarsh Ganeshram, Haydn Maust, Valentin Duruisseaux +6
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs).…