4 papers
Learnable Splines for Unstructured Neural Operators
Vignesh Gopakumar, Zhuoyuan Wang, Ander Gray +12
Neural operators approximate solution operators of partial differential equations at a fraction of the cost of numerical solvers. Efficient grid-based architectures such as the Fou…
Self-Similar Singularity of the Euler Equations on
Adarsh Ganeshram, Valentin Duruisseaux, Anima Anandkumar
We provide evidence of a finite-time singularity in the 3D Euler equations on the unbounded domain. Using a physics-informed neural network (PINN) with a self-similar ansatz, we fi…
Stability Framework for the Singularity of the Euler Equations on
Valentin Duruisseaux, Adarsh Ganeshram, Robert J. George +1
In a recent numerical study, we found a high-precision singular profile for the Euler equations on the unbounded domain . The present manuscript complements that stud…
Equation Recast for Canonical Operator Learning Across Parametric PDEs
Qiyun Cheng, Valentin Duruisseaux, Cesar F. Clauser +7
Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven para…