Add to ORKGSolving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is sometimes inevitably non-equispaced in real-world systems, limiting their applicability. In this paper, we propose a Non-equispaced Fourier PDE Solver (\textsc{NFS}) with adaptive interpolation on resampled equispaced points and a variant of Fourier Neural Operators as its components. Experimental results on complex PDEs demonstrate its advantages in accuracy and efficiency. Compared with the spatially-equispaced benchmark methods, it achieves superior performance with $42.85\%$ improvements on MAE, and ...
Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer ...
The classical development of neural networks has primarily focused on learning mappings between fini...
In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (...
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating ...
The classical development of neural networks has primarily focused on learning mappings between fini...
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). ...
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields...
Solving analytically intractable partial differential equations (PDEs) that involve at least one var...
Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning s...
We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential e...
Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), n...
We introduce an approach for solving PDEs over manifolds using physics informed neural networks whos...
Modeling three-dimensional (3D) turbulence by neural networks is difficult because 3D turbulence is ...
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields...
The Fourier neural operator (FNO) is a powerful technique for learning surrogate maps for partial di...
Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer ...
The classical development of neural networks has primarily focused on learning mappings between fini...
In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (...
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating ...
The classical development of neural networks has primarily focused on learning mappings between fini...
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). ...
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields...
Solving analytically intractable partial differential equations (PDEs) that involve at least one var...
Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning s...
We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential e...
Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), n...
We introduce an approach for solving PDEs over manifolds using physics informed neural networks whos...
Modeling three-dimensional (3D) turbulence by neural networks is difficult because 3D turbulence is ...
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields...
The Fourier neural operator (FNO) is a powerful technique for learning surrogate maps for partial di...
Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer ...
The classical development of neural networks has primarily focused on learning mappings between fini...
In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (...