Search Results for author:
Found 10 papers, 7 papers with code
Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs
Our contributions are threefold: i) we enable parallelization over input samples with a novel multi-grid-based domain decomposition, ii) we represent the parameters of the model in a high-order latent subspace of the Fourier domain, through a global tensor factorization, resulting in an extreme reduction in the number of parameters and improved generalization, and iii) we propose architectural improvements to the backbone FNO.
Neural Operators for Accelerating Scientific Simulations and Design
Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise.
Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems.
Learning Homogenization for Elliptic Operators
However, a major challenge in data-driven learning approaches for this problem has remained unexplored: the impact of discontinuities and corner interfaces in the underlying material.
Physics-Informed Neural Operator for Learning Partial Differential Equations
Specifically, in PINO, we combine coarse-resolution training data with PDE constraints imposed at a higher resolution.
Neural Operator: Learning Maps Between Function Spaces
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets.
Learning Dissipative Dynamics in Chaotic Systems
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping.
Fourier Neural Operator for Parametric Partial Differential Equations
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces.
Multipole Graph Neural Operator for Parametric Partial Differential Equations
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks.
Neural Operator: Graph Kernel Network for Partial Differential Equations
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces.
