Neural network approximation
Neural networks (NNs) are the method of choice for building learning algorithms. They are
now being investigated for other numerical tasks such as solving high-dimensional partial …
now being investigated for other numerical tasks such as solving high-dimensional partial …
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
We formulate a general framework for hp-variational physics-informed neural networks (hp-
VPINNs) based on the nonlinear approximation of shallow and deep neural networks and …
VPINNs) based on the nonlinear approximation of shallow and deep neural networks and …
Model reduction and neural networks for parametric PDEs
We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …
between infinitedimensional spaces. The proposed approach is motivated by the recent …
Opportunities and challenges of diffusion models for generative AI
Diffusion models, a powerful and universal generative artificial intelligence technology, have
achieved tremendous success and opened up new possibilities in diverse applications. In …
achieved tremendous success and opened up new possibilities in diverse applications. In …
Universal approximation with deep narrow networks
P Kidger, T Lyons - Conference on learning theory, 2020 - proceedings.mlr.press
Abstract The classical Universal Approximation Theorem holds for neural networks of
arbitrary width and bounded depth. Here we consider the natural 'dual'scenario for networks …
arbitrary width and bounded depth. Here we consider the natural 'dual'scenario for networks …
Variational physics-informed neural networks for solving partial differential equations
E Kharazmi, Z Zhang, GE Karniadakis - ar** flexible PDE solvers that easily assimilate data. When applied to problems in …