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Found 6 papers, 5 papers with code
Reversible and irreversible bracket-based dynamics for deep graph neural networks
Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing.
Canonical and Noncanonical Hamiltonian Operator Inference
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented.
Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation
Our method contains two major components: one is the pseudo-reversible neural network (PRNN) module that effectively transforms high-dimensional input variables to low-dimensional active variables, and the other is the synthesized regression module for approximating function values based on the transformed data in the low-dimensional space.
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems.
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled.
Stationary Surfaces with Boundaries
This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature.
Differential Geometry Primary 53A05, Secondary 53A10, 53C40, 53C42
