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Found 11 papers, 5 papers with code
Understanding and Mitigating Membership Inference Risks of Neural Ordinary Differential Equations
By accurately learning underlying dynamics in data in the form of differential equations, NODEs have been widely adopted in various domains, such as healthcare, finance, computer vision, and language modeling.
MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data
Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques.
Gaussian Variational Schemes on Bounded and Unbounded Domains
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains.
Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method
This paper presents and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs), following a domain decomposition of the spatial geometry on which a given partial differential equation (PDE) is posed.
Efficiently Parameterized Neural Metriplectic Systems
Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data.
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
