2 citations · 4 across the 10 of their papers we have counts for
10 papers
Structure-Aware Tensorial Model Reduction
Arjun Vijaywargiya, Eric C. Cyr, Anthony Gruber
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established…
Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets
Adrienne M. Propp, Mauro Perego, Eric C. Cyr +5
Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks t…
Deriving Transformer Architectures as Implicit Multinomial Regression
Jonas A. Actor, Anthony Gruber, Eric C. Cyr
While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between att…
Meta-learning Structure-Preserving Dynamics
Cheng Jing, Uvini Balasuriya Mudiyanselage, Woojin Cho +3
Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key…
Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems
Xiaolong He, Yeonjong Shin, Anthony Gruber +3
We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. Th…
Tensor parametric Hamiltonian operator inference
Arjun Vijaywargiya, Shane A. McQuarrie, Anthony Gruber
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian st…
Modeling Neural Networks with Privacy Using Neural Stochastic Differential Equations
Sanghyun Hong, Fan Wu, Anthony Gruber +1
In this work, we study the feasibility of using neural ordinary differential equations (NODEs) to model systems with intrinsic privacy properties. Unlike conventional feedforward n…
MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data
Mingu Kang, Dongseok Lee, Woojin Cho +5
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 p…
Gaussian Variational Schemes on Bounded and Unbounded Domains
Jonas A. Actor, Anthony Gruber, Eric C. Cyr +1
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contr…
Efficiently Parameterized Neural Metriplectic Systems
Anthony Gruber, Kookjin Lee, Haksoo Lim +2
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. Besides being provably energy con…