Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Trask, Nathaniel A."'
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 contrast to standard mesh-free methods, which use GRBFs to discretize stron
Externí odkaz:
http://arxiv.org/abs/2410.06219
We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify structure-preservi
Externí odkaz:
http://arxiv.org/abs/2406.05571
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 conserving and entropy stable, the proposed approach comes with approxima
Externí odkaz:
http://arxiv.org/abs/2405.16305
Autor:
Choi, Jeongwhan, Wi, Hyowon, Kim, Jayoung, Shin, Yehjin, Lee, Kookjin, Trask, Nathaniel, Park, Noseong
Transformers, renowned for their self-attention mechanism, have achieved state-of-the-art performance across various tasks in natural language processing, computer vision, time-series modeling, etc. However, one of the challenges with deep Transforme
Externí odkaz:
http://arxiv.org/abs/2312.04234
Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning algorithms
Externí odkaz:
http://arxiv.org/abs/2310.18471
Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e.g., Hamiltonian)
Externí odkaz:
http://arxiv.org/abs/2305.15616
We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target fun
Externí odkaz:
http://arxiv.org/abs/2210.02694
Autor:
Lee, Kookjin, Trask, Nathaniel
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed variant of NOD
Externí odkaz:
http://arxiv.org/abs/2210.00368
Autor:
Villarreal, Ruben, Vlassis, Nikolaos N., Phan, Nhon N., Catanach, Tommie A., Jones, Reese E., Trask, Nathaniel A., Kramer, Sharlotte L. B., Sun, WaiChing
Experimental data is costly to obtain, which makes it difficult to calibrate complex models. For many models an experimental design that produces the best calibration given a limited experimental budget is not obvious. This paper introduces a deep re
Externí odkaz:
http://arxiv.org/abs/2209.13126
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques, is particu
Externí odkaz:
http://arxiv.org/abs/2208.04169