no code implementations • 23 Apr 2024 • Noujoud Nader, Patrick Diehl, Marta D'Elia, Christian Glusa, Serge Prudhomme
Training is based on datasets of loading functions for which reference coupling configurations are computed using accurate coupled solutions, where accuracy is measured in terms of the relative error between the solution to the coupling approach and the solution to the nonlocal model.
no code implementations • 28 Mar 2023 • Rini Jasmine Gladstone, Helia Rahmani, Vishvas Suryakumar, Hadi Meidani, Marta D'Elia, Ahmad Zareei
Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs.
no code implementations • 11 Jan 2023 • Huaiqian You, Xiao Xu, Yue Yu, Stewart Silling, Marta D'Elia, John Foster
Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion.
no code implementations • 6 Oct 2022 • Tiffany Fan, Nathaniel Trask, Marta D'Elia, Eric Darve
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.
no code implementations • 6 Jan 2022 • Huaiqian You, Yue Yu, Marta D'Elia, Tian Gao, Stewart Silling
In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images.
no code implementations • 4 Aug 2021 • Huaiqian You, Yue Yu, Stewart Silling, Marta D'Elia
Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition.
no code implementations • 4 Jan 2021 • Xiao Xu, Marta D'Elia, John T. Foster
We generate macro-scale deformation training data by averaging over periodic micro-structure unit cells and add a physical energy constraint representing the homogenized elastic modulus of the micro-structure to the regression algorithm.
Numerical Analysis Numerical Analysis Applied Physics
no code implementations • 8 Dec 2020 • Huaiqian You, Yue Yu, Stewart Silling, Marta D'Elia
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials.
no code implementations • 17 May 2020 • Huaiqian You, Yue Yu, Nathaniel Trask, Mamikon Gulian, Marta D'Elia
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori.
no code implementations • 8 Apr 2020 • Guofei Pang, Marta D'Elia, Michael Parks, George E. Karniadakis
In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs).