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Found 9 papers, 0 papers with code
GNN-based physics solver for time-independent PDEs
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.
Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures
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.
Probabilistic partition of unity networks for high-dimensional regression problems
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.
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network
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.
A data-driven peridynamic continuum model for upscaling molecular dynamics
Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition.
A machine-learning framework for peridynamic material models with physical constraints
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
Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials.
Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori.
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
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).
