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05/24/2023
Reversible and irreversible bracket-based dynamics for deep graph neural networks
Recent works have shown that physics-inspired architectures allow the tr...
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10/06/2022
Probabilistic partition of unity networks for high-dimensional regression problems
We explore the probabilistic partition of unity network (PPOU-Net) model...
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10/01/2022
Parameter-varying neural ordinary differential equations with partition-of-unity networks
In this study, we propose parameter-varying neural ordinary differential...
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08/08/2022
A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations
Convection-diffusion equations arise in a variety of applications such a...
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05/16/2022
Scalable algorithms for physics-informed neural and graph networks
Physics-informed machine learning (PIML) has emerged as a promising new ...
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02/07/2022
Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery
We introduce physics-informed multimodal autoencoders (PIMA) - a variati...
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01/28/2022
Efficient optimization-based quadrature for variational discretization of nonlocal problems
Casting nonlocal problems in variational form and discretizing them with...
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12/14/2021
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation
High order schemes are known to be unstable in the presence of shock dis...
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10/26/2021
Polynomial-Spline Neural Networks with Exact Integrals
Using neural networks to solve variational problems, and other scientifi...
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09/11/2021
Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
Discovery of dynamical systems from data forms the foundation for data-d...
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08/25/2021
Coupling of IGA and Peridynamics for Air-Blast Fluid-Structure Interaction Using an Immersed Approach
We present a novel formulation based on an immersed coupling of Isogeome...
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07/27/2021
A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics
We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formu...
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01/05/2021
An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture
Meshfree discretizations of state-based peridynamic models are attractiv...
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12/22/2020
Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
As traditional machine learning tools are increasingly applied to scienc...
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05/17/2020
Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
A key challenge to nonlocal models is the analytical complexity of deriv...
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04/23/2020
A unified, stable and accurate meshfree framework for peridynamic correspondence modeling. Part I: core methods
The overarching goal of this work is to develop an accurate, robust, and...
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09/07/2019
GMLS-Nets: A framework for learning from unstructured data
Data fields sampled on irregularly spaced points arise in many applicati...
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08/11/2019
An Asymptotically Compatible Approach For Neumann-Type Boundary Condition On Nonlocal Problems
In this paper we consider 2D nonlocal diffusion models with a finite non...
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07/28/2019
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Reproducing kernel (RK) approximations are meshfree methods that constru...
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03/01/2019