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Title: A scalable framework for learning the geometry-dependent solution operators of partial differential equations

Journal Article · · Nature Computational Science

Not Available

Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0025592; SC0025593
OSTI ID:
2480598
Journal Information:
Nature Computational Science, Journal Name: Nature Computational Science Journal Issue: 12 Vol. 4; ISSN 2662-8457
Publisher:
Nature Publishing GroupCopyright Statement
Country of Publication:
United States
Language:
English

References (51)

A rule‐based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts
  • Doste, Ruben; Soto‐Iglesias, David; Bernardino, Gabriel
  • International Journal for Numerical Methods in Biomedical Engineering, Vol. 35, Issue 4 https://doi.org/10.1002/cnm.3185
journal February 2019
The Inhomogeneous Dirichlet Problem in Lipschitz Domains journal May 1995
An isogeometric analysis framework for ventricular cardiac mechanics journal August 2023
Physics-informed neural networks (PINNs) for fluid mechanics: a review journal December 2021
A Novel Rule-Based Algorithm for Assigning Myocardial Fiber Orientation to Computational Heart Models journal May 2012
Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics: A Comprehensive Numerical Framework journal January 2023
The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems journal February 2018
A spectral element method for fluid dynamics: Laminar flow in a channel expansion journal June 1984
The p- and h-p versions of the finite element method, an overview journal June 1990
Multipatch Isogeometric Analysis for electrophysiology: Simulation in a human heart journal April 2021
Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads journal October 2023
The openCARP simulation environment for cardiac electrophysiology journal September 2021
Deep neural operators as accurate surrogates for shape optimization journal March 2024
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations journal February 2019
Universal ventricular coordinates: A generic framework for describing position within the heart and transferring data journal April 2018
Geodesic estimation for large deformation anatomical shape averaging and interpolation journal January 2004
Unbiased diffeomorphic atlas construction for computational anatomy journal January 2004
Diffeomorphic demons: Efficient non-parametric image registration journal March 2009
Quasi-isometric parameterization for texture mapping journal May 2008
Finite bandwidth, finite amplitude convection journal September 1969
The Earth Mover's Distance as a Metric for Image Retrieval journal November 2000
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms journal February 2005
Personalized virtual-heart technology for guiding the ablation of infarct-related ventricular tachycardia journal September 2018
Physics-informed machine learning journal May 2021
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators journal March 2021
Laplace neural operator for solving differential equations journal June 2024
Analysis of anatomical variability using diffeomorphic iterative centroid in patients with Alzheimer's disease journal May 2015
Computational anatomy: an emerging discipline journal December 1998
Spectral/hp Element Methods for Computational Fluid Dynamics book January 2005
Characterizing the arrhythmogenic substrate in personalized models of atrial fibrillation: sensitivity to mesh resolution and pacing protocol in AF models journal March 2021
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems journal July 1995
Artificial neural networks for solving ordinary and partial differential equations journal January 1998
Completing 3D object shape from one depth image conference June 2015
A Point Set Generation Network for 3D Object Reconstruction from a Single Image conference July 2017
DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation conference June 2019
Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape journal August 2004
Intrinsic Parameterizations of Surface Meshes journal September 2002
An Operator Approach to Tangent Vector Field Processing journal August 2013
Complex Functional Maps: A Conformal Link Between Tangent Bundles journal February 2022
MIONet: Learning Multiple-Input Operators via Tensor Product journal November 2022
Functional maps journal July 2012
Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes
  • Scroggs, Matthew W.; Dokken, Jørgen S.; Richardson, Chris N.
  • ACM Transactions on Mathematical Software, Vol. 48, Issue 2 https://doi.org/10.1145/3524456
journal May 2022
Spherical parametrization and remeshing journal July 2003
On the Metrics and Euler-Lagrange Equations of Computational Anatomy journal August 2002
Alternans and spiral breakup in a human ventricular tissue model journal September 2006
A model for human ventricular tissue journal April 2004
A Bayesian Generative Model for Surface Template Estimation journal January 2010
Standardized Myocardial Segmentation and Nomenclature for Tomographic Imaging of the Heart journal January 2002
Sensitivity of Ablation Targets Prediction to Electrophysiological Parameter Variability in Image-Based Computational Models of Ventricular Tachycardia in Post-infarction Patients journal May 2019
Sobolev metrics on shape space of surfaces journal January 2011
Data Repository, A Scalable Framework for Learning the Geometry-Dependent Solution Operators of Partial Differential Equations dataset January 2024