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We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment.
Linear and nonlinear programming
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Computational methods for inverse problems
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hypre: A library of high performance preconditioners
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A tutorial on elliptic PDE solvers and their parallelization
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The fenics project
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Convex optimization
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Statistical and computational inverse problems
Jari Kaipio and Erkki Somersalo · 2006
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A review of the adjoint-state method for computing the gradient of a functional with geophysical applications
R-E Plessix · 2006
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A duality between forward adn adjoint mpi communication routines
Benny N Cheng · 2006
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A survey of nonlinear conjugate gradient methods
William W Hager and Hongchao Zhang · 2006
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Toward adjoinable mpi
Jean Utke, Laurent Hascoet, Patrick Heimbach, Chris Hill, Paul Hovland, and Uwe Naumann · 2009
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Efficient pml for the wave equation
Marcus J Grote and Imbo Sim · 2010
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Scaling up machine learning: Parallel and distributed approaches
Ron Bekkerman, Mikhail Bilenko, and John Langford · 2011
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Automated derivation of the adjoint of high-level transient finite element programs
Patrick E Farrell, David A Ham, Simon W Funke, and Marie E Rognes · 2013
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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dolfin-adjoint 2018.1: automated adjoints for fenics and firedrake
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Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
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Deep learning
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