IEEE Access · 2019 · 53 citations · 25 references
Numerical AnalysisGeometric LearningEngineeringMachine LearningComputer-aided DesignComputational MechanicsPde-constrained OptimizationData SciencePhysic Aware Machine LearningNumerical SimulationMulti-physics ModellingPhysicsMultiphysics ModelingPartial Differential EquationsMultiphysics ProblemComputer ScienceNumerical Method For Partial Differential EquationSurfaces PdesSurface PdesNatural SciencesApplied PhysicsSurface ModelingTime Independent ProblemsMultiscale Modeling
Partial differential equations (PDEs) on surfaces are ubiquitous in all the nature science. Many traditional mathematical methods has been developed to solve surfaces PDEs. However, almost all of these methods have obvious drawbacks and complicate in general problems. As the fast growth of machine learning area, we show an algorithm by using the physics-informed neural networks (PINNs) to solve surface PDEs. To deal with the surfaces, our algorithm only need a set of points and their corresponding normal, while the traditional methods need a partition or a grid on the surface. This is a big advantage for real computation. A variety of numerical experiments have been shown to verify our algorithm.
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Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics · 2018 · 14.4K citations · Full text
Engineering, Pde-constrained Optimization, Deep Learning Framework +6
Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot, Yoshua Bengio · 2010 · 12.6K citations