Neural networks catching up with finite differences in solving partial differential equations in higher dimensions
Vsevolod I. Avrutskiy
Topics & Concepts
Artificial neural networkDimension (graph theory)Partial differential equationResidualFunction (biology)Computer scienceBoundary value problemBoundary (topology)MathematicsApplied mathematicsComputational Science and EngineeringSparse gridGridComputational complexity theoryMathematical optimizationActivation functionFinite setMultigrid methodDifferential equationBellman equationAlgorithmFinite element methodOrder (exchange)Stochastic neural networkMethod of mean weighted residualsWork (physics)Value (mathematics)Current (fluid)Partial derivativeTopology (electrical circuits)VC dimensionDifferential (mechanical device)Feature (linguistics)Finite differenceModel Reduction and Neural NetworksNumerical methods for differential equationsNeural Networks and Applications