human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "variational physics informed neural networks for solving partial differential equations"):
  Abstract: Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neural networks (DNNs) by selecting the {\em trial space} to be the space of neural networks and the {\em test space} to be the space of Legendre polynomials. We formulate the \textit{variational residual} of the PDE using the DNN approximation by incorporating the variational form of the problem into the loss function of the network and construct a \textit{variational physics-informed neural network} (VPINN). By integrating by parts the integrand in the variational form, we lower the order of the differential operators represented by the neural networks, hence effectively reducing the training cost in VPINNs while increasing their accuracy compared to PINNs that essentially employ delta test functions. For shallow networks with one hidden layer, we analytically obtain explicit forms of the \textit{variational residual}. We demonstrate the performance of the new formulation for several examples that show clear advantages of VPINNs over PINNs in terms of both accuracy and speed.

Includes members:
  Member "nonlinear approximation and deep relu networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "nonlinear approximation via compositions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "deep network approximation for smooth functions")
  Member "function approximation by deep networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lossless compression of deep neural networks")
  Member "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "barron spaces and the compositional function spaces for neural network models":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a corrective view of neural networks representation memorization and learning")
  Member "hidden physics models machine learning of nonlinear partial differential equations":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "understanding and mitigating gradient pathologies in physics informed neural networks")
  Member "machine learning of linear differential equations using gaussian processes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.NE(Neural and Evolutionary Computing)