human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "understanding and mitigating gradient pathologies in physics informed neural networks"):
  with members:
    - "machine learning in cardiovascular flows modeling predicting arterial blood pressure from non invasive 4d flow mri data using physics informed neural networks"
    - "the mechanics of n player differentiable games"
    - "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data"
    - "covariant compositional networks for learning graphs"
    - "eigenvalues of the hessian in deep learning singularity and beyond"
    - "attention is all you need"
    - "cycles in adversarial regularized learning"
    - "gradnorm gradient normalization for adaptive loss balancing in deep multitask networks"

Connected through hyperedge HE-2 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition"):
  with members:
    - "understanding and mitigating gradient pathologies in physics informed neural networks"
    - "nonlinear approximation and deep relu networks"
    - "varnet variational neural networks for the solution of partial differential equations"
    - "function approximation by deep networks"
    - "d3m a deep domain decomposition method for partial differential equations"
    - "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks"
    - "deepxde a deep learning library for solving differential equations"
    - "robust training and initialization of deep neural networks an adaptive basis viewpoint"

Question: Please tell me which class the center node 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)