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 "distributed physics informed neural network for data efficient solution to partial differential equations"):
  Abstract: The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial differential equations (PDEs). However, the literature lacks detailed investigation of PINNs in terms of their representation capability. In this work, we first test the original PINN method in terms of its capability to represent a complicated function. Further, to address the shortcomings of the PINN architecture, we propose a novel distributed PINN, named DPINN. We first perform a direct comparison of the proposed DPINN approach against PINN to solve a non-linear PDE (Burgers' equation). We show that DPINN not only yields a more accurate solution to the Burgers' equation, but it is found to be more data-efficient as well. At last, we employ our novel DPINN to two-dimensional steady-state Navier-Stokes equation, which is a system of non-linear PDEs. To the best of the authors' knowledge, this is the first such attempt to directly solve the Navier-Stokes equation using a physics informed neural network.

Includes members:
  Member "physics informed extreme learning machine pielm a rapid method for the numerical solution of partial differential equations":
    also connected through other hyperedges:
      (none)
  Member "an introduction to variational autoencoders":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "semi supervised grasp detection by representation learning in a vector quantized latent space")
  Member "hidden physics models machine learning of nonlinear partial differential equations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "machine learning of linear differential equations using gaussian processes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "inferring solutions of differential equations using noisy multi fidelity data":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "symplectic networks intrinsic structure preserving networks for identifying hamiltonian systems")
  Member "automatic differentiation in machine learning a survey":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a workload adaptive mechanism for linear queries under local differential privacy")

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.LG(Machine Learning)