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 "deepxde a deep learning library for solving differential equations"):
  Abstract: Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiation. The PINN algorithm is simple, and it can be applied to different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, PINNs solve inverse problems as easily as forward problems. We propose a new residual-based adaptive refinement (RAR) method to improve the training efficiency of PINNs. For pedagogical reasons, we compare the PINN algorithm to a standard finite element method. We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an education tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering. DeepXDE supports complex-geometry domains based on the technique of constructive solid geometry, and enables the user code to be compact, resembling closely the mathematical formulation. We introduce the usage of DeepXDE and its customizability, and we also demonstrate the capability of PINNs and the user-friendliness of DeepXDE for five different examples. More broadly, DeepXDE contributes to the more rapid development of the emerging Scientific Machine Learning field.

Includes members:
  Member "frequency principle fourier analysis sheds light on deep neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "frequency bias in neural networks for input of non uniform density")
  Member "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "deeponet learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "symplectic networks intrinsic structure preserving networks for identifying hamiltonian systems")
  Member "a review of automatic differentiation and its efficient implementation":
    also connected through other hyperedges:
      (none)
  Member "learning in modal space solving time dependent stochastic pdes using physics informed neural networks":
    also connected through other hyperedges:
      (none)
  Member "physics informed neural networks for multiphysics data assimilation with application to subsurface transport":
    also connected through other hyperedges:
      (none)
  Member "a deep neural network surrogate for high dimensional random partial differential equations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "pydens a python framework for solving differential equations with neural networks")
  Member "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "understanding and mitigating gradient pathologies in physics informed neural networks")

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)