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: "deeponet learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators"
  Abstract: While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear continuous operator \cite{chen1995universal}. This universal approximation theorem is suggestive of the potential application of neural networks in learning nonlinear operators from data. However, the theorem guarantees only a small approximation error for a sufficient large network, and does not consider the important optimization and generalization errors. To realize this theorem in practice, we propose deep operator networks (DeepONets) to learn operators accurately and efficiently from a relatively small dataset. A DeepONet consists of two sub-networks, one for encoding the input function at a fixed number of sensors $x_i, i=1,\dots,m$ (branch net), and another for encoding the locations for the output functions (trunk net). We perform systematic simulations for identifying two types of operators, i.e., dynamic systems and partial differential equations, and demonstrate that DeepONet significantly reduces the generalization error compared to the fully-connected networks. We also derive theoretically the dependence of the approximation error in terms of the number of sensors (where the input function is defined) as well as the input function type, and we verify the theorem with computational results. More importantly, we observe high-order error convergence in our computational tests, namely polynomial rates (from half order to fourth order) and even exponential convergence with respect to the training dataset size.

Connected through hyperedge HE-1 (induced by source paper "symplectic networks intrinsic structure preserving networks for identifying hamiltonian systems"):
  with members:
    - "neural net induced gaussian process regression for function approximation and pde solution"
    - "hidden physics models machine learning of nonlinear partial differential equations"
    - "machine learning of space fractional differential equations"
    - "inferring solutions of differential equations using noisy multi fidelity data"
    - "on the difficulty of training recurrent neural networks"

Connected through hyperedge HE-2 (induced by source paper "deepxde a deep learning library for solving differential equations"):
  with members:
    - "frequency principle fourier analysis sheds light on deep neural networks"
    - "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks"
    - "a review of automatic differentiation and its efficient implementation"
    - "learning in modal space solving time dependent stochastic pdes using physics informed neural networks"
    - "physics informed neural networks for multiphysics data assimilation with application to subsurface transport"
    - "a deep neural network surrogate for high dimensional random partial differential equations"
    - "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data"
    - "model agnostic meta learning for fast adaptation of deep networks"

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.LG(Machine Learning)