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: "nonlinear basis pursuit"
  Abstract: In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm that solves the nonlinear basis pursuit problem is convex and not greedy. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns.

Connected through hyperedge HE-1 (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"
    - "variational physics informed neural networks for solving partial differential equations"
    - "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"

Connected through hyperedge HE-2 (induced by source paper "variational physics informed neural networks for solving partial differential equations"):
  with members:
    - "nonlinear approximation and deep relu networks"
    - "nonlinear approximation via compositions"
    - "function approximation by deep networks"
    - "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks"
    - "barron spaces and the compositional function spaces for neural network models"
    - "hidden physics models machine learning of nonlinear partial differential equations"
    - "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data"
    - "machine learning of linear differential equations using gaussian processes"

Connected through hyperedge HE-3 (induced by source paper "nonlinear approximation via compositions"):
  with members:
    - "exponential convergence of the deep neural network approximation for analytic functions"
    - "optimal approximation of continuous functions by very deep relu networks"
    - "the loss surface of deep and wide neural networks"
    - "the expressive power of neural networks a view from the width"
    - "error bounds for approximations with deep relu networks"
    - "adam a method for stochastic optimization"

Connected through hyperedge HE-4 (induced by source paper "a nonlinear weighted total variation image reconstruction algorithm for electrical capacitance tomography"):
  with members:
    - "an iterative shrinkage approach to total variation image restoration"

Connected through hyperedge HE-5 (induced by source paper "nonlinear compressed sensing based on composite mappings and its pointwise linearization"):
  with members:
    - "invariance of the spark nsp order and rip order under elementary transformations of matrices"
    - "quadratic basis pursuit"
    - "measure what should be measured progress and challenges in compressive sensing"
    - "sparsity constrained nonlinear optimization optimality conditions and algorithms"
    - "one bit compressed sensing by linear programming"
    - "robust 1 bit compressive sensing via binary stable embeddings of sparse vectors"

Connected through hyperedge HE-6 (induced by source paper "sparse phase retrieval via group sparse optimization"):
  with members:
    - "quadratic basis pursuit"
    - "finding sparse solutions of systems of polynomial equations via group sparsity optimization"
    - "phase retrieval for sparse signals uniqueness conditions"
    - "gespar efficient phase retrieval of sparse signals"
    - "on conditions for uniqueness in sparse phase retrieval"
    - "recovery of sparse 1 d signals from the magnitudes of their fourier transform"
    - "phaselift exact and stable signal recovery from magnitude measurements via convex programming"
    - "phase retrieval via matrix completion"

Connected through hyperedge HE-7 (induced by source paper "finding sparse solutions of systems of polynomial equations via group sparsity optimization"):
  with members:
    - "quadratic basis pursuit"
    - "phase retrieval for sparse signals uniqueness conditions"
    - "on conditions for uniqueness in sparse phase retrieval"
    - "generalized principal component analysis gpca"
    - "sparsity constrained nonlinear optimization optimality conditions and algorithms"
    - "phaselift exact and stable signal recovery from magnitude measurements via convex programming"
    - "phase retrieval via matrix completion"

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.IT(Information Theory)