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: "galerkin v least squares petrov galerkin projection in nonlinear model reduction"
  Abstract: Least-squares Petrov--Galerkin (LSPG) model-reduction techniques such as the Gauss--Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge--Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.

Connected through hyperedge HE-1 (induced by source paper "machine learning error models for approximate solutions to parameterized systems of nonlinear equations"):
  with members:
    - "error modeling for surrogates of dynamical systems using machine learning"
    - "multivariate predictions of local reduced order model errors and dimensions"
    - "a new selection operator for the discrete empirical interpolation method improved a priori error bound and extensions"
    - "the romes method for statistical modeling of reduced order model error"
    - "adaptive h refinement for reduced order models"
    - "api design for machine learning software experiences from the scikit learn project"

Connected through hyperedge HE-2 (induced by source paper "statistical closure modeling for reduced order models of stationary systems by the romes method"):
  with members:
    - "machine learning error models for approximate solutions to parameterized systems of nonlinear equations"
    - "error modeling for surrogates of dynamical systems using machine learning"
    - "the romes method for statistical modeling of reduced order model error"
    - "adaptive h refinement for reduced order models"

Connected through hyperedge HE-3 (induced by source paper "online adaptive basis refinement and compression for reduced order models via vector space sieving"):
  with members:
    - "adaptive h refinement for reduced order models"

Connected through hyperedge HE-4 (induced by source paper "model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders"):
  with members:
    - "deep dynamical modeling and control of unsteady fluid flows"
    - "conservative model reduction for finite volume models"
    - "learning koopman invariant subspaces for dynamic mode decomposition"
    - "fast and accurate deep network learning by exponential linear units elus"
    - "delving deep into rectifiers surpassing human level performance on imagenet classification"
    - "adam a method for stochastic optimization"
    - "adaptive h refinement for reduced order models"

Connected through hyperedge HE-5 (induced by source paper "conservative model reduction for finite volume models"):
  with members:
    - "space time least squares petrov galerkin projection for nonlinear model reduction"
    - "preserving lagrangian structure in nonlinear model reduction with application to structural dynamics"
    - "adaptive h refinement for reduced order models"
    - "two step greedy algorithm for reduced order quadratures"

Connected through hyperedge HE-6 (induced by source paper "sns a solution based nonlinear subspace method for time dependent model order reduction"):
  with members:
    - "space time least squares petrov galerkin projection for nonlinear model reduction"
    - "a new selection operator for the discrete empirical interpolation method improved a priori error bound and extensions"

Connected through hyperedge HE-7 (induced by source paper "error modeling for surrogates of dynamical systems using machine learning"):
  with members:
    - "the romes method for statistical modeling of reduced order model error"
    - "adaptive h refinement for reduced order models"

Connected through hyperedge HE-8 (induced by source paper "space time least squares petrov galerkin projection for nonlinear model reduction"):
  with members:
    - "data driven time parallelism via forecasting"
    - "parallel tensor compression for large scale scientific data"

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.NA(Numerical Analysis)