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 "model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders"):
  Abstract: Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) POD. Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov $n$-width (e.g., diffusion-dominated problems). Unfortunately, many problems of interest exhibit a slowly decaying Kolmogorov $n$-width (e.g., advection-dominated problems). To address this, we propose a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to manifold Galerkin projection, while the latter leads to manifold least-squares Petrov--Galerkin (LSPG) projection. We perform analyses that provide insight into the relationship between these proposed approaches and classical linear-subspace reduced-order models; we also derive a posteriori discrete-time error bounds for the proposed approaches. In addition, we propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. Finally, we demonstrate the ability of the method to significantly outperform even the optimal linear-subspace ROM on benchmark advection-dominated problems, thereby demonstrating the method's ability to overcome the intrinsic $n$-width limitations of linear subspaces.

Includes members:
  Member "deep dynamical modeling and control of unsteady fluid flows":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "neural network architectures for stochastic control using the nonlinear feynman kac lemma")
  Member "conservative model reduction for finite volume models":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pressio enabling projection based model reduction for large scale nonlinear dynamical systems")
  Member "learning koopman invariant subspaces for dynamic mode decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "deep learning of dynamical attractors from time series measurements")
  Member "galerkin v least squares petrov galerkin projection in nonlinear model reduction":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "machine learning error models for approximate solutions to parameterized systems of nonlinear equations")
  Member "fast and accurate deep network learning by exponential linear units elus":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "ride rewarding impact driven exploration for procedurally generated environments")
  Member "delving deep into rectifiers surpassing human level performance on imagenet classification":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "adam a method for stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "adaptive h refinement for reduced order models":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "machine learning error models for approximate solutions to parameterized systems of nonlinear equations")

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.NA(Numerical Analysis)