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: "varnet variational neural networks for the solution of partial differential equations"
  Abstract: In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies on the variational (integral) form of PDEs as apposed to their differential form which is commonly used in the literature. Our loss function is discretization-free, highly parallelizable, and more effective in capturing the solution of PDEs since it employs lower-order derivatives and trains over measure non-zero regions of space-time. Given this loss function, we also propose an approach to optimally select the space-time samples, used to train the NN, that is based on the feedback provided from the PDE residual. The models obtained using VarNet are smooth and do not require interpolation. They are also easily differentiable and can directly be used for control and optimization of PDEs. Finally, VarNet can straight-forwardly incorporate parametric PDE models making it a natural tool for model order reduction (MOR) of PDEs. We demonstrate the performance of our method through extensive numerical experiments for the advection-diffusion PDE as an important case-study.

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"
    - "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"
    - "robust training and initialization of deep neural networks an adaptive basis viewpoint"

Connected through hyperedge HE-2 (induced by source paper "deep learning for robotic mass transport cloaking"):
  with members:
    - "model based active source identification in complex environments"
    - "safe learning of regions of attraction for uncertain nonlinear systems with gaussian processes"

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)