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: "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data"
  Abstract: We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hidden quantities of interest such as velocity and pressure fields merely from spatio-temporal visualizations of a passive scaler (e.g., dye or smoke), transported in arbitrarily complex domains (e.g., in human arteries or brain aneurysms). Our approach towards solving the aforementioned data assimilation problem is unique as we design an algorithm that is agnostic to the geometry or the initial and boundary conditions. This makes HFM highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. Consequently, the predictions made by HFM are among those cases where a pure machine learning strategy or a mere scientific computing approach simply cannot reproduce. The proposed algorithm achieves accurate predictions of the pressure and velocity fields in both two and three dimensional flows for several benchmark problems motivated by real-world applications. Our results demonstrate that this relatively simple methodology can be used in physical and biomedical problems to extract valuable quantitative information (e.g., lift and drag forces or wall shear stresses in arteries) for which direct measurements may not be possible.

Connected through hyperedge HE-1 (induced by source paper "understanding and mitigating gradient pathologies in physics informed neural networks"):
  with members:
    - "machine learning in cardiovascular flows modeling predicting arterial blood pressure from non invasive 4d flow mri data using physics informed neural networks"
    - "variational physics informed neural networks for solving partial differential equations"
    - "the mechanics of n player differentiable games"
    - "covariant compositional networks for learning graphs"
    - "eigenvalues of the hessian in deep learning singularity and beyond"
    - "attention is all you need"
    - "cycles in adversarial regularized learning"
    - "gradnorm gradient normalization for adaptive loss balancing in deep multitask networks"

Connected through hyperedge HE-2 (induced by source paper "a derivative free method for solving elliptic partial differential equations with deep neural networks"):
  with members:
    - "hidden physics models machine learning of nonlinear partial differential equations"
    - "learning across scales a multiscale method for convolution neural networks"
    - "searching for activation functions"
    - "swish a self gated activation function"
    - "highway and residual networks learn unrolled iterative estimation"
    - "tensorflow large scale machine learning on heterogeneous distributed systems"
    - "deep residual learning for image recognition"
    - "adam a method for stochastic optimization"

Connected through hyperedge HE-3 (induced by source paper "learning to control pdes with differentiable physics"):
  with members:
    - "learning particle dynamics for manipulating rigid bodies deformable objects and fluids"
    - "flexible neural representation for physics prediction"
    - "neural ordinary differential equations"
    - "tangent automatic differentiation using source code transformation for dynamically typed array programming"
    - "neural message passing for quantum chemistry"
    - "u net convolutional networks for biomedical image segmentation"
    - "deep residual learning for image recognition"

Connected through hyperedge HE-4 (induced by source paper "physics guided machine learning for scientific discovery an application in simulating lake temperature profiles"):
  with members:
    - "heavy rain image restoration integrating physics model and conditional adversarial learning"
    - "a domain guided cnn architecture for predicting age from structural brain images"
    - "physics based generative adversarial models for image restoration and beyond"
    - "physics guided neural networks pgnn an application in lake temperature modeling"
    - "label free supervision of neural networks with physics and domain knowledge"

Connected through hyperedge HE-5 (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"
    - "deeponet learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators"
    - "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"
    - "model agnostic meta learning for fast adaptation of deep networks"

Connected through hyperedge HE-6 (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"
    - "machine learning of linear differential equations using gaussian processes"
    - "deep vs shallow networks an approximation theory perspective"

Connected through hyperedge HE-7 (induced by source paper "general solutions for nonlinear differential equations a rule based self learning approach using deep reinforcement learning"):
  with members:
    - "a cooperative game for automated learning of elasto plasticity knowledge graphs and models with ai guided experimentation"
    - "meta modeling game for deriving theory consistent microstructure based traction separation laws via deep reinforcement learning"
    - "model agnostic meta learning for fast adaptation of deep networks"
    - "learning to reinforcement learn"
    - "adam a method for stochastic optimization"
    - "playing atari with deep reinforcement learning"

Connected through hyperedge HE-8 (induced by source paper "learning in modal space solving time dependent stochastic pdes using physics informed neural networks"):
  with members:
    - "hidden physics models machine learning of nonlinear partial differential equations"
    - "physics informed deep learning part ii data driven discovery of nonlinear partial differential equations"
    - "tensorflow a system for large scale machine learning"

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.CE(Computational Engineering, Finance, and Science)