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 "physics informed neural networks for multiphysics data assimilation with application to subsurface transport"):
  Abstract: Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual DNNs to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head and concentration) of a physical system, and jointly train these DNNs by minimizing the loss function that consists of the governing equations residuals in addition to the error with respect to measurement data. We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for joint inversion of the conductivity, hydraulic head, and concentration fields in a steady-state advection--dispersion problem. We study the accuracy of the physics-informed DNN approach with respect to data size, number of variables (conductivity and head versus conductivity, head, and concentration), DNNs size, and DNN initialization during training. We demonstrate that the physics-informed DNNs are significantly more accurate than standard data-driven DNNs when the training set consists of sparse data. We also show that the accuracy of parameter estimation increases as additional variables are inverted jointly.

Includes members:
  Member "deepxde a deep learning library for solving differential equations":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition")
  Member "physics informed regularization of deep neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "an axiomatic approach to regularizing neural ranking models")
  Member "automatic differentiation in machine learning a survey":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a workload adaptive mechanism for linear queries under local differential privacy")
  Member "adam a method for stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")

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.LG(Machine Learning)