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 "understanding and mitigating gradient pathologies in physics informed neural networks"):
  Abstract: The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at \url{this https URL}.

Includes members:
  Member "machine learning in cardiovascular flows modeling predicting arterial blood pressure from non invasive 4d flow mri data using physics informed neural networks":
    also connected through other hyperedges:
      (none)
  Member "variational physics informed neural networks for solving partial 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 "the mechanics of n player differentiable games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners")
  Member "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a derivative free method for solving elliptic partial differential equations with deep neural networks")
  Member "covariant compositional networks for learning graphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a survey on the expressive power of graph neural networks")
  Member "eigenvalues of the hessian in deep learning singularity and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "rethinking parameter counting in deep models effective dimensionality revisited")
  Member "attention is all you need":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "cycles in adversarial regularized learning":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "from poincar e recurrence to convergence in imperfect information games finding equilibrium via regularization")

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)