Fetching the paper…
Reading the bibliography…
Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is required.
Dota 2 with large scale deep reinforcement learning
Berner, C., Brockman, G., Chan, B., Cheung, V., Dębiak, P., Dennison, C., Farhi, D., Fischer, Q., Hashme, S., Hesse, C., et al · 1912
Earlier work this paper cites.
Effective and practical h–p-version adaptive analysis procedures for the finite element method
Zienkiewicz, O., Zhu, J., and Gong, N. (1989) · 1989
Earlier work this paper cites.
Determining an approximate finite element mesh density using neural network techniques
Dyck, D., Lowther, D., and McFee, S. (1992) · 1992
Earlier work this paper cites.
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
Zienkiewicz, O. C. and Zhu, J. Z. (1992) · 1992
Earlier work this paper cites.
Automatic finite-element mesh generation using artificial neural networks-Part I: Prediction of mesh density
Chedid, R. and Najjar, N. (1996) · 1996
Earlier work this paper cites.
Flux-corrected transport
Boris, J. P. and Book, D. L. (1997) · 1997
Earlier work this paper cites.
Supervised neural networks for the classification of structures
Sperduti, A. and Starita, A. (1997) · 1997
Earlier work this paper cites.
Policy invariance under reward transformations: Theory and application to reward shaping
Ng, A. Y., Harada, D., and Russell, S. J. (1999) · 1999
Earlier work this paper cites.
Policy gradient methods for reinforcement learning with function approximation
Sutton, R. S., McAllester, D. A., Singh, S. P., and Mansour, Y. (2000) · 2000
Earlier work this paper cites.
An optimal control approach to a posteriori error estimation in finite element methods
Becker, R. and Rannacher, R. (2001) · 2001
Earlier work this paper cites.
Data-driven finite elements methods: Machine learning acceleration of goal-oriented computations
Brevis, I., Muga, I., and van der Zee, K. G. (2020) · 2003
Earlier work this paper cites.
Finite element methods for Maxwell’s equations
Monk, P. et al · 2003
Earlier work this paper cites.
A new model for learning in graph domains
Gori, M., Monfardini, G., and Scarselli, F. (2005) · 2005
Earlier work this paper cites.
The mathematical theory of finite element methods
Brenner, S. and Scott, R. (2007) · 2007
Earlier work this paper cites.
The graph neural network model
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., and Monfardini, G. (2008) · 2008
Earlier work this paper cites.
Adaptive moving mesh methods
Huang, W. and Russell, R. D. (2010) · 2010
Earlier work this paper cites.
The finite element method in heat transfer and fluid dynamics
Reddy, J. N. and Gartling, D. K. (2010) · 2010
Earlier work this paper cites.
Adaptive finite element methods for differential equations
Bangerth, W. and Rannacher, R. (2013) · 2013
Cited alongside, same era.
Graded meshes in optimal control for elliptic partial differential equations: an overview
Apel, T., Pfefferer, J., and Rösch, A. (2014) · 2014
Cited alongside, same era.
Markov decision processes: discrete stochastic dynamic programming
Puterman, M. L. (2014) · 2014
Cited alongside, same era.
Model reduction by adaptive discretization in optimal control
Rannacher, R. (2014) · 2014
Cited alongside, same era.
Human-level control through deep reinforcement learning
Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidjeland, A. K., Ostrovski, G., et al · 2015
Cited alongside, same era.
Interaction networks for learning about objects, relations and physics
Battaglia, P., Pascanu, R., Lai, M., Rezende, D. J., et al · 2016
Nonconforming mesh refinement for high-order finite elements
Červený, J., Dobrev, V., and Kolev, T. (2019) · 2019
Later among the works it cites.
The Target-Matrix Optimization Paradigm for high-order meshes
Dobrev, V., Knupp, P., Kolev, T., Mittal, K., and Tomov, V. (2019) · 2019
Later among the works it cites.
Behaviour suite for reinforcement learning
Osband, I., Doron, Y., Hessel, M., Aslanides, J., Sezener, E., Saraiva, A., McKinney, K., Lattimore, T., Szepesvari, C., Singh, S., et al · 2019
Later among the works it cites.
Grandmaster level in StarCraft II using multi-agent reinforcement learning
Vinyals, O., Babuschkin, I., Czarnecki, W. M., Mathieu, M., Dudzik, A., Chung, J., Choi, D. H., Powell, R., Ewalds, T., Georgiev, P., et al · 2019
Later among the works it cites.
Combining differentiable PDE solvers and graph neural networks for fluid flow prediction
Belbute-Peres, F. d. A., Economon, T., and Kolter, Z. (2020) · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Brockman, G., Cheung, V., Pettersson, L., Schneider, J., Schulman, J., Tang, J., and Zaremba, W. (2016) · 2016
Cited alongside, same era.
Hypernetworks
Ha, D., Dai, A., and Le, Q. V. (2017) · 2017
Cited alongside, same era.
Adjoint error estimators and adaptive mesh refinement in nek5000
Offermans, N., Peplinski, A., Marin, O., and Schlatter, P. (2017) · 2017
Cited alongside, same era.
Proximal policy optimization algorithms
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. (2017) · 2017
Cited alongside, same era.
# exploration: A study of count-based exploration for deep reinforcement learning
Tang, H., Houthooft, R., Foote, D., Stooke, A., Chen, X., Duan, Y., Schulman, J., De Turck, F., and Abbeel, P. (2017) · 2017
Cited alongside, same era.
Relational inductive biases, deep learning, and graph networks
Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., et al · 2018
Cited alongside, same era.
Output-based error estimation and mesh adaptation using convolutional neural networks: Application to a scalar advection-diffusion problem
Chen, G. and Fidkowski, K. (2020) · 2020
Later among the works it cites.
Analysis and performance evaluation of adjoint-guided adaptive mesh refinement for linear hyperbolic pdes using clawpack
Davis, B. N. and LeVeque, R. J. (2020) · 2020
Later among the works it cites.
Learning algebraic multigrid using graph neural networks
Luz, I., Galun, M., Maron, H., Basri, R., and Yavneh, I. (2020) · 2020
Later among the works it cites.
MFEM: Modular finite element methods [Software]
MFEM (2020) · 2020
Later among the works it cites.
Learning mesh-based simulation with graph networks
Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., and Battaglia, P. (2020) · 2020
Later among the works it cites.
Graphopt: Learning optimization models of graph formation
Trivedi, R., Yang, J., and Zha, H. (2020) · 2020
Later among the works it cites.
Meshingnet: a new mesh generation method based on deep learning
Zhang, Z., Wang, Y., Jimack, P. K., and Wang, H. (2020) · 2020
Later among the works it cites.
MFEM: A modular finite element methods library
Anderson, R., Andrej, J., Barker, A., Bramwell, J., Camier, J.-S., Cerveny, J., Dobrev, V., Dudouit, Y., Fisher, A., Kolev, T., Pazner, W., Stowell, M., Tomov, V., Akkerman, I., Dahm, J., Medina, D., and Zampini, S. (2021) · 2021
Closest in time.
Recurrent neural networks as optimal mesh refinement strategies
Bohn, J. and Feischl, M. (2021) · 2021
Closest in time.
Deep reinforcement learning for adaptive mesh refinement
Foucart, C., Charous, A., and Lermusiaux, P. F. (2022) · 2022
Closest in time.
Reinforcement learning for automatic quadrilateral mesh generation: A soft actor–critic approach
Pan, J., Huang, J., Cheng, G., and Zeng, Y. (2023) · 2023
Closest in time.