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We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation.
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Y. Yang, H. Wang, S. B. Pope, J. H. Chen, Large-eddy simulation/probability density function modeling of a non-premixed CO/H2 temporally evolving jet flame, Proceedings of the Combustion Institute 34 (1) (2013) 1241–1249
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A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, TensorfFlow: A System for Large-Scale Machine Learning, in: Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation, USENIX Association, 2016
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J.-X. Wang, J.-L. Wu, H. Xiao, A Physics-Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data, Physical Review Fluids 2 (3) (2017) 034603
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A. Karpatne, G. Atluri, J. H. Faghmous, M. Steinbach, A. Banerjee, A. Ganguly, S. Shekhar, N. Samatova, V. Kumar, Theory-guided data science: A new paradigm for scientific discovery from data, IEEE Transactions on Knowledge and Data Engineering 29 (10) (2017) 2318–2331
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S. Yang, R. Ranjan, V. Yang, W. Sun, S. Menon, Sensitivity of predictions to chemical kinetics models in a temporally evolving turbulent non-premixed flame, Combustion and Flame 183 (2017) 224–241
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S. Vo, A. Kronenburg, O. T. Stein, M. J. Cleary, MMC-LES of a syngas mixing layer using an anisotropic mixing time scale model, Combustion and Flame 189 (2018) 311–314
2018
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W. Ji, W. Qiu, Z. Shi, S. Pan, S. Deng, Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics, The Journal of Physical Chemistry A 125 (36) (2021) 8098–8106
2021
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S. Kim, W. Ji, S. Deng, Y. Ma, C. Rackauckas, Stiff Neural Ordinary Differential Equations, Chaos: An Interdisciplinary Journal of Nonlinear Science 31 (9) (2021) 093122
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A. Nouri, H. Babaee, P. Givi, H. Chelliah, D. Livescu, Skeletal Model Reduction with Forced Optimally Time Dependent Modes, Combustion and Flame 235 (2022) 111684
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M. De Florio, E. Schiassi, R. Furfaro, Physics-informed neural networks and functional interpolation for stiff chemical kinetics, Chaos: An Interdisciplinary Journal of Nonlinear Science 32 (6) (2022) 063107
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M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational physics 378 (2019) 686–707
2019
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K. Aditya, A. Gruber, C. Xu, T. Lu, A. Krisman, M. R. Bothien, J. H. Chen, Direct numerical simulation of flame stabilization assisted by autoignition in a reheat gas turbine combustor, Proceedings of the Combustion Institute 37 (2) (2019) 2635–2642
2019
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A. D. Jagtap, K. Kawaguchi, G. E. Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics 404 (2020) 109136
2020
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A. D. Jagtap, K. Kawaguchi, G. Em Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A 476 (2239) (2020) 20200334
2020
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L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Nature Machine Intelligence 3 (3) (2021) 218–229
2021
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T. S. Brown, H. Antil, R. Löhner, F. Togashi, D. Verma, Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows, in: International Conference on High Performance Computing, Springer, 2021, pp. 23–39
2021
Cited alongside, same era.
R. T. Chen, Y. Rubanova, J. Bettencourt, D. K. Duvenaud, Neural Ordinary Differential Equations, Advances in Neural Information Processing Systems 31
Cited in the paper.
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L. Lu, X. Meng, S. Cai, Z. Mao, S. Goswami, Z. Zhang, G. E. Karniadakis, A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data, Computer Methods in Applied Mechanics and Engineering 393 (2022) 114778
2022
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V. Oommen, K. Shukla, S. Goswami, R. Dingreville, G. E. Karniadakis, Learning two-phase microstructure evolution using neural operators and autoencoder architectures, npj Computational Materials 8 (1) (2022) 190
2022
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A. D. Jagtap, Y. Shin, K. Kawaguchi, G. E. Karniadakis, Deep kronecker neural networks: A general framework for neural networks with adaptive activation functions, Neurocomputing 468 (2022) 165–180
2022
Later among the works it cites.
2022
Later among the works it cites.
S. Goswami, K. Kontolati, M. D. Shields, G. E. Karniadakis, Deep transfer operator learning for partial differential equations under conditional shift, Nature Machine Intelligence (2022) 1–10
2022
Later among the works it cites.
K. Kontolati, S. Goswami, M. D. Shields, G. E. Karniadakis, On the influence of over-parameterization in manifold based surrogates and deep neural operators, Journal of Computational Physics (2023) 112008
2023
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