Details
Title
Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysisJournal title
Bulletin of the Polish Academy of Sciences Technical SciencesYearbook
2021Volume
69Issue
6Affiliation
Borzyszkowski, Bartłomiej : Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland ; Damaszke, Karol : Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland ; Romankiewicz, Jakub : Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland ; Świniarski, Marcin : Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland ; Moszyński, Marek : Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, PolandAuthors
Keywords
physics-guided neural networks ; spatial analysis ; differential equations ; machine learningDivisions of PAS
Nauki TechniczneCoverage
e139391Bibliography
- R. Vinuesa et al., “The role of artificial intelligence in achieving the Sustainable Development Goals,” Nat. Commun., vol. 11, no. 1, pp. 1‒10, 2020.
- M. Grochowski, A. Kwasigroch, and A. Mikołajczyk, “Selected technical issues of deep neural networks for image classification purposes,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 67, no. 2, pp. 363–376, 2019.
- T. Poggio and Q. Liao, “Theory II: Deep learning and optimization,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 66, no. 6, pp. 775–787, 2018.
- A. Lüdeling, M. Walter, E. Kroymann, and P. Adolphs, “Multilevel error annotation in learner corpora,” Proc. Corpus Linguistics Conf., vol. 1, pp. 14–17, 2005.
- A. Mikołajczyk and M. Grochowski, “Data augmentation for improving deep learning in image classification problem,” Proc. Int. Interdiscipl. PhD Workshop (IIPhDW), 2018, pp. 117–122.
- A.W. Moore and M.S. Lee, “Efficient algorithms for minimizing cross validation error,” Proc. 11th Int’l Conf. Machine Learning, 1994, pp. 190–198.
- J.M. Benitez, J.L. Castro, and I. Requena, “Are artificial neural networks black boxes?,” IEEE Trans. Neural Networks, vol. 8, pp. 1156– 1164, 1997.
- T. Hagendorff, “The ethics of AI ethics: An evaluation of guidelines,” Minds Mach., vol. 30, pp. 99–120, 2020.
- T. Miller, P. Howe, and L. Sonenberg, “Explainable AI: Beware of inmates running the asylum,” Proc. IJCAI Workshop Explainable AI (XAI), 2017, pp. 36–42.
- A. Rai, “Explainable AI: from black box to glass box,” Journal of the Academy of Marketing Science, vol. 48, pp. 137–141, 2020.
- G. Shortley and G. Weller, “Numerical solution of Laplace’s equation,” J. Appl. Phys., vol. 9, no. 1, pp. 334–336, 1938.
- R.C. Mittal and P. Singhal, “Numerical solution of Burger’s equation,” Commun. Numer. Methods Eng., vol. 9, no. 5, pp. 397–406, 1993.
- R. French, “Subcognition and the limits of the Turing test,” Mind, vol. 99, no. 393, pp. 53–65, 1990.
- J. McCarthy, “What is artificial intelligence?,” 1998.
- I. Rojek, M. Macko, D. Mikołajewski, M. Saga, and T. Burczyński, “Modern methods in the field of machine modelling and simulation as a research and practical issue related to industry 4.0,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 69, no. 2, p. e136717, 2021.
- A. Karpatne, W. Watkins, J. Read, and V. Kumar, “Physicsguided neural networks (PGNN): An application in lake temperature modeling,” 2017, [Online], Available: http://arxiv.orgabs/1710.11431.
- J. Willard et al., “Integrating Physics-Based Modeling with Machine Learning: A Survey,” 2020, [Online], Available: http://arxiv.org/abs/2003.04919.
- X. Jia et al., “Physics guided RNNs for modeling dynamical systems: A case study in simulating lake temperature profiles,” Proc. SIAM Int. Conf. Data Mining, pp. 558–566, 2019.
- A. Daw et al., “Physics-Guided Architecture (PGA) of neural networks for quantifying uncertainty in lake temperature modeling,” Proc. SIAM Int. Conf. Data Mining, pp. 532–540, 2020.
- Y. Yang and P. Perdikaris, “Physics-informed deep generative models,” 2018, [Online], Available: http://arxiv.org/abs/1812. 03511.
- R. Singh, V. Shah, B. Pokuri, and S. Sarkar, “Physics-aware deep generative models for creating synthetic microstructures,” 2018, [Online], Available: http://arxiv.org/abs/1811.09669.
- L. Wang, Q. Zhou, and S. Jin, “Physics-guided deep learning for power system state estimation,” J. Mod. Power Syst. Clean Energy, vol. 8, no. 4, pp. 607–615, 2020.
- N. Muralidhar et al., “Physics-guided design and learning of neural networks for predicting drag force on particle suspensions in moving fluids,” 2019, [Online], Available: http://arxiv.org/abs/1911.04240.
- J. Park and J. Park, “Physics-induced graph neural network: An application to wind-farm power estimation,” Energy, vol. 187, p. 115883, 2019.
- R. Wang, K. Kashinath, M. Mustafa, A. Albert, and R. Yu, “Towards physics-informed deep learning for turbulent flow prediction,” Proc. 26th SIGKDD Int. Conf. Knowledge Discovery and Data Mining, 2020, pp. 1457–1466.
- T. Yang et al., “Evaluation and machine learning improvement of global hydrological model-based flood simulations,” Environ. Res. Lett., vol. 14, no. 11, p. 114027, 2019.
- Y. Zhang et al., “Pgnn: Physics-guided neural network for fourier ptychographic microscopy,” 2019, [Online], Available: http://arxiv.org/ abs/1909.08869.
- M.G. Poirot et al., “Physics-informed deep learning for dualenergy computed tomography image processing,” Sci. Rep., vol. 9, no. 1, 2019.
- F. Sahli Costabal, Y. Yang, P. Perdikaris, D. E. Hurtado, E. Kuhl, “Physics-informed neural networks for cardiac activation mapping,” Front. Phys., vol. 8, p. 42, 2020.
- M. Raissi, P. Perdikaris, and G.E. Karniadakis, “Physics informed deep learning (part I): Data-driven solutions of nOnlinear partial dif- ferential equations,” 2017, [Online], Available: http://arxiv.org/abs/1711.10561.
- M. Raissi, P. Perdikaris, and G.E. Karniadakis, “Physics informed deep learning (part II): Data-driven solutions of nOnlinear partial differential equations,” 2017, [Online], Available: http://arxiv.org/abs/1711.10566.
- Z. Fang and J. Zhan, “A physics-informed neural network framework for PDEs on 3D surfaces: Time independent problems,” IEEE Access, vol. 8, pp. 26328–26335, 2019.
- B. Paprocki, A. Pregowska, and J. Szczepanski, “Optimizing information processing in brain-inspired neural networks,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 68, no. 2, pp. 225–233, 2020.
- M. Pfeiffer and T. Pfeil, “Deep learning with spiking neurons: opportunities and challenges,” Front. Neurosci., vol. 12, pp. 774, 2018.
- Z. Bing et al., “A survey of robotics control based on learninginspired spiking neural networks,” Front. Neurorob., vol. 12, pp. 35, 2018.
- B. Borzyszkowski, “Neuromorphic Computing in High Energy Physics,” 2020, doi: 10.5281/zenodo.3755310.
- J. George, C. Soci, M. Miscuglio, and V. Sorger, “Symmetry perception with spiking neural networks,” Sci. Rep., vol. 11, no. 1. pp. 1–14, 2021.
- K. Janocha and W.M. Czarnecki, “On loss functions for deep neural networks in classification,” 2017, [Online], Available: http://arxiv. org/abs/1702.05659.
- L. Bottou, “Stochastic gradient descent tricks,” in Neural networks: Tricks of the trade, Berlin, Heidelberg: Springer 2012, pp. 421–436.
- T. Dockhorn, “A discussion on solving partial differential equations using neural networks,” 2019, [Online], Available: https://arxiv.org/abs/1904.07200.
- A. Blumer, A. Ehrenfeucht, D. Haussler, and M.K. Warmuth, “Occam’s razor,” Inf. Process. Lett., vol. 24, no. 6, pp. 377–380, 1987.
- A. Marreiros, J. Daunizeau, S. Kiebel, and K. Friston, “Population dynamics: variance and the sigmoid activation function,” Neuroimage, vol. 42, no. 1, pp. 147–157, 2008.
- S.K. Kumar, “On weight initialization in deep neural networks.” 2017, [Online]. Available: http://arxiv.org/abs/1704.08863.
- N. Nawi, M. Ransing, and R. Ransing, “An improved learning algorithm based on the Broyden-fletcher-goldfarb-shanno (BFGS) method for back propagation neural networks,” Proc. 6th Int. Conf. Intell. Syst. Design Appl., 2006, vol. 1, pp. 152–157.
- P. Constantin and C. Foias, “Navier-stokes equations,” Chicago: University of Chicago Press, 1988.
- G.A. Anastassiou, “Multivariate hyperbolic tangent neural network approximation,” Comput. Math. Appl., vol. 61, no. 4, pp. 809–821, 2011.
- B. Hanin and D. Rolnick, “How to start training: The effect of initialization and architecture,” Proc. Adv. Neural Inf. Process. Syst., 2018, pp. 571–581.
- R. Ghanem and P. Spanos, “Stochastic finite elements: a spectral approach,” New York: Springer, 1991.