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Nonlinear Finite Elements for Continua and Structures
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A. Kehlet, B. Logg, A. ...and Wells, G. N.
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Deep Neural Networks: Algorithmic Structure, Data
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Appl. 2023, 28, 91. DOI: 10.3390/mca28040091.
[26] Kovachki, N. Li, Z. Liu, B. Azizzadenesheli, K.
Bhattacharya, K. Stuart, A. Anandkumar, A. (2023).
Neural Operator: Learning Maps Between Function
Spaces With Applications to PDEs. Journal of Machine
Learning Research. 24(89). 1–97.
[27] Lu, L. Jin, P. Pang, G. et al. (2021). Learning non-
linear operators via DeepONet based on the universal
approximation theorem of operators. Nat Mach Intell
3, 218–229.
[28] Li, Z. Kovachki, N. Azizzadenesheli, K. Liu,
B. Bhattacharya, K. Stuart, A. Anandkumar, A.
(2021). Fourier neural operator for parametric partial
differential equations. ICLR 2021. DOI: 10.48550
/arXiv.2010.08895.
[29] Kovachki, N. B. Lanthaler, S. Stuart, A. M.
(2024). Operator Learning: Algorithms and Analysis.
DOI: 10.48550/arXiv.2402.15715.
[30] Lu, L. Meng, X Cai, S. Mao, Z. Goswami, S.
Zhang, Z. Karniadakis, G.E. (2022). A comprehensive
Health Monitoring. 12. 1317–1327. DOI: 10.1007
/s13349-022-00560-w.
[7] Barrias, A. Casas, J. R. Villalba, S. (2016). A review
of distributed optical fiber sensors for civil engineer-
ing applications. Sensors. 16(5). 748. DOI: 10.3390
/s16050748.
[8] Monsberger, C.M. (2022). Distributed fiber optic
shape sensing in structural and geotechnical engineering:
Principles and applications. Shaker Verlag. Düren 2022.
DOI: 10.2370/9783844088250.
[9] Woschitz, W. Winkler, M. Račanský, V. (2023).
Distributed fibre optic sensing during different anchor
pullout tests. Proc. SPIE 12643. European Workshop
on Optical Fibre Sensors (EWOFS 2023). 126432L.
DOI: 10.1117/12.2678521.
[10] Račanský, V. Fabris, C. Schweiger, H. Woschitz,
H. (2022). Use of Distributed Fibre Optic Sensing on
Ground Anchors: Case Studies. In Proceedings of 11th
International Symposium on Field Monitoring in
Geomechanics.
[11] Nikles, M. Thevenaz, L. Robert, P. A. (1996). Simple
distributed fiber sensor based on Brillouin gain spectrum
analysis. Opt. Lett. 21(10). 758.
[12] Taheri, H. Xia, Z.C. (2021) SLAM Definition
and Evolution. Engineering Applications of
Artificial Intelligence. 97. DOI: 10.1016
/j.engappai.2020.104032.
[13] McNeel, R. (2023). Rhinoceros 3D, Version 8. Robert
McNeel &Associates. Underground Laboratory.
[14] Paffenholz, J.-A. Wujanz, D. (2019). Spatio-temporal
monitoring of a bridge based on 3D point clouds -A
comparison among several deformation measurement
approaches. Proceedings of the 4th Joint International
Symposium on Deformation Monitoring (JISDM),
Athens, Greece, 2019.
[15] Singh, S. Banerjee, B. P. Raval, S. (2023). A Review
of Laser Scanning for Geological and Geotechnical
Applications in Underground Mining. International
Journal of Mining Science and Technology. Volume
33. 2. 133–54. DOI: 10.1016/j.ijmst.2022.09.022.
[16] Ostendorf,J. Henjes-Kunst, F. Seifert, T Gutzmer,
J. (2018). Age and genesis of polymetallic vein-type
mineralization in the Freiberg ore district, Erzgebirge
(Germany): Constraints from radiogenic isotopes.
Mineralium Deposita. 54. 263–280.
[17] Harmening, C. (2020). Spatio-Temporal Deformation
Analysis Using Enhanced B-Spline Models of Laser
Scanning Point Clouds. TU Wien. DOI: 10.34726
/hss.2020.57320.
[18] Danesc, A. Voinea, S. (2019). COMSOL model for
simulating the mine natural ventilation to power a wind
turbine. 14th ICVL. 452–458.
[19] Lundquist, T. Nordström, J. Malan, A. (2021). Stable
Dynamical Adaptive Mesh Refinement. J Sci Comput
86. 43. DOI: 10.1007/s10915-021-01414-1.
[20] Zienkiewicz, O. C. Taylor, R. L. Zhu, J. Z. (2013).
The Finite Element Method: Its Basis and Fundamentals.
(7th ed.). Butterworth-Heinemann. DOI: 10.1016
/C2009-0-24909-9.
[21] Boese, C. M. Kwiatek, G. Fischer, T. Plenkers, K.
Starke, J. Blümle, F. Janssen, C. Dresen, G. (2013).
Seismic monitoring of the STIMTEC hydraulic stimula-
tion experiment in anisotropic metamorphic gneiss. Solid
Earth. 13. 323–346. DOI: 10.5194/se‑13-323-2022.
[22] Belytschko, T. Liu, W. K. Moran, B. (2013).
Nonlinear Finite Elements for Continua and Structures
(2nd ed.). DOI: 10.5860/choice.38-3926.
[23] Wang, H. F. (2000). Theory of Linear Poroelasticity
with Applications to Geomechanics and Hydrogeology.
Princeton University Press.
[24] Alnæs, M. S. Blechta, J. Hake, J. Johansson,
A. Kehlet, B. Logg, A. ...and Wells, G. N.
(2015). The FEniCS Project Version 1.5. Archive
of Numerical Software. 3(100). DOI: 10.11588
/ans.2015.100.20553.
[25] Eivazi, H. Tröger, J.-A. Wittek, S. Hartmann,
S. Rausch, A. (2023). FE2 Computations with
Deep Neural Networks: Algorithmic Structure, Data
Generation and Implementation. Math. Comput.
Appl. 2023, 28, 91. DOI: 10.3390/mca28040091.
[26] Kovachki, N. Li, Z. Liu, B. Azizzadenesheli, K.
Bhattacharya, K. Stuart, A. Anandkumar, A. (2023).
Neural Operator: Learning Maps Between Function
Spaces With Applications to PDEs. Journal of Machine
Learning Research. 24(89). 1–97.
[27] Lu, L. Jin, P. Pang, G. et al. (2021). Learning non-
linear operators via DeepONet based on the universal
approximation theorem of operators. Nat Mach Intell
3, 218–229.
[28] Li, Z. Kovachki, N. Azizzadenesheli, K. Liu,
B. Bhattacharya, K. Stuart, A. Anandkumar, A.
(2021). Fourier neural operator for parametric partial
differential equations. ICLR 2021. DOI: 10.48550
/arXiv.2010.08895.
[29] Kovachki, N. B. Lanthaler, S. Stuart, A. M.
(2024). Operator Learning: Algorithms and Analysis.
DOI: 10.48550/arXiv.2402.15715.
[30] Lu, L. Meng, X Cai, S. Mao, Z. Goswami, S.
Zhang, Z. Karniadakis, G.E. (2022). A comprehensive