Machine learning for modelling unstructured grid data in computational physics: A review.

Matthew D. Piggott M. D. Piggott

Sibo Cheng Marc Bocquet Weiping Ding 0001 Tobias Sebastian Finn Rui Fu Jinlong Fu Yike Guo Eleda Johnson Siyi Li Che Liu 0002 Eric Newton Moro Jie Pan 0007 Matthew D. Piggott César Quilodrán Casas Prakhar Sharma Kun Wang Dunhui Xiao Xiao Xue 0002 Yong Zeng Mingrui Zhang Hao Zhou 0020 Kewei Zhu Rossella Arcucci Machine learning for modelling unstructured grid data in computational physics: A review. 103255 2025 123 Inf. Fusion https://doi.org/10.1016/j.inffus.2025.103255 db/journals/inffus/inffus123.html#ChengBDFFFGJLLMPPCSWXXZ25 streams/journals/inffus

Kun Wang Gabriele Bertoli Sibo Cheng Kai Schröter Enrica Caporali Matthew D. Piggott Yanghua Wang Rossella Arcucci AI-Empowered Latent Four-dimensional Variational Data Assimilation for River Discharge Forecasting. 24676-24689 2025 18 IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens. https://doi.org/10.1109/JSTARS.2025.3611136 db/journals/staeors/staeors18.html#WangBCSCPWA25 streams/journals/staeors

Kun Wang Gabriele Bertoli Kai Schröter Enrica Caporali Matthew D. Piggott Yanghua Wang Rossella Arcucci Latent Three-Dimensional Variational Data Assimilation with Convolutional Autoencoder and LSTM for Flood Forecasting. 43-56 2025 ICCS (Workshops 4) https://doi.org/10.1007/978-3-031-97567-7_4 conf/iccS/2025-w4 db/conf/iccS/iccS2025-w4.html#WangBSCPWA25 streams/conf/iccS

Sibo Cheng Marc Bocquet Weiping Ding 0001 Tobias Sebastian Finn Rui Fu Jinlong Fu Yike Guo Eleda Johnson Siyi Li Che Liu 0002 Eric Newton Moro Jie Pan 0007 Matthew D. Piggott César Quilodrán Casas Prakhar Sharma Kun Wang Dunhui Xiao Xiao Xue 0002 Yong Zeng Mingrui Zhang Hao Zhou 0020 Kewei Zhu Rossella Arcucci Machine learning for modelling unstructured grid data in computational physics: a review. 2025 February abs/2502.09346 CoRR https://doi.org/10.48550/arXiv.2502.09346 db/journals/corr/corr2502.html#abs-2502-09346 streams/journals/corr

Kun Wang Matthew D. Piggott Yanghua Wang Rossella Arcucci Neural Network as Transformation Function in Data Assimilation. 322-329 2024 ICCS (5) https://doi.org/10.1007/978-3-031-63775-9_23 conf/iccS/2024-5 db/conf/iccS/iccS2024-5.html#WangPWA24 Mingrui Zhang Chunyang Wang Stephan C. Kramer Joseph G. Wallwork Siyi Li Jiancheng Liu Xiang Chen Matthew D. Piggott Towards Universal Mesh Movement Networks. 2024 NeurIPS http://papers.nips.cc/paper_files/paper/2024/hash/1b0da24d136f46bfaee78e8da907127e-Abstract-Conference.html conf/nips/2024 db/conf/nips/neurips2024.html#ZhangWKWLLCP24

Mingrui Zhang Chunyang Wang Stephan Kramer Joseph G. Wallwork Siyi Li Jiancheng Liu Xiang Chen Matthew D. Piggott Towards Universal Mesh Movement Networks. 2024 abs/2407.00382 CoRR https://doi.org/10.48550/arXiv.2407.00382 db/journals/corr/corr2407.html#abs-2407-00382 streams/journals/corr

Mariana C. A. Clare Simon C. Warder Robert Neal B. Bhaskaran Matthew D. Piggott An unsupervised learning approach for predicting wind farm power and downstream wakes using weather patterns. 2023 abs/2302.05886 CoRR https://doi.org/10.48550/arXiv.2302.05886 db/journals/corr/corr2302.html#abs-2302-05886

Sokratis Anagnostopoulos Jens Bauer Mariana C. A. Clare Matthew D. Piggott Accelerated wind farm yaw and layout optimisation with multi-fidelity deep transfer learning wake models. 2023 abs/2303.16274 CoRR https://doi.org/10.48550/arXiv.2303.16274 db/journals/corr/corr2303.html#abs-2303-16274

Siyi Li Arnaud Robert A. Aldo Faisal Matthew D. Piggott Learning to Optimise Wind Farms with Graph Transformers. 2023 abs/2311.12750 CoRR https://doi.org/10.48550/arXiv.2311.12750 db/journals/corr/corr2311.html#abs-2311-12750

Joseph G. Wallwork Nicolas Barral David A. Ham Matthew D. Piggott Goal-Oriented Error Estimation and Mesh Adaptation for Tracer Transport Modelling. 103187 2022 145 Comput. Aided Des. https://doi.org/10.1016/j.cad.2021.103187 db/journals/cad/cad145.html#WallworkBHP22

Mariana C. A. Clare Stephan C. Kramer Colin J. Cotter Matthew D. Piggott Calibration, inversion and sensitivity analysis for hydro-morphodynamic models through the application of adjoint methods. 105104 2022 163 Comput. Geosci. https://doi.org/10.1016/j.cageo.2022.105104 db/journals/gandc/gandc163.html#ClareKCP22

Alexander Kier Christensen Matthew D. Piggott Erik van Sebille Maarten van Reeuwijk Samraat Pawar Investigating microscale patchiness of motile microbes under turbulence in a simulated convective mixed layer. 2022 18 PLoS Comput. Biol. 7 https://doi.org/10.1371/journal.pcbi.1010291 https://www.wikidata.org/entity/Q113308415 db/journals/ploscb/ploscb18.html#ChristensenPSRP22

Mingrui Zhang Jianhong Wang James B. Tlhomole Matthew D. Piggott Learning to Estimate and Refine Fluid Motion with Physical Dynamics. 26575-26590 2022 ICML https://proceedings.mlr.press/v162/zhang22ad.html conf/icml/2022 db/conf/icml/icml2022.html#ZhangWTP22 Wenbin Song Mingrui Zhang Joseph G. Wallwork Junpeng Gao Zheng Tian 0002 Fanglei Sun Matthew D. Piggott Junqing Chen Zuoqiang Shi Xiang Chen Jun Wang 0012 M2N: Mesh Movement Networks for PDE Solvers. 2022 conf/nips/2022 NeurIPS http://papers.nips.cc/paper_files/paper/2022/hash/2f88d8061f12abae9d14d376fd69c933-Abstract-Conference.html db/conf/nips/neurips2022.html#SongZWGTSPCSCW22

Joseph G. Wallwork Matthew G. Knepley Nicolas Barral Matthew D. Piggott Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg. 2022 abs/2201.02806 CoRR https://arxiv.org/abs/2201.02806 db/journals/corr/corr2201.html#abs-2201-02806

Wenbin Song Mingrui Zhang Joseph G. Wallwork Junpeng Gao Zheng Tian 0002 Fanglei Sun Matthew D. Piggott Junqing Chen Zuoqiang Shi Xiang Chen Jun Wang 0012 M2N: Mesh Movement Networks for PDE Solvers. 2022 abs/2204.11188 CoRR https://doi.org/10.48550/arXiv.2204.11188 db/journals/corr/corr2204.html#abs-2204-11188

Mariana C. A. Clare Matthew D. Piggott Bayesian neural networks for the probabilistic forecasting of wind direction and speed using ocean data. 2022 abs/2206.08953 CoRR https://doi.org/10.48550/arXiv.2206.08953 db/journals/corr/corr2206.html#abs-2206-08953

Mingrui Zhang Jianhong Wang James Tlhomole Matthew D. Piggott Learning to Estimate and Refine Fluid Motion with Physical Dynamics. 2022 abs/2206.10480 CoRR https://doi.org/10.48550/arXiv.2206.10480 db/journals/corr/corr2206.html#abs-2206-10480

Joseph G. Wallwork Jingyi Lu Mingrui Zhang Matthew D. Piggott E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation. 2022 abs/2207.11233 CoRR https://doi.org/10.48550/arXiv.2207.11233 db/journals/corr/corr2207.html#abs-2207-11233

Siyi Li Mingrui Zhang Matthew D. Piggott End-to-end Wind Turbine Wake Modelling with Deep Graph Representation Learning. 2022 abs/2211.13649 CoRR https://doi.org/10.48550/arXiv.2211.13649 db/journals/corr/corr2211.html#abs-2211-13649

Mariana C. A. Clare James R. Percival Athanasios Angeloudis Colin J. Cotter Matthew D. Piggott Hydro-morphodynamics 2D modelling using a discontinuous Galerkin discretisation. 104658 2021 146 Comput. Geosci. https://doi.org/10.1016/j.cageo.2020.104658 db/journals/gandc/gandc146.html#ClarePACP21

Mingrui Zhang Matthew D. Piggott Unsupervised Learning of Particle Image Velocimetry. 102-115 2020 ISC Workshops https://doi.org/10.1007/978-3-030-59851-8_7 conf/supercomputer/2020w db/conf/supercomputer/isc2020w.html#ZhangP20

Mingrui Zhang Matthew D. Piggott Unsupervised Learning of Particle Image Velocimetry. 2020 abs/2007.14487 CoRR https://arxiv.org/abs/2007.14487 db/journals/corr/corr2007.html#abs-2007-14487

J. M. Nunez Rattia James R. Percival S. J. Neethling M. D. Piggott Modelling local scour near structures with combined mesh movement and mesh optimisation. 1220-1237 2018 375 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2018.09.026 db/journals/jcphy/jcphy375.html#RattiaPNP18

Alexandros Adam Andrew G. Buchan Matthew D. Piggott Christopher C. Pain Jon Hill Mark A. Goffin Adaptive Haar wavelets for the angular discretisation of spectral wave models. 521-538 2016 305 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2015.10.046 db/journals/jcphy/jcphy305.html#AdamBPPHG16

Christian T. Jacobs Matthew D. Piggott Stephan C. Kramer Simon W. Funke On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation. 2016 abs/1601.08091 CoRR http://arxiv.org/abs/1601.08091 db/journals/corr/corr1601.html#JacobsPKF16

Nicolas Barral Matthew G. Knepley Michael Lange 0001 Matthew D. Piggott Gerard J. Gorman Anisotropic mesh adaptation in Firedrake with PETSc DMPlex. 2016 abs/1610.09874 CoRR http://arxiv.org/abs/1610.09874 db/journals/corr/corr1610.html#BarralKLPG16

Christian T. Jacobs Alexandros Avdis Simon L. Mouradian Matthew D. Piggott Integrating Research Data Management into Geographical Information Systems. 7-17 2015 SDA@TPDL https://ceur-ws.org/Vol-1529/paper2.pdf conf/ercimdl/2015sda db/conf/ercimdl/sda2015.html#JacobsAMP15

Stephan C. Kramer Matthew D. Piggott A correction to the enhanced bottom drag parameterisation of tidal turbines. 2015 abs/1506.03611 CoRR http://arxiv.org/abs/1506.03611 db/journals/corr/corr1506.html#KramerP15

Simon W. Funke Stephan C. Kramer Matthew D. Piggott Design optimisation and resource assessment for tidal-stream renewable energy farms using a new continuous turbine approach. 2015 abs/1507.05795 CoRR http://arxiv.org/abs/1507.05795 db/journals/corr/corr1507.html#FunkeKP15

Christian T. Jacobs Alexandros Avdis Simon L. Mouradian Matthew D. Piggott Integrating Research Data Management into Geographical Information Systems. 2015 abs/1509.04729 CoRR http://arxiv.org/abs/1509.04729 db/journals/corr/corr1509.html#JacobsAMP15

Alexandros Avdis Christian T. Jacobs Jon Hill Matthew D. Piggott Gerard J. Gorman Shoreline and Bathymetry Approximation in Mesh Generation for Tidal Renewable Simulations. 2015 abs/1510.01560 CoRR http://arxiv.org/abs/1510.01560 db/journals/corr/corr1510.html#AvdisJHPG15

Christian T. Jacobs Alexandros Avdis Gerard J. Gorman Matthew D. Piggott PyRDM: A Python-based library for automating the management and online publication of scientific software and data. 2014 abs/1405.7290 CoRR http://arxiv.org/abs/1405.7290 db/journals/corr/corr1405.html#JacobsAGP14

George L. Barnett Simon W. Funke Matthew D. Piggott Hybrid global-local optimisation algorithms for the layout design of tidal turbine arrays. 2014 abs/1410.2476 CoRR http://arxiv.org/abs/1410.2476 db/journals/corr/corr1410.html#BarnettFP14

Simon W. Funke Patrick E. Farrell M. D. Piggott Tidal turbine array optimisation using the adjoint approach http://arxiv.org/abs/1304.1768 2013 CoRR abs/1304.1768 db/journals/corr/corr1304.html#abs-1304-1768

James Southern Gerard J. Gorman M. D. Piggott Patrick E. Farrell Parallel anisotropic mesh adaptivity with dynamic load balancing for cardiac electrophysiology. 8-16 2012 3 J. Comput. Sci. 1-2 https://doi.org/10.1016/j.jocs.2011.11.002 db/journals/jocs/jocs3.html#SouthernGPF12

Gerard J. Gorman James Southern Patrick E. Farrell M. D. Piggott Georgios Rokos Paul H. J. Kelly Hybrid OpenMP/MPI Anisotropic Mesh Smoothing. 1513-1522 2012 conf/iccS/2012 ICCS https://doi.org/10.1016/j.procs.2012.04.166 db/journals/procedia/procedia9.html#GormanSFPRK12

James Southern Gerard J. Gorman M. D. Piggott Patrick E. Farrell Miguel O. Bernabeu Joe Pitt-Francis Simulating cardiac electrophysiology using anisotropic mesh adaptivity. 82-88 2010 1 J. Comput. Sci. 2 https://doi.org/10.1016/j.jocs.2010.03.010 db/journals/jocs/jocs1.html#SouthernGPFBP10

James Southern Gerard J. Gorman M. D. Piggott Patrick E. Farrell Miguel O. Bernabeu Joe Pitt-Francis Anisotropic mesh adaptivity for cardiac electrophysiology. 935-944 2010 conf/iccS/2010 ICCS 1 https://doi.org/10.1016/j.procs.2010.04.103 db/journals/procedia/procedia1.html#SouthernGPFBP10

Gerard J. Gorman M. D. Piggott M. R. Wells Christopher C. Pain Peter A. Allison A systematic approach to unstructured mesh generation for ocean modelling using GMT and Terreno. 1721-1731 2008 34 Comput. Geosci. 12 https://doi.org/10.1016/j.cageo.2007.06.014 db/journals/gandc/gandc34.html#GormanPWPA08

Gerard J. Gorman M. D. Piggott Christopher C. Pain Shoreline approximation for unstructured mesh generation. 666-677 2007 33 Comput. Geosci. 5 https://doi.org/10.1016/j.cageo.2006.09.007 db/journals/gandc/gandc33.html#GormanPP07

P. W. Power Christopher C. Pain M. D. Piggott Fangxin Fang Gerard J. Gorman A. P. Umpleby Anthony J. H. Goddard I. M. Navon Adjoint A Posteriori Error Measures for Anisotropic Mesh Optimisation. 1213-1242 2006 52 Comput. Math. Appl. 8-9 https://doi.org/10.1016/j.camwa.2006.11.003 db/journals/cma/cma52.html#PowerPPFGUGN06

Alexandros Adam Peter A. Allison Sokratis Anagnostopoulos Athanasios Angeloudis Rossella Arcucci Alexandros Avdis George L. Barnett Nicolas Barral Jens Bauer Miguel O. Bernabeu Gabriele Bertoli B. Bhaskaran Marc Bocquet Andrew G. Buchan Enrica Caporali César Quilodrán Casas Junqing Chen Xiang Chen Sibo Cheng Alexander Kier Christensen Mariana C. A. Clare Colin J. Cotter Weiping Ding 0001 A. Aldo Faisal Fangxin Fang Patrick E. Farrell Tobias Sebastian Finn Jinlong Fu Rui Fu Simon W. Funke Junpeng Gao Anthony J. H. Goddard Mark A. Goffin Gerard GormanGerard J. Gorman Yike Guo David A. Ham Jon Hill Christian T. Jacobs Eleda Johnson Paul H. J. Kelly Matthew G. Knepley Stephan Kramer Stephan C. Kramer Michael Lange 0001 Siyi Li Che Liu 0002 Jiancheng Liu Jingyi Lu Eric Newton Moro Simon L. Mouradian Ionel Michael NavonI. M. Navon Robert Neal S. J. Neethling Christopher C. Pain Jie Pan 0007 Samraat Pawar James R. Percival Joe Pitt-Francis P. W. Power J. M. Nunez Rattia Maarten van Reeuwijk Arnaud Robert Georgios Rokos Kai Schröter Erik van Sebille Prakhar Sharma Zuoqiang Shi Wenbin Song James Southern Fanglei Sun Zheng Tian 0002 James TlhomoleJames B. Tlhomole A. P. Umpleby Joseph G. Wallwork Chunyang Wang Jianhong Wang Jun Wang 0012 Kun Wang Yanghua Wang Simon C. Warder M. R. Wells Dunhui Xiao Xiao Xue 0002 Yong Zeng Mingrui Zhang Hao Zhou 0020 Kewei Zhu