{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T01:55:45Z","timestamp":1778637345866,"version":"3.51.4"},"reference-count":64,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Access"],"published-print":{"date-parts":[[2024]]},"DOI":"10.1109\/access.2024.3504962","type":"journal-article","created":{"date-parts":[[2024,11,22]],"date-time":"2024-11-22T19:05:57Z","timestamp":1732302357000},"page":"176982-176998","source":"Crossref","is-referenced-by-count":41,"title":["Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks"],"prefix":"10.1109","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2352-8709","authenticated-orcid":false,"given":"Spyros","family":"Rigas","sequence":"first","affiliation":[{"name":"Department of Digital Industry Technologies, School of Science, National and Kapodistrian University of Athens (NKUA), Psachna, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5650-4206","authenticated-orcid":false,"given":"Michalis","family":"Papachristou","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8534-785X","authenticated-orcid":false,"given":"Theofilos","family":"Papadopoulos","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0176-4144","authenticated-orcid":false,"given":"Fotios","family":"Anagnostopoulos","sequence":"additional","affiliation":[{"name":"Department of Informatics and Telecommunications, University of the Peloponnese, Tripoli, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3611-8292","authenticated-orcid":false,"given":"Georgios","family":"Alexandridis","sequence":"additional","affiliation":[{"name":"Department of Digital Industry Technologies, School of Science, National and Kapodistrian University of Athens (NKUA), Psachna, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","article-title":"Physics informed deep learning (Part I): Data-driven solutions of nonlinear partial differential equations","author":"Raissi","year":"2017","journal-title":"arXiv:1711.10561"},{"key":"ref2","article-title":"Physics informed deep learning (Part II): Data-driven discovery of nonlinear partial differential equations","author":"Raissi","year":"2017","journal-title":"arXiv:1711.10566"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112789"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112732"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109951"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2020.00042"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1038\/s41746-023-00853-4"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/PESGM41954.2020.9282004"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsr.2022.108412"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/acf116"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN55064.2022.9891944"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/20M1318043"},{"key":"ref14","first-page":"5301","article-title":"On the spectral bias of neural networks","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Rahaman"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.05.024"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113226"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-023-10065-9"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-023-08654-w"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110768"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2022.05.015"},{"key":"ref21","article-title":"Multi-objective loss balancing for physics-informed deep learning","author":"Bischof","year":"2021","journal-title":"arXiv:2110.09813"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.116805"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114823"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2023.v21.n6.a11"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1111\/mice.12685"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.115671"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109136"},{"key":"ref28","article-title":"Self-scalable tanh (Stan): Faster convergence and better generalization in physics-informed neural networks","author":"Gnanasambandam","year":"2022","journal-title":"arXiv:2204.12589"},{"key":"ref29","article-title":"KAN: Kolmogorov\u2013Arnold networks","author":"Liu","year":"2024","journal-title":"arXiv:2404.19756"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.4825654"},{"key":"ref31","article-title":"Kolmogorov\u2013Arnold networks (KANs) for time series analysis","author":"Vaca-Rubio","year":"2024","journal-title":"arXiv:2405.08790"},{"key":"ref32","article-title":"A temporal Kolmogorov\u2013Arnold transformer for time series forecasting","author":"Genet","year":"2024","journal-title":"arXiv:2406.02486"},{"key":"ref33","article-title":"Kolmogorov\u2013Arnold network for satellite image classification in remote sensing","author":"Cheon","year":"2024","journal-title":"arXiv:2406.00600"},{"key":"ref34","article-title":"Suitability of KANs for computer vision: A preliminary investigation","author":"Azam","year":"2024","journal-title":"arXiv:2406.09087"},{"key":"ref35","article-title":"U-KAN makes strong backbone for medical image segmentation and generation","author":"Li","year":"2024","journal-title":"arXiv:2406.02918"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1145\/3675095.3676618"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117290"},{"key":"ref38","article-title":"RoPINN: Region optimized physics-informed neural networks","author":"Wu","year":"2024","journal-title":"arXiv:2405.14369"},{"key":"ref39","article-title":"Kolmogorov\u2013Arnold networks are radial basis function networks","author":"Li","year":"2024","journal-title":"arXiv:2405.06721"},{"key":"ref40","article-title":"Chebyshev polynomial-based Kolmogorov\u2013Arnold networks: An efficient architecture for nonlinear function approximation","author":"Sidharth","year":"2024","journal-title":"arXiv:2405.07200"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.4835325"},{"key":"ref42","article-title":"ReLU-KAN: New Kolmogorov\u2013Arnold networks that only need matrix addition, dot multiplication, and ReLU","author":"Qiu","year":"2024","journal-title":"arXiv:2406.02075"},{"key":"ref43","volume-title":"JAX: Composable Transformations of Python+NumPy Programs","author":"Bradbury","year":"2024"},{"key":"ref44","volume-title":"Flax: A Neural Network Library and Ecosystem for JAX","author":"Heek","year":"2024"},{"key":"ref45","article-title":"An expert\u2019s guide to training physics-informed neural networks","author":"Wang","year":"2023","journal-title":"arXiv:2308.08468"},{"key":"ref46","first-page":"1","article-title":"Automatic differentiation in machine learning: A survey","volume":"18","author":"Baydin","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"ref47","volume-title":"Automatic Differentiation in PyTorch","author":"Paszke","year":"2017"},{"key":"ref48","volume-title":"TensorFlow: Large-scale Machine Learning on Heterogeneous Systems","author":"Abadi","year":"2015"},{"key":"ref49","volume-title":"JaxKAN: A JAX-Based Implementation of Kolmogorov\u2013Arnold Networks","author":"Rigas","year":"2014"},{"key":"ref50","article-title":"Finite basis Kolmogorov\u2013Arnold networks: Domain decomposition for data-driven and physics-informed problems","author":"Howard","year":"2024","journal-title":"arXiv:2406.19662"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9045(72)90080-9"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/10.2.134"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/bf01589116"},{"key":"ref54","first-page":"1","article-title":"Adam: A method for stochastic optimization","volume-title":"Proc. 3rd Int. Conf. Learn. Representations (ICLR)","author":"Kingma"},{"key":"ref55","volume-title":"The DeepMind JAX Ecosystem","year":"2024"},{"key":"ref56","volume-title":"An Efficient Implementation of Kolmogorov\u2013Arnold Network","author":"Cao","year":"2024"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.116813"},{"key":"ref58","volume-title":"Incorporating Nesterov Momentum Into Adam","author":"Dozat","year":"2016"},{"key":"ref59","article-title":"FKAN: Fractional Kolmogorov\u2013Arnold networks with trainable Jacobi basis functions","author":"Aghaei","year":"2024","journal-title":"arXiv:2406.07456"},{"key":"ref60","article-title":"Kolmogorov\u2013Arnold networks in molecular dynamics","author":"Nagai","year":"2024","journal-title":"arXiv:2407.17774"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1140\/epjqt\/s40507-024-00289-z"},{"key":"ref62","article-title":"2D and 3D deep learning models for MRI-based Parkinson\u2019s disease classification: A comparative analysis of convolutional Kolmogorov\u2013Arnold networks, convolutional neural networks, and graph convolutional networks","author":"Patel","year":"2024","journal-title":"arXiv:2407.17380"},{"key":"ref63","article-title":"Deep state space recurrent neural networks for time series forecasting","author":"Inzirillo","year":"2024","journal-title":"arXiv:2407.15236"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90144-9"}],"container-title":["IEEE Access"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/6287639\/10380310\/10763509.pdf?arnumber=10763509","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T06:42:21Z","timestamp":1733294541000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10763509\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"references-count":64,"URL":"https:\/\/doi.org\/10.1109\/access.2024.3504962","relation":{},"ISSN":["2169-3536"],"issn-type":[{"value":"2169-3536","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]}}}