{"id":63112,"date":"2025-04-14T12:00:19","date_gmt":"2025-04-14T12:00:19","guid":{"rendered":""},"modified":"2025-04-14T12:00:19","modified_gmt":"2025-04-14T12:00:19","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPhysics-informed graph neural networks for flow field estimation in carotid arteries<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nJulian Suk, Dieuwertje Alblas, Barbara A. Hutten, Albert Wiegman, Christoph Brune, Pim van Ooij, Jelmer M. Wolterink<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n10<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nQuantitative Methods,Machine Learning,Fluid Dynamics,\u0631\u0648\u0634\u0647\u0627\u06cc \u06a9\u0645\u06cc , \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 , \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9 \u0633\u06cc\u0627\u0644 ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 13 August, 2024; originally announced August 2024. , Comments: Preprint. Under Review<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 13 \u0627\u0648\u062a 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0648\u062a 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f. \u060c \u0646\u0638\u0631\u0627\u062a: preprint.\u062a\u062d\u062a \u0628\u0631\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not widely available, such as 4D flow magnetic resonance imaging (MRI). In this work, we create a surrogate model for hemodynamic flow field estimation, powered by machine learning. We train graph neural networks that include priors about the underlying symmetries and physics, limiting the amount of data required for training. This allows us to train the model using moderately-sized, in-vivo 4D flow MRI datasets, instead of large in-silico datasets obtained by computational fluid dynamics (CFD), as is the current standard. We create an efficient, equivariant neural network by combining the popular PointNet++ architecture with group-steerable layers. To incorporate the physics-informed priors, we derive an efficient discretisation scheme for the involved differential operators. We perform extensive experiments in carotid arteries and show that our model can accurately estimate low-noise hemodynamic flow fields in the carotid artery. Moreover, we show how the learned relation between geometry and hemodynamic quantities transfers to 3D vascular models obtained using a different imaging modality than the training data. This shows that physics-informed graph neural networks can be trained using 4D flow MRI data to estimate blood flow in unseen carotid artery geometries.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0645\u0642\u0627\u062f\u06cc\u0631 \u0647\u0645\u0648\u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u0639\u0648\u0627\u0645\u0644 \u062e\u0637\u0631 \u0632\u06cc\u0633\u062a \u067e\u0632\u0634\u06a9\u06cc \u0628\u0627 \u0627\u0631\u0632\u0634 \u0628\u0631\u0627\u06cc \u0622\u0633\u06cc\u0628 \u0634\u0646\u0627\u0633\u06cc \u0642\u0644\u0628\u06cc \u0639\u0631\u0648\u0642\u06cc \u0645\u0627\u0646\u0646\u062f \u0622\u062a\u0631\u0648\u0627\u0633\u06a9\u0644\u0631\u0648\u0632 \u0647\u0633\u062a\u0646\u062f.\u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u063a\u06cc\u0631 \u062a\u0647\u0627\u062c\u0645\u06cc \u0648 \u062f\u0627\u062e\u0644\u06cc \u0627\u06cc\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0641\u0642\u0637 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0639\u062f\u0627\u062f \u0627\u0646\u062a\u062e\u0627\u0628\u06cc \u0627\u0632 \u0631\u0648\u0634\u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u062f\u0633\u062a\u0631\u0633 \u0646\u06cc\u0633\u062a \u060c \u0645\u0627\u0646\u0646\u062f \u062a\u0635\u0648\u06cc\u0631\u0628\u0631\u062f\u0627\u0631\u06cc \u0631\u0632\u0648\u0646\u0627\u0646\u0633 \u0645\u063a\u0646\u0627\u0637\u06cc\u0633\u06cc 4D (MRI).\u062f\u0631 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u060c \u0645\u0627 \u06cc\u06a9 \u0645\u062f\u0644 \u062c\u0627\u0646\u0634\u06cc\u0646 \u0628\u0631\u0627\u06cc \u0628\u0631\u0622\u0648\u0631\u062f \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u0647\u0645\u0648\u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u060c \u06a9\u0647 \u0627\u0632 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u060c \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0645\u0627 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627 \u0622\u0645\u0648\u0632\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0634\u0627\u0645\u0644 \u0645\u0642\u062f\u0645\u0627\u062a\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u062a\u0642\u0627\u0631\u0646 \u0648 \u0641\u06cc\u0632\u06cc\u06a9 \u0627\u0633\u0627\u0633\u06cc \u0627\u0633\u062a \u0648 \u0645\u06cc\u0632\u0627\u0646 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0622\u0645\u0648\u0632\u0634 \u0631\u0627 \u0645\u062d\u062f\u0648\u062f \u0645\u06cc \u06a9\u0646\u062f.\u0627\u06cc\u0646 \u0628\u0647 \u0645\u0627 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u0628\u0647 \u062c\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u062f\u0631\u0648\u0646 \u0633\u06cc\u0644\u06cc\u06a9\u0648 \u06a9\u0647 \u062a\u0648\u0633\u0637 \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9 \u0633\u06cc\u0627\u0644 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc (CFD) \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u060c \u0645\u0627\u0646\u0646\u062f \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0641\u0639\u0644\u06cc \u060c \u0645\u062f\u0644 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc MRI \u062f\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u062a\u0648\u0633\u0637 \u200b\u200b4D 4D \u0622\u0645\u0648\u0632\u0634 \u062f\u0647\u06cc\u0645.\u0645\u0627 \u0628\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u0639\u0645\u0627\u0631\u06cc \u0645\u062d\u0628\u0648\u0628 PointNET ++ \u0628\u0627 \u0644\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06af\u0631\u0648\u0647\u06cc \u0628\u0647 \u062d\u0627\u0644\u062a \u06af\u0631\u0648\u0647\u06cc \u060c \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u0645\u0639\u062a\u0628\u0631 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0628\u0631\u0627\u06cc \u062a\u0631\u06a9\u06cc\u0628 \u0645\u0642\u062f\u0645\u0627\u062a \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u060c \u0645\u0627 \u06cc\u06a9 \u0637\u0631\u062d \u062a\u0641\u0633\u06cc\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0631\u0627\u06cc \u0627\u067e\u0631\u0627\u062a\u0648\u0631\u0647\u0627\u06cc \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062f\u0631\u06af\u06cc\u0631 \u0631\u0627 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0645\u0627 \u0622\u0632\u0645\u0627\u06cc\u0634 \u0647\u0627\u06cc \u06af\u0633\u062a\u0631\u062f\u0647 \u0627\u06cc \u0631\u0627 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0648 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0645\u062f\u0644 \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0637\u0648\u0631 \u062f\u0642\u06cc\u0642 \u0632\u0645\u06cc\u0646\u0647 \u0647\u0627\u06cc \u062c\u0631\u06cc\u0627\u0646 \u0647\u0645\u0648\u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u06a9\u0645 \u0646\u0648\u06cc\u0632 \u0631\u0627 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f \u062a\u062e\u0645\u06cc\u0646 \u0628\u0632\u0646\u062f.\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646 \u060c \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0631\u0627\u0628\u0637\u0647 \u0622\u0645\u0648\u062e\u062a\u0647 \u0634\u062f\u0647 \u0628\u06cc\u0646 \u0647\u0646\u062f\u0633\u0647 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0647\u0645\u0648\u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u0628\u0647 \u0645\u062f\u0644\u0647\u0627\u06cc \u0639\u0631\u0648\u0642\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u0631\u0648\u0634 \u062a\u0635\u0648\u06cc\u0631\u0628\u0631\u062f\u0627\u0631\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0622\u0645\u0648\u0632\u0634 \u0645\u0646\u062a\u0642\u0644 \u0645\u06cc \u0634\u0648\u062f.\u0627\u06cc\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc MRI \u062c\u0631\u06cc\u0627\u0646 4D \u0628\u0631\u0627\u06cc \u0628\u0631\u0622\u0648\u0631\u062f \u062c\u0631\u06cc\u0627\u0646 \u062e\u0648\u0646 \u062f\u0631 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627\u06cc \u0634\u0631\u06cc\u0627\u0646 \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f \u063a\u06cc\u0628 \u0622\u0645\u0648\u0632\u0634 \u062f\u0627\u062f\u0647 \u0634\u0648\u0646\u062f.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Physics-informed graph neural networks for flow field estimation in carotid arteries \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"open","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[21],"product_tag":[],"class_list":{"0":"post-63112","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-21","7":"pmpro-has-access","8":"desktop-align-left","9":"tablet-align-left","10":"mobile-align-left","12":"first","13":"instock","14":"downloadable","15":"shipping-taxable","16":"purchasable","17":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63112\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"og:description\" content=\"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Physics-informed graph neural networks for flow field estimation in carotid arteries \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63112\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"og:image\" content=\"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png\" \/>\n\t<meta property=\"og:image:width\" content=\"440\" \/>\n\t<meta property=\"og:image:height\" content=\"486\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/\",\"url\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/\",\"name\":\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"isPartOf\":{\"@id\":\"https:\/\/express24.ir\/d\/#website\"},\"datePublished\":\"2025-04-14T12:00:19+00:00\",\"dateModified\":\"2025-04-14T12:00:19+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/#breadcrumb\"},\"inLanguage\":\"fa-IR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u062e\u0627\u0646\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/express24.ir\/d\/#website\",\"url\":\"https:\/\/express24.ir\/d\/\",\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/express24.ir\/d\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fa-IR\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63112\/","og_locale":"fa_IR","og_type":"article","og_title":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","og_description":"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Physics-informed graph neural networks for flow field estimation in carotid arteries \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 […]","og_url":"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63112\/","og_site_name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","og_image":[{"width":440,"height":486,"url":"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png","type":"image\/png"}],"twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/","url":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/","name":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","isPartOf":{"@id":"https:\/\/express24.ir\/d\/#website"},"datePublished":"2025-04-14T12:00:19+00:00","dateModified":"2025-04-14T12:00:19+00:00","breadcrumb":{"@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/#breadcrumb"},"inLanguage":"fa-IR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63112\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u062e\u0627\u0646\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":2,"name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":3,"name":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0622\u06af\u0627\u0647 \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062a\u062e\u0645\u06cc\u0646 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0634\u0631\u06cc\u0627\u0646 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0648\u062a\u06cc\u062f"}]},{"@type":"WebSite","@id":"https:\/\/express24.ir\/d\/#website","url":"https:\/\/express24.ir\/d\/","name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/express24.ir\/d\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fa-IR"}]}},"_links":{"self":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product\/63112","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/comments?post=63112"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media\/27"}],"wp:attachment":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media?parent=63112"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_cat?post=63112"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_tag?post=63112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}