Solving PDEs using Machine Learning by Balaji Srinivasan, IIT Madras
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0:00:00 [Talk: Solving PDEs using Machine Learning]
0:01:02 Outline
0:01:04 Diverse applications of PDEs
0:01:44 PDEs and flow solvers (CFD)
0:02:51 Overall solution process for typical mesh-based flow solvers
0:03:42 Can we have autonomous flow solvers?
0:04:15 Autonomous Thermal Learning Systems research group
0:05:02 Mesh Based Approach
0:05:56 Why Neural Networks?
0:07:49 Problem formulation
0:08:40 Problem formulation (contd...)
0:08:50 Physics Informed Neural Network (PINN)
0:09:23 Conventional methods vs PINN
0:09:54 Some issues with PINN
0:10:09 Extreme Learning Machine (Huang,2006)
0:11:55 Results - An example of complicated geometry
0:12:18 Rapid solution of biharmonic equation
0:12:28 PIELM versus PINN: Solution of biharmonic equation
0:12:31 PIELM vs PINN (contd...)
0:12:50 PIELM versus FEM
0:13:01 PIELM vs FEM (contd...)
0:13:19 Limitations of PIELM: representation of functions
0:13:38 Limitations of PIELM: 2D unsteady advection-diffusion
0:14:14 Summary and future work
0:15:31 Q&A
Please visit this website for more information about the conference:
https://conf.iiserb.ac.in/thefourthparadigm/
Видео Solving PDEs using Machine Learning by Balaji Srinivasan, IIT Madras канала Fourth Paradigm conference
0:00:00 [Talk: Solving PDEs using Machine Learning]
0:01:02 Outline
0:01:04 Diverse applications of PDEs
0:01:44 PDEs and flow solvers (CFD)
0:02:51 Overall solution process for typical mesh-based flow solvers
0:03:42 Can we have autonomous flow solvers?
0:04:15 Autonomous Thermal Learning Systems research group
0:05:02 Mesh Based Approach
0:05:56 Why Neural Networks?
0:07:49 Problem formulation
0:08:40 Problem formulation (contd...)
0:08:50 Physics Informed Neural Network (PINN)
0:09:23 Conventional methods vs PINN
0:09:54 Some issues with PINN
0:10:09 Extreme Learning Machine (Huang,2006)
0:11:55 Results - An example of complicated geometry
0:12:18 Rapid solution of biharmonic equation
0:12:28 PIELM versus PINN: Solution of biharmonic equation
0:12:31 PIELM vs PINN (contd...)
0:12:50 PIELM versus FEM
0:13:01 PIELM vs FEM (contd...)
0:13:19 Limitations of PIELM: representation of functions
0:13:38 Limitations of PIELM: 2D unsteady advection-diffusion
0:14:14 Summary and future work
0:15:31 Q&A
Please visit this website for more information about the conference:
https://conf.iiserb.ac.in/thefourthparadigm/
Видео Solving PDEs using Machine Learning by Balaji Srinivasan, IIT Madras канала Fourth Paradigm conference
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