Jakub Lengiewicz

Video recording:

Abstract: Complementary to conventional numerical methods, physics-informed neural networks (PINNs) have recently emerged as alternative approximators for the solution of partial differential equations (PDEs). The main benefit of PINNs versus the conventional methods is their tremendous computational efficiency in terms of predictive speed, once the PINN model has been trained. Leveraging on their swift predictive capability, we integrate PINNs within the finite element solver and utilize them to approximate the solution of mechanics-governing PDEs. This step allows us to bypass the direct numerical discretization of the PDE, approximating the solution field at a fraction of time compared to traditional FEM. The developed framework is termed I-FENN (Integrated Finite Element Neural Network), and in this talk I will present its application in the case of nonlocal gradient continuum damage. A series of benchmark numerical examples will be presented, showcasing the computational efficiency and generalization capability of I-FENN, along with an extensive error convergence and hyperparameter analysis to solidify its background.

Additional material:

1. Pantidis and Mobasher (2023), Integrated Finite Element Neural Network (I-FENN) for non-local continuum damage mechanics, Computer Methods in Applied Mechanics and Engineering, 404: 115766 (link).
2. Pantidis and Mobasher (2023), Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance, Computer Methods in Applied Mechanics and Engineering, accepted (link for arXiv version).

Panos Pantidis obtained his BSc from the Aristotle University of Thessaloniki, Greece, in 2015. In 2019 he received his PhD from the Civil Engineering Department of the University of Massachusetts, Amherst. He then joined Thornton Tomasetti, working at their New York City Forensics practice. Dr. Pantidis is now a Postdoctoral Associate at New York University Abu Dhabi. His research focuses on computational mechanics and machine learning for multi-physics problems.