Is this project an undergraduate, graduate, or faculty project?
Undergraduate
individual
What campus are you from?
Daytona Beach
Authors' Class Standing
Anthony LoRe Starleaf, Junior
Lead Presenter's Name
Anthony LoRe Starleaf
Faculty Mentor Name
Siddharth Parida
Abstract
This research introduces a novel framework called Finite Element Physics-Informed Neural Networks (FE-PINNs) for solving complex problems in engineering. Building upon the strengths of traditional Physics-Informed Neural Networks (PINNs) and the Finite Element (FE) method, FE-PINN offers an efficient and accurate approach for solving challenging inverse problems in civil engineering. PINNs use neural networks to approximate physical systems while enforcing conformance with the systems' governing equations as a soft constraint during the optimization process, which allows system parameters to be updated alongside the weights of the PINN. FE-PINN extends this approach by using PINNs to solve the system of equations resulting from applying the FE method to potentially complicated real-world systems, while updating unknown system parameters simultaneously with neural network weights. The architecture closely resembles traditional PINNs but exhibits advantages such as faster convergence, reduced data requirements, and simplified loss functions. The effectiveness of FE-PINN is demonstrated through a 2D linear elastic full waveform inversion problem, where it not only accurately estimates elastic modulus values with less than 0.01% error, but also provides an efficient surrogate model which can be used for forecasting. The success of FE-PINN in this simplified problem provides grounds for optimism that it can be applied to more intricate systems - a direction the authors intend to explore in future research endeavors.
Did this research project receive funding support from the Office of Undergraduate Research.
Yes, SURF
Integrating Physics Informed Neural Networks with the Finite Element Method for Solving Inverse Problems
This research introduces a novel framework called Finite Element Physics-Informed Neural Networks (FE-PINNs) for solving complex problems in engineering. Building upon the strengths of traditional Physics-Informed Neural Networks (PINNs) and the Finite Element (FE) method, FE-PINN offers an efficient and accurate approach for solving challenging inverse problems in civil engineering. PINNs use neural networks to approximate physical systems while enforcing conformance with the systems' governing equations as a soft constraint during the optimization process, which allows system parameters to be updated alongside the weights of the PINN. FE-PINN extends this approach by using PINNs to solve the system of equations resulting from applying the FE method to potentially complicated real-world systems, while updating unknown system parameters simultaneously with neural network weights. The architecture closely resembles traditional PINNs but exhibits advantages such as faster convergence, reduced data requirements, and simplified loss functions. The effectiveness of FE-PINN is demonstrated through a 2D linear elastic full waveform inversion problem, where it not only accurately estimates elastic modulus values with less than 0.01% error, but also provides an efficient surrogate model which can be used for forecasting. The success of FE-PINN in this simplified problem provides grounds for optimism that it can be applied to more intricate systems - a direction the authors intend to explore in future research endeavors.