Session: 01-05-03: Data-Driven Design and Optimization of Aerospace Structures Using AI/ML

Paper Number: 190358

190358 - Pgi-Deeponet: A Physics-Informed Neural Operator Network for Acoustic Scattering Simulations 

The design of materials for dynamic and acoustic applications often requires complex and frequency-dependent optimization of various design parameters, which can include material properties, dimensions, and even shapes. The resulting design space is so vast that the classical inverse design methods, which rely on iterative evaluation of the forward problem, rapidly become computationally intractable. When traditional computational methods, such as Finite Element Analysis (FEA), are used to solve the forward problem the intrinsic size-dependence of the mesh and the steep overhead associated with the numerical inversion of large matrices makes the evaluation of multiple design configurations a very cumbersome and time-consuming task. In recent years, Physics-Informed Neural Networks (PINNs) have provided an alternative pathway to mesh-free computations. However, most machine learning methods typically require lengthy training phases that, if repeated for every new system configuration, end up providing no net gains by simply offsetting the computational burden to different parts of the analysis.

This work presents a physics-informed Deep Operator Network (DeepONet) framework designed for the simulation of acoustic scattering problems in presence of rigid scatterers of arbitrary geometries. The framework does not require training data and integrates Non-Uniform Rational B-Splines (NURBS) for geometry parameterization. By embedding a NURBS-based geometry descriptor into the network architecture, the model achieves superior generalization performance resulting in zero-shot inference of the physical acoustic field around scatterers of varying shapes and sizes. This is possible because the network effectively learns the operator that maps a geometric configuration to its corresponding acoustic pressure field. The underlying physics is enforced via a purely physics-driven, PDE-constrained, loss function that incorporates the governing Helmholtz equation and the associated boundary conditions. Unlike standard data-driven models, our approach utilizes a composite loss function that simultaneously minimizes the residual of the wave equation over the computational domain and enforces the Sommerfeld radiation condition to ensure far-field accuracy. By leveraging a foundational DeepONet’s architecture, in which the trunk network processes spatial coordinates and the branch network captures the NURBS parameters, the resulting Physics- and Geometry-Informed (PGI) DeepONet architecture can learn the intricate relationship between the scatterers geometry and the resulting wave scattering patterns.

The proposed PGI-DeepONet requires only one-time training while being applicable to any arbitrary shape scatterer. Numerical results clearly indicate that the proposed framework accurately predicts the scattered pressure fields for unseen geometries, while achieving at least an order-of-magnitude speedup in computational time (when considering the inference phase). The prediction accuracy and computational efficiency of the proposed method are compared with the results of a high-fidelity commercial finite element software. By decoupling the computational cost from the geometric complexity, the PGI-DeepONet can offer a powerful approach to synthesize accurate and computationally efficient reduced-order models in support of the rapid design and analysis of materials and structures for acoustics applications. As an example, this methodology can be leveraged to perform rapid parametric sweeps and inverse optimization for the design of acoustic materials or for acoustic sensing. At the same time, the technology proposed is very general and can be extended to other physics by simply updating the differential equations used in the loss function.

Presenting Author: Fabio Semperlotti Purdue

Presenting Author Biography: Dr. Fabio Semperlotti is a Professor in the School of Mechanical Engineering and the Perry Academic Excellence Scholar at Purdue University; he also holds a courtesy appointment in the School of Aeronautics and Astronautics Engineering. He directs the Structural Health Monitoring and Dynamics laboratory (SHMD) where he conducts, together with his group, research on several aspects of structures and materials design including structural dynamics and wave propagation, elastic metamaterials, structural health monitoring, and computational and experimental mechanics. His research has received financial support from a variety of sources including the National Science Foundation, the Department of Defense, the Department of Energy, and industrial sponsors. Dr. Semperlotti was the recipient of the National Science Foundation CAREER award (2015), the Air Force Office of Scientific Research Young Investigator Program (YIP) (2015), the DARPA Young Faculty Award (YFA) 2019, and the ASME C.D. Mote Jr. Early Career Award 2019.
Dr. Semperlotti received a M.S. in Aerospace Engineering, and a M.S. in Astronautic Engineering both from the University of Rome “La Sapienza” (Italy), and a Ph.D. in Aerospace engineering from the Pennsylvania State University (USA). In 2010, he was a postdoctoral research associate in the Mechanical Engineering department at the University of Michigan. Prior to joining Penn State, Dr. Semperlotti served as a structural engineer for a few European aerospace industries, including the French Space Agency (CNES), working on the structural design of space launch systems and satellite platforms.