Figure 1. Physics-informed neural network architecture illustrating the integration of data and physics constraints in the loss function. Reproduced from Dadras Eslamlou, A., & Huang, S. (2022), Artificial-Neural-Network-Based Surrogate Models for Structural Health Monitoring of Civil Structures: A Literature Review, Buildings, 12(12), 2067. https://doi.org/10.3390/buildings12122067
FINDING NUMERICAL SOLUTIONS FOR NONLINEAR STRUCTURAL PROBLEMS UTILIZING PHYSICS INFORMED DEEP LEARNING John Anderson , Aerospace Engineering MENTOR Yabin Liao , Aerospace Engineering In many practical cases, developing closed-form analytical solutions for structural dynamics is infeasible, particularly for complex or nonlinear systems such as the damped Duffing oscillator, which admits no closed-form analytical solution. However, in many applications, the functional form of the governing ordinary differential equations (ODEs) is known prior to searching for solutions, while the system parameters remain unknown. Traditionally, parametric identification in such systems relies on numerical optimization techniques, which can suffer from convergence, conditioning, and computational cost issues, especially as the number of parameters increases or strong nonlinearities are present, leading to curse-of-dimensionality and identifiability challenges. We propose a physics-informed Long Short-Term Memory (LSTM) framework as an alternative to traditional optimization methods. The proposed model leverages the known structure of the governing equations to identify unknown ODE coefficients while simultaneously learning the system dynamics. The challenges addressed are twofold. First, broadband or random forcing inputs reduce temporal smoothness and increase spectral complexity, making learning difficult for standard neural networks. Second, nonlinear dynamics and higher- dimensional parameter spaces significantly increase training complexity and computational cost for neural networks. Prior work has demonstrated the viability of LSTMs for dynamic system modeling, and our results indicate that incorporating physics-informed loss terms improves parameter identification robustness and numerical solution accuracy for nonlinear structural dynamics systems.
SPACE GRANT AWARD
UNDERGRADUATE RESEARCH INSTITUTE | 13
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