Novel Physics-Informed Artificial Neural Network Architectures for System and Input Identification of Structural Dynamics PDEs

Abstract

Herein, two novel Physics Informed Neural Network (PINN) architectures are proposed for output-only system identification and input estimation of dynamic systems. Using merely sparse output-only measurements, the proposed PINNs architectures furnish a novel approach to input, state, and parameter estimation of linear and nonlinear systems with multiple degrees of freedom. These architectures are comprised of parallel and sequential PINNs that act upon a set of ordinary differential equations (ODEs) obtained from spatial discretization of the partial differential equation (PDE). The performance of this framework for dynamic system identification and input estimation was ascertained by extensive numerical experiments on linear and nonlinear systems. The advantage of the proposed approach, when compared with system identification, lies in its computational efficiency. When compared with traditional Artificial Neural Networks (ANNs), this approach requires substantially smaller training data and does not suffer from generalizability issues. In this regard, the states, inputs, and parameters of dynamic state-space equations of motion were estimated using simulated experiments with “noisy” data. The proposed framework for PINN showed excellent great generalizability for various types of applications. Furthermore, it was found that the proposed architectures significantly outperformed ANNs in generalizability and estimation accuracy.

Material Data Identification in an Induction Hardening Test Rig with Physics-Informed Neural Networks

“…This is because physics-based models incorporate regularization constraints based on the underlying physics of the process. There are also other studies in the literature that demonstrate the noise robustness of PINNs, as mentioned in references [ 43 , 44 , 45 ].…”

A Compact Memristor Model Based on Physics-Informed Neural Networks

“…Given a function N(w, b) that has undergone PINN training, the final solution with the initial condition C can be represented as follows [29]:…”

“…2 signifies the mean square error (MSE) on the residuals of the ODE [29,31]. N ODE is the number of input data and L IC is denoted as MSE between the initial conditions for state training value at its coordinates.…”

“…PINN is an artificial neural network (ANN) for numerically solving differential equations and has a more intuitive and simpler structure than the traditional LSTM model. It can also obtain solutions to differential equations faster and more accurately than traditional models [29][30][31]. PINN can be used to predict the I-V characteristics of a memristor and extract the weight and bias of the predicted function.…”

Physics-Informed Machine Learning—An Emerging Trend in Tribology

“…The applications of PIML are wide-ranging and can be found in various scientific and engineering domains. It has been employed in fluid dynamics for flow prediction and turbulence modeling [52][53][54], in material science to predict material behavior [55][56][57][58] and discover new materials [59], in structural mechanics [60,61], medical imaging [62,63], and many other fields where physical laws play crucial roles. By integrating physics-based knowledge into machine learning models, PIML also offers a powerful tool for understanding and optimizing tribological phenomena and thus represents a very recent and emerging trend in the domain of tribology.…”