Session: 02-04-02: Computer Methods and Reduced Order Modeling

Paper Number: 161180

161180 - Physics-Augmented Latent Fourier Neural Operator for Dynamic Response Prediction 

Fourier neural operator (FNO) models have achieved remarkable success in the analysis and response prediction of dynamic systems, yet their performance degrades with an increase in system dimensionality. For many engineering systems, there is additional information about physics and knowledge beyond pure data. Most existing pure data-driven FNO ignores these types of information, which are important for practical usage. To address these challenges, this study proposes a Physics-augmented Latent Fourier Neural Operator (PAL-FNO) framework for more efficient and scalable dynamic response prediction.

The interplay between the constraints and the regularity of solutions implies that the high-dimensional solution space often resides on a much lower-dimensional manifold. Inspired by that, learning neural operators on latent spaces consists of two steps: first, training a suitable autoencoder (AE) model to identify a latent representation for the high-dimensional inputs and outputs, and second, training an FNO model on latent space by employing the pre-trained AE decoder to project samples back to the physically interpretable high-dimensional space, where physics loss from controlling equations or boundary conditions are enforced. Through the above improvement compared to traditional classical FNO, the PAL-FNO framework not only accelerates model training due to the low dimensionality of the data on latent space but also augments the connection of output data points by physics constraints for more robust output prediction, which ensures accurate prediction under sparse labels.

It is well known that numerical derivative computing is very sensitive to noise and is thus difficult to directly implement in the constraint equations. For example, finite difference methods are widely used to calculate partial derivatives and are shown to be highly sensitive to reconstruction errors of AE. The proposed PAL-FNO includes alternative algorithms for derivative estimation and is illustrated in two numerical cases with distinct approaches. The first case introduces a smoothness module and difference loss terms during AE training that achieves a reduction of physics error from 4.69e5 to 9.30e-8 for the Burgers equation, and the other case employs additional data-driven models to approximate differentiation solvers, suppressing the initial physics error 2.25e-1 into 5.77e-6 in the wave equation.

Following this, numerical studies demonstrate an efficiency improvement with a maximum reduction in time consumption of 83.3%, in which the original size of 1024 is reduced into the latent size of 20, while the accuracy of the predicted temporal snapshots remains largely unaffected. This highlights the advantages of enhanced autoencoder training and latent-space prediction.

Presenting Author: Xuandong Lu Arizona State University

Presenting Author Biography: Xuandong Lu is a Ph.D. student at Arizona State University. His research focuses on the mechanical application machine learning, with particular interest in structural dynamics, computational fluid dynamics and physics-informed neural network.