Ishan D. Khurjekar

Ishan Khurjekar, Indrashish Saha, Lori Graham-Brady et al.

Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference with ML models suffer from error accumulation over successive predictions, limiting their long-term accuracy. We propose a deep ensemble framework to address this challenge, where multiple ML surrogate models with random weight initializations are trained in parallel and aggregated during inference. This approach leverages the diversity of model predictions to mitigate error propagation while retaining the autoregressive strategies ability to capture the system's time dependent relations. We validate the framework on three PDE-driven dynamical systems - stress evolution in heterogeneous microstructures, Gray-Scott reaction-diffusion, and planetary-scale shallow water system - demonstrating consistent reduction in error accumulation over time compared to individual models. Critically, the method requires only a few time steps as input, enabling full trajectory predictions with inference times significantly faster than numerical solvers. Our results highlight the robustness of ensemble methods in diverse physical systems and their potential as efficient and accurate alternatives to traditional solvers. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

Ishan D. Khurjekar, Joel B. Harley

Guided wave testing is a popular approach for monitoring the structural integrity of infrastructures. We focus on the primary task of damage detection, where signal processing techniques are commonly employed. The detection performance is affected by a mismatch between the wave propagation model and experimental wave data. External variations, such as temperature, which are difficult to model, also affect the performance. While deep learning models can be an alternative detection method, there is often a lack of real-world training datasets. In this work, we counter this challenge by training an ensemble of variational autoencoders only on simulation data with a wave physics-guided adversarial component. We set up an experiment with non-uniform temperature variations to test the robustness of the methods. We compare our scheme with existing deep learning detection schemes and observe superior performance on experimental data.

Ishan D. Khurjekar, Joel B. Harley

Guided ultrasonic wave localization uses spatially distributed multistatic sensor arrays and generalized beamforming strategies to detect and locate damage across a structure. The propagation channel is often very complex. Methods can compare data with models of wave propagation to locate damage. Yet, environmental uncertainty (e.g., temperature or stress variations) often degrade accuracies. This paper uses an uncertainty-aware deep neural network framework to learn robust localization models and represent uncertainty. We use mixture density networks to generate damage location distributions based on training data uncertainty. This is in contrast with most localization methods, which output point estimates. We compare our approach with matched field processing (MFP), a generalized beamforming framework. The proposed approach achieves a localization error of 0.0625 m as compared to 0.1425 m with MFP when data has environmental uncertainty and noise. We also show that the predictive uncertainty scales as environmental uncertainty increases to provide a statistically meaningful metric for assessing localization accuracy.

Ishan D. Khurjekar, Joel B. Harley

Ultrasonic guided waves are commonly used to localize structural damage in infrastructures such as buildings, airplanes, bridges. Damage localization can be viewed as an inverse problem. Physical model based techniques are popular for guided wave based damage localization. The performance of these techniques depend on the degree of faithfulness with which the physical model describes wave propagation. External factors such as environmental variations and random noise are a source of uncertainty in wave propagation. The physical modeling of uncertainty in an inverse problem is still a challenging problem. In this work, we propose a deep learning based model for robust damage localization in presence of uncertainty. Wave data with uncertainty is simulated to reflect variations due to external factors and Gaussian noise is added to reflect random noise in the environment. After evaluating the localization error on test data with uncertainty, we observe that the deep learning model trained with uncertainty can learn robust representations. The approach shows potential for dealing with uncertainty in physical science problems using deep learning models.