Embedded Nonlocal Operator Regression (ENOR): Quantifying model error in learning nonlocal operators

Nonlocal, integral operators have become an efficient surrogate for bottom-up homogenization, due to their ability to represent long-range dependence and multiscale effects. However, the nonlocal homogenized model has unavoidable discrepancy from the microscale model. Such errors accumulate and propagate in long-term simulations, making the resultant prediction unreliable. To develop a robust and reliable bottom-up homogenization framework, we propose a new framework, which we coin Embedded Nonlocal Operator Regression (ENOR), to learn a nonlocal homogenized surrogate model and its structural model error. This framework provides discrepancy-adaptive uncertainty quantification for homogenized material response predictions in long-term simulations. The method is built on Nonlocal Operator Regression (NOR), an optimization-based nonlocal kernel learning approach, together with an embedded model error term in the trainable kernel. Then, Bayesian inference is employed to infer the model error term parameters together with the kernel parameters. To make the problem computationally feasible, we use a multilevel delayed acceptance Markov chain Monte Carlo (MLDA-MCMC) method, enabling efficient Bayesian model calibration and model error estimation. We apply this technique to predict long-term wave propagation in a heterogeneous one-dimensional bar, and compare its performance with additive noise models. Owing to its ability to capture model error, the learned ENOR achieves improved estimation of posterior predictive uncertainty.

Data-driven Framework for Forward and Inverse Problem in Guided Waves Based Structural Healthy Monitoring Under Varying Environmental and Operating Conditions

Recently, guided wave-based techniques have garnered increased attention from researchers in the field of Structural Health Monitoring (SHM) for damage detection and quantification. Extracting features that are sensitive to changes in structural conditions has become a critical step. Guided waves, being one of the most widely used techniques, are highly responsive to structural changes caused by various types of damage. However, due to disturbances from environmental and operational conditions (EOCs) and waveforms reflected from boundaries and damage in complex systems, manually extracting features related to the system state is challenging. To address this, various neural networks, capable of automatically deriving features, have been developed and applied to system identification tasks. Among these, Convolutional Autoencoders (CAEs) have proven effective as damage detectors, projecting data efficiently into a latent space. However, existing CAE-based models for damage diagnosis often overlook the influence of EOCs, which can significantly impact model performance. In this work, a scheme that provides accurate damage level classification while estimating EOCs, such as loading conditions, making the model adaptable to varying external factors is introduced. By restructuring and combining the CAE with feedforward neural networks (FFNNs), the proposed scheme also enables signal reconstruction, a potentially valuable feature when data is limited. The method has been validated on an aluminum plate with various damage levels under different loading conditions, achieving near-perfect state classification and low-error signal reconstruction. The framework has also been tested on incomplete datasets to verify its robustness.

Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws

Neural operators (NOs) have emerged as effective tools for modeling complex physical systems in scientific machine learning. In NOs, a central characteristic is to learn the governing physical laws directly from data. In contrast to other machine learning applications, partial knowledge is often known a priori about the physical system at hand whereby quantities such as mass, energy and momentum are exactly conserved. Currently, NOs have to learn these conservation laws from data and can only approximately satisfy them due to finite training data and random noise. In this work, we introduce conservation law-encoded neural operators (clawNOs), a suite of NOs that endow inference with automatic satisfaction of such conservation laws. ClawNOs are built with a divergence-free prediction of the solution field, with which the continuity equation is automatically guaranteed. As a consequence, clawNOs are compliant with the most fundamental and ubiquitous conservation laws essential for correct physical consistency. As demonstrations, we consider a wide variety of scientific applications ranging from constitutive modeling of material deformation, incompressible fluid dynamics, to atmospheric simulation. ClawNOs significantly outperform the state-of-the-art NOs in learning efficacy, especially in small-data regimes.

Traversability Analysis for Autonomous Driving in Complex Environment: A LiDAR-based Terrain Modeling Approach

For autonomous driving, traversability analysis is one of the most basic and essential tasks. In this paper, we propose a novel LiDAR-based terrain modeling approach, which could output stable, complete and accurate terrain models and traversability analysis results. As terrain is an inherent property of the environment that does not change with different view angles, our approach adopts a multi-frame information fusion strategy for terrain modeling. Specifically, a normal distributions transform mapping approach is adopted to accurately model the terrain by fusing information from consecutive LiDAR frames. Then the spatial-temporal Bayesian generalized kernel inference and bilateral filtering are utilized to promote the stability and completeness of the results while simultaneously retaining the sharp terrain edges. Based on the terrain modeling results, the traversability of each region is obtained by performing geometric connectivity analysis between neighboring terrain regions. Experimental results show that the proposed method could run in real-time and outperforms state-of-the-art approaches.

Zero-sample surface defect detection and classification based on semantic feedback neural network

Defect detection and classification technology has changed from traditional artificial visual inspection to current intelligent automated inspection, but most of the current defect detection methods are training related detection models based on a data-driven approach, taking into account the difficulty of collecting some sample data in the industrial field. We apply zero-shot learning technology to the industrial field. Aiming at the problem of the existing "Latent Feature Guide Attribute Attention" (LFGAA) zero-shot image classification network, the output latent attributes and artificially defined attributes are different in the semantic space, which leads to the problem of model performance degradation, proposed an LGFAA network based on semantic feedback, and improved model performance by constructing semantic embedded modules and feedback mechanisms. At the same time, for the common domain shift problem in zero-shot learning, based on the idea of co-training algorithm using the difference information between different views of data to learn from each other, we propose an Ensemble Co-training algorithm, which adaptively reduces the prediction error in image tag embedding from multiple angles. Various experiments conducted on the zero-shot dataset and the cylinder liner dataset in the industrial field provide competitive results.

A self-adapting super-resolution structures framework for automatic design of GAN

With the development of deep learning, the single super-resolution image reconstruction network models are becoming more and more complex. Small changes in hyperparameters of the models have a greater impact on model performance. In the existing works, experts have gradually explored a set of optimal model parameters based on empirical values or performing brute-force search. In this paper, we introduce a new super-resolution image reconstruction generative adversarial network framework, and a Bayesian optimization method used to optimizing the hyperparameters of the generator and discriminator. The generator is made by self-calibrated convolution, and discriminator is made by convolution lays. We have defined the hyperparameters such as the number of network layers and the number of neurons. Our method adopts Bayesian optimization as a optimization policy of GAN in our model. Not only can find the optimal hyperparameter solution automatically, but also can construct a super-resolution image reconstruction network, reducing the manual workload. Experiments show that Bayesian optimization can search the optimal solution earlier than the other two optimization algorithms.

Super-Resolution Image Reconstruction Based on Self-Calibrated Convolutional GAN

With the effective application of deep learning in computer vision, breakthroughs have been made in the research of super-resolution images reconstruction. However, many researches have pointed out that the insufficiency of the neural network extraction on image features may bring the deteriorating of newly reconstructed image. On the other hand, the generated pictures are sometimes too artificial because of over-smoothing. In order to solve the above problems, we propose a novel self-calibrated convolutional generative adversarial networks. The generator consists of feature extraction and image reconstruction. Feature extraction uses self-calibrated convolutions, which contains four portions, and each portion has specific functions. It can not only expand the range of receptive fields, but also obtain long-range spatial and inter-channel dependencies. Then image reconstruction is performed, and finally a super-resolution image is reconstructed. We have conducted thorough experiments on different datasets including set5, set14 and BSD100 under the SSIM evaluation method. The experimental results prove the effectiveness of the proposed network.