Research in neural models inspired by mammal's visual cortex has led to many spiking neural networks such as pulse-coupled neural networks (PCNNs). These models are oscillating, spatio-temporal models stimulated with images to produce several time-based responses. This paper reviews PCNN's state of the art, covering its mathematical formulation, variants, and other simplifications found in the literature. We present several applications in which PCNN architectures have successfully addressed some fundamental image processing and computer vision challenges, including image segmentation, edge detection, medical imaging, image fusion, image compression, object recognition, and remote sensing. Results achieved in these applications suggest that the PCNN architecture generates useful perceptual information relevant to a wide variety of computer vision tasks.

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier-Stokes equations.

Woven fabrics play an essential role in everyday textiles for clothing/sportswear, water filtration, and retaining walls, to reinforcements in stiff composites for lightweight structures like aerospace, sporting, automotive, and marine industries. Several possible combinations of weave patterns and material choices, which comprise weave architecture, present a challenging question about how they could influence the physical and mechanical properties of woven fabrics and reinforced structures. In this paper, we present a novel Physics-Constrained Neural Network (PCNN) to predict the mechanical properties like the modulus of weave architectures and the inverse problem of predicting pattern/material sequence for a design/target modulus value. The inverse problem is particularly challenging as it usually requires many iterations to find the appropriate architecture using traditional optimization approaches. We show that the proposed PCNN can effectively predict weave architecture for the desired modulus with higher accuracy than several baseline models considered. We present a feature-based optimization strategy to improve the predictions using features in the Grey Level Co-occurrence Matrix (GLCM) space. We combine PCNN with this feature-based optimization to discover near-optimal weave architectures to facilitate the initial design of weave architecture. The proposed frameworks will primarily enable the woven composite analysis and optimization process, and be a starting point to introduce Knowledge-guided Neural Networks into the complex structural analysis.

With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be hindered by their limited expressiveness. On the other hand, classical black-box methods, typically relying on Neural Networks (NNs) nowadays, often achieve impressive performance, even at scale, by deriving statistical patterns from data. However, they remain completely oblivious to the underlying physical laws, which may lead to potentially catastrophic failures if decisions for real-world physical systems are based on them. Physically Consistent Neural Networks (PCNNs) were recently developed to address these aforementioned issues, ensuring physical consistency while still leveraging NNs to attain state-of-the-art accuracy. In this work, we scale PCNNs to model building temperature dynamics and propose a thorough comparison with classical gray-box and black-box methods. More precisely, we design three distinct PCNN extensions, thereby exemplifying the modularity and flexibility of the architecture, and formally prove their physical consistency. In the presented case study, PCNNs are shown to achieve state-of-the-art accuracy, even outperforming classical NN-based models despite their constrained structure. Our investigations furthermore provide a clear illustration of NNs achieving seemingly good performance while remaining completely physics-agnostic, which can be misleading in practice. While this performance comes at the cost of computational complexity, PCNNs on the other hand show accuracy improvements of 17-35% compared to all other physically consistent methods, paving the way for scalable physically consistent models with state-of-the-art performance.

We present a physics-constrained neural network (PCNN) approach to solving Maxwell's equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and charge densities J(r,t) and p(r,t) to vector and scalar potentials A(r,t) and V(r,t) from which we generate electromagnetic fields according to Maxwell's equations: B=curl(A), E=-div(V)-dA/dt. Our PCNNs satisfy hard constraints, such as div(B)=0, by construction. Soft constraints push A and V towards satisfying the Lorenz gauge.

Due to their high energy intensity, buildings play a major role in the current worldwide energy transition. Building models are ubiquitous since they are needed at each stage of the life of buildings, i.e. for design, retrofitting, and control operations. Classical white-box models, based on physical equations, are bound to follow the laws of physics but the specific design of their underlying structure might hinder their expressiveness and hence their accuracy. On the other hand, black-box models are better suited to capture nonlinear building dynamics and thus can often achieve better accuracy, but they require a lot of data and might not follow the laws of physics, a problem that is particularly common for neural network (NN) models. To counter this known generalization issue, physics-informed NNs have recently been introduced, where researchers introduce prior knowledge in the structure of NNs to ground them in known underlying physical laws and avoid classical NN generalization issues. In this work, we present a novel physics-informed NN architecture, dubbed Physically Consistent NN (PCNN), which only requires past operational data and no engineering overhead, including prior knowledge in a linear module running in parallel to a classical NN. We formally prove that such networks are physically consistent -- by design and even on unseen data -- with respect to different control inputs and temperatures outside and in neighboring zones. We demonstrate their performance on a case study, where the PCNN attains an accuracy up to $50\%$ better than a classical physics-based resistance-capacitance model on $3$-day long prediction horizons. Furthermore, despite their constrained structure, PCNNs attain similar performance to classical NNs on the validation data, overfitting the training data less and retaining high expressiveness to tackle the generalization issue.

Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were developed to reduce the required amount of training data. However, the weights of different losses from data and physical constraints are adjusted empirically in PCNNs. In this paper, a new physics-constrained neural network with the minimax architecture (PCNNMM) is proposed so that the weights of different losses can be adjusted systematically. The training of the PCNN-MM is searching the high-order saddle points of the objective function. A novel saddle point search algorithm called Dual-Dimer method is developed. It is demonstrated that the Dual-Dimer method is computationally more efficient than the gradient descent ascent method for nonconvex-nonconcave functions and provides additional eigenvalue information to verify search results. A heat transfer example also shows that the convergence of PCNN-MMs is faster than that of traditional PCNNs.

Weight pruning is a powerful technique to realize model compression. We propose PCNN, a fine-grained regular 1D pruning method. A novel index format called Sparsity Pattern Mask (SPM) is presented to encode the sparsity in PCNN. Leveraging SPM with limited pruning patterns and non-zero sequences with equal length, PCNN can be efficiently employed in hardware. Evaluated on VGG-16 and ResNet-18, our PCNN achieves the compression rate up to 8.4X with only 0.2% accuracy loss. We also implement a pattern-aware architecture in 55nm process, achieving up to 9.0X speedup and 28.39 TOPS/W efficiency with only 3.1% on-chip memory overhead of indices.

Sentiment analysis of online user generated content is important for many social media analytics tasks. Researchers have largely relied on textual sentiment analysis to develop systems to predict political elections, measure economic indicators, and so on. Recently, social media users are increasingly using images and videos to express their opinions and share their experiences. Sentiment analysis of such large scale visual content can help better extract user sentiments toward events or topics, such as those in image tweets, so that prediction of sentiment from visual content is complementary to textual sentiment analysis. Motivated by the needs in leveraging large scale yet noisy training data to solve the extremely challenging problem of image sentiment analysis, we employ Convolutional Neural Networks (CNN). We first design a suitable CNN architecture for image sentiment analysis. We obtain half a million training samples by using a baseline sentiment algorithm to label Flickr images. To make use of such noisy machine labeled data, we employ a progressive strategy to fine-tune the deep network. Furthermore, we improve the performance on Twitter images by inducing domain transfer with a small number of manually labeled Twitter images. We have conducted extensive experiments on manually labeled Twitter images. The results show that the proposed CNN can achieve better performance in image sentiment analysis than competing algorithms.