We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy of the system. Additionally, we modify the neural network output such that the boundary conditions associated with the problem are exactly satisfied. Compared to conventional residual based PINN, the proposed approach has two major advantages. First, the imposition of boundary conditions is relatively simpler and more robust. Second, the order of derivatives present in the functional form of the variational energy is of lower order than in the residual form. Hence, training the network is faster. To compute the total variational energy of the system, an efficient scheme that takes as input a geometry described by spline based CAD model and employs Gauss quadrature rules for numerical integration has been proposed. Moreover, we utilize the concept of transfer learning to obtain the crack path in an efficient manner. The proposed approach is used to solve four fracture mechanics problems. For all the examples, results obtained using the proposed approach match closely with the results available in the literature. For the first two examples, we compare the results obtained using the proposed approach with the conventional residual based neural network results. For both the problems, the proposed approach is found to yield better accuracy compared to conventional residual based PINN algorithms.

In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding of a numerical algorithm into a neural network form, resulting in a substantial reduction of the computational complexity. In this paper, we consider the recovery of a target signal with the aid of a correlated signal, the so-called side information (SI), and propose a deep unfolding model that incorporates SI. The proposed model is used to learn coupled representations of correlated signals from different modalities, enabling the recovery of multimodal data at a low computational cost. As such, our work introduces the first deep unfolding method with SI, which actually comes from a different modality. We apply our model to reconstruct near-infrared images from undersampled measurements given RGB images as SI. Experimental results demonstrate the superior performance of the proposed framework against single-modal deep learning methods that do not use SI, multimodal deep learning designs, and optimization algorithms.

We address the problem of unsupervised domain adaptation (UDA) by learning a cross-domain agnostic embedding space, where the distance between the probability distributions of the two source and target visual domains is minimized. We use the output space of a shared cross-domain deep encoder to model the embedding space anduse the Sliced-Wasserstein Distance (SWD) to measure and minimize the distance between the embedded distributions of two source and target domains to enforce the embedding to be domain-agnostic.Additionally, we use the source domain labeled data to train a deep classifier from the embedding space to the label space to enforce the embedding space to be discriminative.As a result of this training scheme, we provide an effective solution to train the deep classification network on the source domain such that it will generalize well on the target domain, where only unlabeled training data is accessible. To mitigate the challenge of class matching, we also align corresponding classes in the embedding space by using high confidence pseudo-labels for the target domain, i.e. assigning the class for which the source classifier has a high prediction probability. We provide theoretical justification as well as experimental results on UDA benchmark tasks to demonstrate that our method is effective and leads to state-of-the-art performance.

Research on style transfer and domain translation has clearly demonstrated the ability of deep learning-based algorithms to manipulate images in terms of artistic style. More recently, several attempts have been made to extend such approaches to music (both symbolic and audio) in order to enable transforming musical style in a similar manner. In this study, we focus on symbolic music with the goal of altering the 'style' of a piece while keeping its original 'content'. As opposed to the current methods, which are inherently restricted to be unsupervised due to the lack of 'aligned' data (i.e. the same musical piece played in multiple styles), we develop the first fully supervised algorithm for this task. At the core of our approach lies a synthetic data generation scheme which allows us to produce virtually unlimited amounts of aligned data, and hence avoid the above issue. In view of this data generation scheme, we propose an encoder-decoder model for translating symbolic music accompaniments between a number of different styles. Our experiments show that our models, although trained entirely on synthetic data, are capable of producing musically meaningful accompaniments even for real (non-synthetic) MIDI recordings.

Graph Convolution Networks (GCNs) are becoming more and more popular for learning node representations on graphs. Though there exist various developments on sampling and aggregation to accelerate the training process and improve the performances, limited works focus on dealing with the dimensional information imbalance of node representations. To bridge the gap, we propose a method named Dimensional reweighting Graph Convolution Network (DrGCN). We theoretically prove that our DrGCN can guarantee to improve the stability of GCNs via mean field theory. Our dimensional reweighting method is very flexible and can be easily combined with most sampling and aggregation techniques for GCNs. Experimental results demonstrate its superior performances on several challenging transductive and inductive node classification benchmark datasets. Our DrGCN also outperforms existing models on an industrial-sized Alibaba recommendation dataset.

Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as operators on probability distributions for observed data, we show that the distribution of outputs for any node in a neural network can be interpreted as a nonlinear projection along hypersurfaces defined by level surfaces over the input data space. We utilize these descriptions to provide new interpretation for phenomena such as nonlinearity, pooling, activation functions, and adversarial examples in neural network-based learning problems.

Machine learning is often used in virtual screening to find compounds that are pharmacologically active on a target protein. The weave module is a type of graph convolutional deep neural network that uses not only features focusing on atoms alone (atom features) but also features focusing on atom pairs (pair features); thus, it can consider information of nonadjacent atoms. However, the correlation between the distance on the graph and the three-dimensional coordinate distance is uncertain. In this paper, we propose three improvements for modifying the weave module. First, the distances between ring atoms on the graph were modified to bring the distances on the graph closer to the coordinate distance. Second, different weight matrices were used depending on the distance on the graph in the convolution layers of the pair features. Finally, a weighted sum, by distance, was used when converting pair features to atom features. The experimental results show that the performance of the proposed method is slightly better than that of the weave module, and the improvement in the distance representation might be useful for compound activity prediction.

We will first briefly consider how DL has contributed to the research on visual object recognition. In the main part we will assess whether DL could also help us to clarify the computations underlying higher cognitive functions such as Theory of Mind. In addition, we will compare the objectives and learning signals of brains and machines, leading us to conclude that simply scaling up the current DL algorithms will most likely not lead to human level Theory of Mind.

This article studies the financial time series data processing for machine learning. It introduces the most frequent scaling methods, then compares the resulting stationarity and preservation of useful information for trend forecasting. It proposes an empirical test based on the capability to learn simple data relationship with simple models. It also speaks about the data split method specific to time series, avoiding unwanted overfitting and proposes various labelling for classification and regression.

Convolutional Neural Networks (CNNs) have had great success in many machine vision as well as machine audition tasks. Many image recognition network architectures have consequently been adapted for audio processing tasks. However, despite some successes, the performance of many of these did not translate from the image to the audio domain. For example, very deep architectures such as ResNet and DenseNet, which significantly outperform VGG in image recognition, do not perform better in audio processing tasks such as Acoustic Scene Classification (ASC). In this paper, we investigate the reasons why such powerful architectures perform worse in ASC compared to simpler models (e.g., VGG). To this end, we analyse the receptive field (RF) of these CNNs and demonstrate the importance of the RF to the generalization capability of the models. Using our receptive field analysis, we adapt both ResNet and DenseNet, achieving state-of-the-art performance and eventually outperforming the VGG-based models. We introduce systematic ways of adapting the RF in CNNs, and present results on three data sets that show how changing the RF over the time and frequency dimensions affects a model's performance. Our experimental results show that very small or very large RFs can cause performance degradation, but deep models can be made to generalize well by carefully choosing an appropriate RF size within a certain range.