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With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned representation. As one example, in many applications that involve a signal propagating through physical media (e.g., optics, acoustics, fluid dynamics, etc.), it is known that the dynamics of the signal must satisfy constraints imposed by the wave equation. Here we propose a matrix factorization technique that decomposes such signals into a sum of components, where each component is regularized to ensure that it nearly satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality. Through this line of work we establish theoretical connections between wave-informed learning and filtering theory in signal processing. We further demonstrate the application of this work on modal analysis problems commonly arising in structural diagnostics and prognostics. 

Ultrasonic wavefields are widely employed in nondestructive testing and structural health monitoring to detect and evaluate structural damage. However, measuring wavefields continuously throughout space poses challenges and can be costly. To address this, we propose a novel approach that combines the wave equation with computer vision algorithms to visualize wavefields. Our algorithm incorporates the wave equation, which encapsulates our knowledge of wave propagation, to infer the wavefields in regions where direct measurement is not feasible. Specifically, we focus on reconstructing wavefields from partial measurements, where the wavefield data from large continuous regions are missing. The algorithm is tested on experimental data demonstrating its effectiveness in reconstructing the wavefields at unmeasured regions. This also benefits in reducing the need for expensive equipment and enhancing the accuracy of structural health monitoring at a lower cost. The results highlight the potential of our approach to advance ultrasonic wavefield imaging capabilities and open new avenues for Nondestructive testing and structural health monitoring. 

Recent advancements in physics-informed machine learning have contributed to solving partial differential equations through means of a neural network. Following this, several physics-informed neural network works have followed to solve inverse problems arising in structural health monitoring. Other works involving physics-informed neural networks solve the wave equation with partial data and modeling wavefield data generator for efficient sound data generation. While a lot of work has been done to show that partial differential equations can be solved and identified using a neural network, little work has been done the same with more basic machine learning (ML) models. The advantage with basic ML models is that the parameters learned in a simpler model are both more interpretable and extensible. For applications such as ultrasonic nondestructive evaluation, this interpretability is essential for trustworthiness of the methods and characterization of the material system under test. In this work, we show an interpretable, physics-informed representation learning framework that can analyze data across multiple dimensions (e.g., two dimensions of space and one dimension of time). The algorithm comes with convergence guarantees. In addition, our algorithm provides interpretability of the learned model as the parameters correspond to the individual solutions extracted from data. We demonstrate how this algorithm functions with wavefield videos. 

Taking an answer and its context as input, sequence-to-sequence models have made considerable progress on question generation. However, we observe that these approaches often generate wrong question words or keywords and copy answer-irrelevant words from the input. We believe that lacking global question semantics and exploiting answer position-awareness not well are the key root causes. In this paper, we propose a neural question generation model with two general modules: sentence-level semantic matching and answer position inferring. Further, we enhance the initial state of the decoder by leveraging the answer-aware gated fusion mechanism. Experimental results demonstrate that our model outperforms the state-of-the-art (SOTA) models on SQuAD and MARCO datasets. Owing to its generality, our work also improves the existing models significantly. 

We propose a deep reinforcement learning (DRL) methodology for the tracking, obstacle avoidance, and formation control of nonholonomic robots. By separating vision-based control into a perception module and a controller module, we can train a DRL agent without sophisticated physics or 3D modeling. In addition, the modular framework averts daunting retrains of an image-to-action end-to-end neural network, and provides flexibility in transferring the controller to different robots. First, we train a convolutional neural network (CNN) to accurately localize in an indoor setting with dynamic foreground/background. Then, we design a new DRL algorithm named Momentum Policy Gradient (MPG) for continuous control tasks and prove its convergence. We also show that MPG is robust at tracking varying leader movements and can naturally be extended to problems of formation control. Leveraging reward shaping, features such as collision and obstacle avoidance can be easily integrated into a DRL controller. 

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appropriate choice for the centering and scaling procedure within the BN transformation, particularly if ReLU follows the normalization step. We present a Generalized Batch Normalization (GBN) transformation, which can utilize a variety of alternative deviation measures for scaling and statistics for centering, choices which naturally arise from the theory of generalized deviation measures and risk theory in general. When used in conjunction with the ReLU non- linearity, the underlying risk theory suggests natural, arguably optimal choices for the deviation measure and statistic. Utilizing the suggested deviation measure and statistic, we show experimentally that training is accelerated more so than with conventional BN, often with improved error rate as well. Overall, we propose a more flexible BN transformation supported by a complimentary theoretical framework that can potentially guide design choices. 

Discovering the latent topics within texts has been a fundamental task for many applica- tions. However, conventional topic models suffer different problems in different settings. The Latent Dirichlet Allocation (LDA) may not work well for short texts due to the data sparsity (i.e., the sparse word co-occurrence patterns in short documents). The Biterm Topic Model (BTM) learns topics by mod- eling the word-pairs named biterms in the whole corpus. This assumption is very strong when documents are long with rich topic in- formation and do not exhibit the transitivity of biterms. In this paper, we propose a novel way called GraphBTM to represent biterms as graphs and design Graph Convolutional Net- works (GCNs) with residual connections to extract transitive features from biterms. To overcome the data sparsity of LDA and the strong assumption of BTM, we sample a fixed number of documents to form a mini-corpus as a training instance. We also propose a dataset called All News extracted from (Thompson, 2017), in which documents are much longer than 20 Newsgroups. We present an amortized variational inference method for GraphBTM. Our method generates more coherent topics compared with previous approaches. Exper- iments show that the sampling strategy im- proves performance by a large margin. 

Discovering the latent topics within texts has been a fundamental task for many applica- tions. However, conventional topic models suffer different problems in different settings. The Latent Dirichlet Allocation (LDA) may not work well for short texts due to the data sparsity (i.e., the sparse word co-occurrence patterns in short documents). The Biterm Topic Model (BTM) learns topics by mod- eling the word-pairs named biterms in the whole corpus. This assumption is very strong when documents are long with rich topic in- formation and do not exhibit the transitivity of biterms. In this paper, we propose a novel way called GraphBTM to represent biterms as graphs and design Graph Convolutional Net- works (GCNs) with residual connections to extract transitive features from biterms. To overcome the data sparsity of LDA and the strong assumption of BTM, we sample a fixed number of documents to form a mini-corpus as a training instance. We also propose a dataset called All News extracted from (Thompson, 2017), in which documents are much longer than 20 Newsgroups. We present an amortized variational inference method for GraphBTM. Our method generates more coherent topics compared with previous approaches. Exper- iments show that the sampling strategy im- proves performance by a large margin.