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Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates efficient numerical methods. In this paper, we propose a novel approach for solving parametric PDEs using a Finite Element Operator Network (FEONet). Our proposed method leverages the power of deep learning in conjunction with traditional numerical methods, specifically the finite element method, to solve parametric PDEs in the absence of any paired input-output training data. We demonstrate the effectiveness of our approach on several benchmark problems and show that it outperforms existing state-of-the-art methods in terms of accuracy, generalization, and computational flexibility. Our FEONet framework shows potential for application in various fields where PDEs play a crucial role in modeling complex domains with diverse boundary conditions and singular behavior. Furthermore, we provide theoretical convergence analysis to support our approach, utilizing finite element approximation in numerical analysis.

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The generation of adversarial inputs has become a crucial issue in establishing the robustness and trustworthiness of deep neural nets, especially when they are used in safety-critical application domains such as autonomous vehicles and precision medicine. However, the problem poses multiple practical challenges, including scalability issues owing to large-sized networks, and the generation of adversarial inputs that lack important qualities such as naturalness and output-impartiality. This problem shares its end goal with the task of patching neural nets where small changes in some of the network's weights need to be discovered so that upon applying these changes, the modified net produces the desirable output for a given set of inputs. We exploit this connection by proposing to obtain an adversarial input from a patch, with the underlying observation that the effect of changing the weights can also be brought about by changing the inputs instead. Thus, this paper presents a novel way to generate input perturbations that are adversarial for a given network by using an efficient network patching technique. We note that the proposed method is significantly more effective than the prior state-of-the-art techniques.

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms. In this paper, we propose a novel neural-ODE based method that uses spectral expansions in space to learn spatiotemporal DEs. The major advantage of our spectral neural DE learning approach is that it does not rely on spatial discretization, thus allowing the target spatiotemporal equations to contain long range, nonlocal spatial interactions that act on unbounded spatial domains. Our spectral approach is shown to be as accurate as some of the latest machine learning approaches for learning PDEs operating on bounded domains. By developing a spectral framework for learning both PDEs and integro-differential equations, we extend machine learning methods to apply to unbounded DEs and a larger class of problems.

An emerging direction of quantum computing is to establish meaningful quantum applications in various fields of artificial intelligence, including natural language processing (NLP). Although some efforts based on syntactic analysis have opened the door to research in Quantum NLP (QNLP), limitations such as heavy syntactic preprocessing and syntax-dependent network architecture make them impracticable on larger and real-world data sets. In this paper, we propose a new simple network architecture, called the quantum self-attention neural network (QSANN), which can compensate for these limitations. Specifically, we introduce the self-attention mechanism into quantum neural networks and then utilize a Gaussian projected quantum self-attention serving as a sensible quantum version of self-attention. As a result, QSANN is effective and scalable on larger data sets and has the desirable property of being implementable on near-term quantum devices. In particular, our QSANN outperforms the best existing QNLP model based on syntactic analysis as well as a simple classical self-attention neural network in numerical experiments of text classification tasks on public data sets. We further show that our method exhibits robustness to low-level quantum noises and showcases resilience to quantum neural network architectures.

There has been a recent emphasis on integrating physical models and deep neural networks (DNNs) for SAR target recognition, to improve performance and achieve a higher level of physical interpretability. The attributed scattering center (ASC) parameters garnered the most interest, being considered as additional input data or features for fusion in most methods. However, the performance greatly depends on the ASC optimization result, and the fusion strategy is not adaptable to different types of physical information. Meanwhile, the current evaluation scheme is inadequate to assess the model's robustness and generalizability. Thus, we propose a physics inspired hybrid attention (PIHA) mechanism and the once-for-all (OFA) evaluation protocol to address the above issues. PIHA leverages the high-level semantics of physical information to activate and guide the feature group aware of local semantics of target, so as to re-weight the feature importance based on knowledge prior. It is flexible and generally applicable to various physical models, and can be integrated into arbitrary DNNs without modifying the original architecture. The experiments involve a rigorous assessment using the proposed OFA, which entails training and validating a model on either sufficient or limited data and evaluating on multiple test sets with different data distributions. Our method outperforms other state-of-the-art approaches in 12 test scenarios with same ASC parameters. Moreover, we analyze the working mechanism of PIHA and evaluate various PIHA enabled DNNs. The experiments also show PIHA is effective for different physical information. The source code together with the adopted physical information is available at //github.com/XAI4SAR.

Advances in neural speech synthesis have brought us technology that is not only close to human naturalness, but is also capable of instant voice cloning with little data, and is highly accessible with pre-trained models available. Naturally, the potential flood of generated content raises the need for synthetic speech detection and watermarking. Recently, considerable research effort in synthetic speech detection has been related to the Automatic Speaker Verification and Spoofing Countermeasure Challenge (ASVspoof), which focuses on passive countermeasures. This paper takes a complementary view to generated speech detection: a synthesis system should make an active effort to watermark the generated speech in a way that aids detection by another machine, but remains transparent to a human listener. We propose a collaborative training scheme for synthetic speech watermarking and show that a HiFi-GAN neural vocoder collaborating with the ASVspoof 2021 baseline countermeasure models consistently improves detection performance over conventional classifier training. Furthermore, we demonstrate how collaborative training can be paired with augmentation strategies for added robustness against noise and time-stretching. Finally, listening tests demonstrate that collaborative training has little adverse effect on perceptual quality of vocoded speech.

While the design of blind image quality assessment (IQA) algorithms has improved significantly, the distribution shift between the training and testing scenarios often leads to a poor performance of these methods at inference time. This motivates the study of test time adaptation (TTA) techniques to improve their performance at inference time. Existing auxiliary tasks and loss functions used for TTA may not be relevant for quality-aware adaptation of the pre-trained model. In this work, we introduce two novel quality-relevant auxiliary tasks at the batch and sample levels to enable TTA for blind IQA. In particular, we introduce a group contrastive loss at the batch level and a relative rank loss at the sample level to make the model quality aware and adapt to the target data. Our experiments reveal that even using a small batch of images from the test distribution helps achieve significant improvement in performance by updating the batch normalization statistics of the source model.

Solutions of certain partial differential equations (PDEs) are often represented by the steepest descent curves of corresponding functionals. Minimizing movement scheme was developed in order to study such curves in metric spaces. Especially, Jordan-Kinderlehrer-Otto studied the Fokker-Planck equation in this way with respect to the Wasserstein metric space. In this paper, we propose a deep learning-based minimizing movement scheme for approximating the solutions of PDEs. The proposed method is highly scalable for high-dimensional problems as it is free of mesh generation. We demonstrate through various kinds of numerical examples that the proposed method accurately approximates the solutions of PDEs by finding the steepest descent direction of a functional even in high dimensions.

Behaviors of the synthetic characters in current military simulations are limited since they are generally generated by rule-based and reactive computational models with minimal intelligence. Such computational models cannot adapt to reflect the experience of the characters, resulting in brittle intelligence for even the most effective behavior models devised via costly and labor-intensive processes. Observation-based behavior model adaptation that leverages machine learning and the experience of synthetic entities in combination with appropriate prior knowledge can address the issues in the existing computational behavior models to create a better training experience in military training simulations. In this paper, we introduce a framework that aims to create autonomous synthetic characters that can perform coherent sequences of believable behavior while being aware of human trainees and their needs within a training simulation. This framework brings together three mutually complementary components. The first component is a Unity-based simulation environment - Rapid Integration and Development Environment (RIDE) - supporting One World Terrain (OWT) models and capable of running and supporting machine learning experiments. The second is Shiva, a novel multi-agent reinforcement and imitation learning framework that can interface with a variety of simulation environments, and that can additionally utilize a variety of learning algorithms. The final component is the Sigma Cognitive Architecture that will augment the behavior models with symbolic and probabilistic reasoning capabilities. We have successfully created proof-of-concept behavior models leveraging this framework on realistic terrain as an essential step towards bringing machine learning into military simulations.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

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