Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning

Neural operators have gained significant attention recently due to their ability to approximate high-dimensional parametric maps between function spaces. At present, only parametric function approximation has been addressed in the neural operator literature. In this work we investigate incorporating parametric derivative information in neural operator training; this information can improve function approximations, additionally it can be used to improve the approximation of the derivative with respect to the parameter, which is often the key to scalable solution of high-dimensional outer-loop problems (e.g. Bayesian inverse problems). Parametric Jacobian information is formally intractable to incorporate due to its high-dimensionality, to address this concern we propose strategies based on reduced SVD, randomized sketching and the use of reduced basis surrogates. All of these strategies only require only $O(r)$ Jacobian actions to construct sample Jacobian data, and allow us to reduce the linear algebra and memory costs associated with the Jacobian training from the product of the input and output dimensions down to $O(r^2)$, where $r$ is the dimensionality associated with the dimension reduction technique. Numerical results for parametric PDE problems demonstrate that the addition of derivative information to the training problem can significantly improve the parametric map approximation, particularly given few data. When Jacobian actions are inexpensive compared to the parametric map, this information can be economically substituted for parametric map data. Additionally we show that Jacobian error approximations improve significantly with the introduction of Jacobian training data. This result opens the door to the use of derivative-informed neural operators (DINOs) in outer-loop algorithms where they can amortize the additional training data cost via repeated evaluations.

Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization

The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the variational problem in the family of two-layer networks with squared-ReLU activations, towards which we derive a semi-definite programming (SDP) relaxation. This SDP can be viewed as an approximation of the Wasserstein gradient in a broader function family including two-layer networks. By solving the convex SDP, we obtain the optimal approximation of the Wasserstein gradient direction in this class of functions. Numerical experiments including PDE-constrained Bayesian inference and parameter estimation in COVID-19 modeling demonstrate the effectiveness of the proposed method.

Scalable Multi-view Clustering with Graph Filtering

With the explosive growth of multi-source data, multi-view clustering has attracted great attention in recent years. Most existing multi-view methods operate in raw feature space and heavily depend on the quality of original feature representation. Moreover, they are often designed for feature data and ignore the rich topology structure information. Accordingly, in this paper, we propose a generic framework to cluster both attribute and graph data with heterogeneous features. It is capable of exploring the interplay between feature and structure. Specifically, we first adopt graph filtering technique to eliminate high-frequency noise to achieve a clustering-friendly smooth representation. To handle the scalability challenge, we develop a novel sampling strategy to improve the quality of anchors. Extensive experiments on attribute and graph benchmarks demonstrate the superiority of our approach with respect to state-of-the-art approaches.

A Rapid Power-iterative Root-MUSIC Estimator for Massive/Ultra-massive MIMO Receiver

For a passive direction of arrival (DOA) measurement system using massive multiple input multiple output (MIMO), the complexity of the covariance matrix decompositionbased DOA measurement method is extremely high. To significantly reduce the computational complexity, two strategies are proposed. Firstly, a rapid power-iterative estimation of signal parameters via rotational invariance technique (RPI-ESPRIT) method is proposed, which not only reduces the complexity but also achieves good directional measurement results. However, the general complexity is still high. In order to further the complexity, a rapid power-iterative root Multiple Signal Classification (RPIRoot-MUSIC) method is proposed. Simulation results show that the two proposed methods outperform the classical DOA estimation method in terms of computational complexity. In particular, the lowest complexity achieved by the RPI-Root-MUSIC method is about two-order-magnitude lower than that of Root-MUSIC in terms of FLOP. In addition, it is verified that the initial vector and relative error have a substantial effect on the performance of computational complexity.

Image Gradient Decomposition for Parallel and Memory-Efficient Ptychographic Reconstruction

Ptychography is a popular microscopic imaging modality for many scientific discoveries and sets the record for highest image resolution. Unfortunately, the high image resolution for ptychographic reconstruction requires significant amount of memory and computations, forcing many applications to compromise their image resolution in exchange for a smaller memory footprint and a shorter reconstruction time. In this paper, we propose a novel image gradient decomposition method that significantly reduces the memory footprint for ptychographic reconstruction by tessellating image gradients and diffraction measurements into tiles. In addition, we propose a parallel image gradient decomposition method that enables asynchronous point-to-point communications and parallel pipelining with minimal overhead on a large number of GPUs. Our experiments on a Titanate material dataset (PbTiO3) with 16632 probe locations show that our Gradient Decomposition algorithm reduces memory footprint by 51 times. In addition, it achieves time-to-solution within 2.2 minutes by scaling to 4158 GPUs with a super-linear speedup at 364% efficiency. This performance is 2.7 times more memory efficient, 9 times more scalable and 86 times faster than the state-of-the-art algorithm.

A RIS-Based Passive DOA Estimation Method for Integrated Sensing and Communication System

Integrated sensing and communication (ISAC) system has received growing attention, especially in the context of B5G/6G development. Combining the reconfigurable intelligent surface (RIS) with wireless communication process, a novel passive sensing technique is formulated in this paper to estimate the direction of arrival (DOA) of the targets, where the control matrix of the RIS is used to to realize the multiple measurements with only one full-functional receiving channel. Unlike the existing methods, the interference signals introduced by wireless communication are also considered. To improve the DOA estimation, a novel atomic norm-based method is proposed to remove the interference signals by the sparse reconstruction. The DOA is estimated after the interference removal by a novel Hankel-based multiple signal classification (MUSIC) method. Then, an optimization method is also developed for the measurement matrix to reduce the power interference signals and keep the measurement matrix's randomness, which guarantees the performance of the sparse reconstruction. Finally, we derive the theoretical Cram\'{e}r-Rao lower bound (CRLB) for the proposed system on the DOA estimation. Simulation results show that the proposed method outperforms the existing methods in the DOA estimation and shows the corresponding CRLB with different distributions of the sensing node. The code about the proposed method is available online https://github.com/chenpengseu/PassiveDOA-ISAC-RIS.git.

Learning Video Salient Object Detection Progressively from Unlabeled Videos

Recent deep learning-based video salient object detection (VSOD) has achieved some breakthrough, but these methods rely on expensive annotated videos with pixel-wise annotations, weak annotations, or part of the pixel-wise annotations. In this paper, based on the similarities and the differences between VSOD and image salient object detection (SOD), we propose a novel VSOD method via a progressive framework that locates and segments salient objects in sequence without utilizing any video annotation. To use the knowledge learned in the SOD dataset for VSOD efficiently, we introduce dynamic saliency to compensate for the lack of motion information of SOD during the locating process but retain the same fine segmenting process. Specifically, an algorithm for generating spatiotemporal location labels, which consists of generating high-saliency location labels and tracking salient objects in adjacent frames, is proposed. Based on these location labels, a two-stream locating network that introduces an optical flow branch for video salient object locating is presented. Although our method does not require labeled video at all, the experimental results on five public benchmarks of DAVIS, FBMS, ViSal, VOS, and DAVSOD demonstrate that our proposed method is competitive with fully supervised methods and outperforms the state-of-the-art weakly and unsupervised methods.

SDOAnet: An Efficient Deep Learning-Based DOA Estimation Network for Imperfect Array

Direction of arrival (DOA) estimation is a fundamental problem in both conventional radar and wireless communication applications and emerging integrated sensing and communication (ISAC) systems. Due to many imperfect factors in the low-cost systems, including the antenna position perturbations, the inconsistent gains/phases, the mutual coupling effect, the nonlinear amplifier effect, etc., the performance of the DOA estimation often degrades significantly. To characterize the realistic array more accurately, a novel deep learning (DL)-based DOA estimation method named super-resolution DOA network (SDOAnet) is proposed in this paper. Different from the existing DL-based DOA methods, our proposed SDOAnet employs the sampled received signals, instead of the covariance matrices of the received signals, as the input of the convolution layers for extracting data features. Moreover, the output of SDOAnet is a vector that is independent of the DOA of targets but can be used to estimate their spatial spectrum. As a result, the same training network can be applied with any number of targets, which significantly reduce the implementation complexity. At last, the convergence speed of our SDOAnet with a low-dimension network structure is much faster than existing DL-based methods. Simulation results show that the proposed SDOAnet outperforms the existing DOA estimation methods with the effect of the imperfect array. The code about the SDOAnet is available online https://github.com/chenpengseu/SDOAnet.git.

Reconfigurable Intelligent Surface Aided Sparse DOA Estimation Method With Non-ULA

The direction of arrival (DOA) estimation problem is addressed in this letter. A reconfigurable intelligent surface (RIS) aided system for the DOA estimation is proposed. Unlike traditional DOA estimation systems, a low-cost system with only one complete functional receiver is given by changing the phases of the reflected signals at the RIS elements to realize the multiple measurements. Moreover, an atomic norm-based method is proposed for the DOA estimation by exploiting the target sparsity in the spatial domain and solved by a semi-definite programming (SDP) method. Furthermore, the RIS elements can be any geometry array for practical consideration, so a transformation matrix is formulated and different from the conventional SDP method. Simulation results show that the proposed method can estimate the DOA more accurately than the existing methods in the non-uniform linear RIS array.

Efficient DOA Estimation Method for Reconfigurable Intelligent Surfaces Aided UAV Swarm

The conventional direction of arrival (DOA) estimation methods are performed with multiple receiving channels. In this paper, a changeling DOA estimation problem is addressed in a different scenario with only one full-functional receiving channel. A new unmanned aerial vehicle (UAV) swarm system using multiple lifted reconfigurable intelligent surface (RIS) is proposed for the DOA estimation. The UAV movement degrades the DOA estimation performance significantly, and the existing atomic norm minimization (ANM) methods cannot be used in the scenario with array perturbation. Specifically, considering the position perturbation of UAVs, a new atomic norm-based DOA estimation method is proposed, where an atomic norm is defined with the parameter of the position perturbation. Then, a customized semi-definite programming (SDP) method is derived to solve the atomic norm-based method, where different from the traditional SDP method, an additional transforming matrix is formulated. Moreover, a gradient descent method is applied to refine the estimated DOA and the position perturbation further. Simulation results show that the proposed method achieves much better DOA estimation performance in the RIS-aided UAV swarm system with only one receiving channel than various benchmark schemes.