Using an amalgamation of techniques from classical radar, computer vision, and deep learning, we characterize our ongoing data-driven approach to space-time adaptive processing (STAP) radar. We generate a rich example dataset of received radar signals by randomly placing targets of variable strengths in a predetermined region using RFView, a site-specific radio frequency modeling and simulation tool developed by ISL Inc. For each data sample within this region, we generate heatmap tensors in range, azimuth, and elevation of the output power of a minimum variance distortionless response (MVDR) beamformer, which can be replaced with a desired test statistic. These heatmap tensors can be thought of as stacked images, and in an airborne scenario, the moving radar creates a sequence of these time-indexed image stacks, resembling a video. Our goal is to use these images and videos to detect targets and estimate their locations, a procedure reminiscent of computer vision algorithms for object detection$-$namely, the Faster Region-Based Convolutional Neural Network (Faster R-CNN). The Faster R-CNN consists of a proposal generating network for determining regions of interest (ROI), a regression network for positioning anchor boxes around targets, and an object classification algorithm; it is developed and optimized for natural images. Our ongoing research will develop analogous tools for heatmap images of radar data. In this regard, we will generate a large, representative adaptive radar signal processing database for training and testing, analogous in spirit to the COCO dataset for natural images. As a preliminary example, we present a regression network in this paper for estimating target locations to demonstrate the feasibility of and significant improvements provided by our data-driven approach.
Recently Reinforcement Learning (RL) has been applied as an anti-adversarial remedy in wireless communication networks. However, studying the RL-based approaches from the adversary's perspective has received little attention. Additionally, RL-based approaches in an anti-adversary or adversarial paradigm mostly consider single-channel communication (either channel selection or single channel power control), while multi-channel communication is more common in practice. In this paper, we propose a multi-agent adversary system (MAAS) for modeling and analyzing adversaries in a wireless communication scenario by careful design of the reward function under realistic communication scenarios. In particular, by modeling the adversaries as learning agents, we show that the proposed MAAS is able to successfully choose the transmitted channel(s) and their respective allocated power(s) without any prior knowledge of the sender strategy. Compared to the single-agent adversary (SAA), multi-agents in MAAS can achieve significant reduction in signal-to-noise ratio (SINR) under the same power constraints and partial observability, while providing improved stability and a more efficient learning process. Moreover, through empirical studies we show that the results in simulation are close to the ones in communication in reality, a conclusion that is pivotal to the validity of performance of agents evaluated in simulations.
Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients. The accuracy of the model is assessed using statistical, comparison-based similarity and physics-based metrics. The training data set is produced from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow. The performance of this lossy data compression scheme is evaluated not only with unseen data from the stationary, isotropic turbulent flow, but also with data from decaying isotropic turbulence, and a Taylor-Green vortex flow. Defining the compression ratio (CR) as the ratio of original data size to the compressed one, the results show that our model based on vector quantization can offer CR $=85$ with a mean square error (MSE) of $O(10^{-3})$, and predictions that faithfully reproduce the statistics of the flow, except at the very smallest scales where there is some loss. Compared to the recent study based on a conventional autoencoder where compression is performed in a continuous space, our model improves the CR by more than $30$ percent, and reduces the MSE by an order of magnitude. Our compression model is an attractive solution for situations where fast, high quality and low-overhead encoding and decoding of large data are required.
We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and global statistical invariants of velocity gradient tensor. The accuracy of the model is assessed using statistical and physics-based metrics. The data set comes from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow in a cubic box. Since the size of the dataset is memory intensive, we first generate a low-dimensional representation of the velocity data, and then pass it to a sequence prediction network that learns the spatial and temporal correlations of the underlying data. The dimensionality reduction is performed via extraction using Vector-Quantized Autoencoder (VQ-AE), which learns the discrete latent variables. For the sequence forecasting, the idea of Transformer architecture from natural language processing is used, and its performance compared against more standard Recurrent Networks (such as Convolutional LSTM). These architectures are designed and trained to perform a sequence to sequence multi-class classification task in which they take an input sequence with a fixed length (k) and predict a sequence with a fixed length (p), representing the future time instants of the flow. Our results for the short-term predictions show that the accuracy of results for both models deteriorates across predicted snapshots due to autoregressive nature of the predictions. Based on our diagnostics tests, the trained Conv-Transformer model outperforms the Conv-LSTM one and can accurately, both quantitatively and qualitatively, retain the large scales and capture well the inertial scales of flow but fails at recovering the small and intermittent fluid motions.
Numerous physical systems are described by ordinary or partial differential equations whose solutions are given by holomorphic or meromorphic functions in the complex domain. In many cases, only the magnitude of these functions are observed on various points on the purely imaginary jw-axis since coherent measurement of their phases is often expensive. However, it is desirable to retrieve the lost phases from the magnitudes when possible. To this end, we propose a physics-infused deep neural network based on the Blaschke products for phase retrieval. Inspired by the Helson and Sarason Theorem, we recover coefficients of a rational function of Blaschke products using a Blaschke Product Neural Network (BPNN), based upon the magnitude observations as input. The resulting rational function is then used for phase retrieval. We compare the BPNN to conventional deep neural networks (NNs) on several phase retrieval problems, comprising both synthetic and contemporary real-world problems (e.g., metamaterials for which data collection requires substantial expertise and is time consuming). On each phase retrieval problem, we compare against a population of conventional NNs of varying size and hyperparameter settings. Even without any hyper-parameter search, we find that BPNNs consistently outperform the population of optimized NNs in scarce data scenarios, and do so despite being much smaller models. The results can in turn be applied to calculate the refractive index of metamaterials, which is an important problem in emerging areas of material science.
We propose Characteristic Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of the latent state as the solution to an ODE, the proposed C-NODE models the evolution of the latent state as the solution of a family of first-order quasi-linear partial differential equations (PDE) on their characteristics, defined as curves along which the PDEs reduce to ODEs. The reduction, in turn, allows the application of the standard frameworks for solving ODEs to PDE settings. Additionally, the proposed framework can be cast as an extension of existing NODE architectures, thereby allowing the use of existing black-box ODE solvers. We prove that the C-NODE framework extends the classical NODE by exhibiting functions that cannot be represented by NODEs but are representable by C-NODEs. We further investigate the efficacy of the C-NODE framework by demonstrating its performance in many synthetic and real data scenarios. Empirical results demonstrate the improvements provided by the proposed method for CIFAR-10, SVHN, and MNIST datasets under a similar computational budget as the existing NODE methods.
A long-standing challenge in Recommender Systems (RCs) is the data sparsity problem that often arises when users rate very few items. Multi-Target Multi-Domain Recommender Systems (MTMDR) aim to improve the recommendation performance in multiple domains simultaneously. The existing works assume that the data of different domains can be fully shared, and the computation can be performed in a centralized manner. However, in many realistic scenarios, separate recommender systems are operated by different organizations, which do not allow the sharing of private data, models, and recommendation tasks. This work proposes an MTMDR based on Assisted AutoEncoders (AAE) and Multi-Target Assisted Learning (MTAL) to help organizational learners improve their recommendation performance simultaneously without sharing sensitive assets. Moreover, AAE has a broad application scope since it allows explicit or implicit feedback, user- or item-based alignment, and with or without side information. Extensive experiments demonstrate that our method significantly outperforms the case where each domain is locally trained, and it performs competitively with the centralized training where all data are shared. As a result, AAE can effectively integrate organizations from different domains to form a community of shared interest.
We propose an asymmetric affinity score for representing the complexity of utilizing the knowledge of one task for learning another one. Our method is based on the maximum bipartite matching algorithm and utilizes the Fisher Information matrix. We provide theoretical analyses demonstrating that the proposed score is mathematically well-defined, and subsequently use the affinity score to propose a novel algorithm for the few-shot learning problem. In particular, using this score, we find relevant training data labels to the test data and leverage the discovered relevant data for episodically fine-tuning a few-shot model. Results on various few-shot benchmark datasets demonstrate the efficacy of the proposed approach by improving the classification accuracy over the state-of-the-art methods even when using smaller models.
We introduce and demonstrate a semi-empirical procedure for determining approximate objective functions suitable for optimizing arbitrarily parameterized proposal distributions in MCMC methods. Our proposed Ab Initio objective functions consist of the weighted combination of functions following constraints on their global optima and of coordinate invariance that we argue should be upheld by general measures of MCMC efficiency for use in proposal optimization. The coefficients of Ab Initio objective functions are determined so as to recover the optimal MCMC behavior prescribed by established theoretical analysis for chosen reference problems. Our experimental results demonstrate that Ab Initio objective functions maintain favorable performance and preferable optimization behavior compared to existing objective functions for MCMC optimization when optimizing highly expressive proposal distributions. We argue that Ab Initio objective functions are sufficiently robust to enable the confident optimization of MCMC proposal distributions parameterized by deep generative networks that extend beyond the traditional limitations of individual MCMC schemes.