Toros Arikan

Amir Weiss, Toros Arikan, Gregory W. Wornell

Direct localization (DLOC) methods, which use the observed data to localize a source at an unknown position in a one-step procedure, generally outperform their indirect two-step counterparts (e.g., using time-difference of arrivals). However, underwater acoustic DLOC methods require prior knowledge of the environment, and are computationally costly, hence slow. We propose, what is to the best of our knowledge, the first data-driven DLOC method. Inspired by classical and contemporary optimal model-based DLOC solutions, and leveraging the capabilities of convolutional neural networks (CNNs), we devise a holistic CNN-based solution. Our method includes a specifically-tailored input structure, architecture, loss function, and a progressive training procedure, which are of independent interest in the broader context of machine learning. We demonstrate that our method outperforms attractive alternatives, and asymptotically matches the performance of an oracle optimal model-based solution.

Gabriel Díaz Ramos, Toros Arikan, Richard G. Baraniuk

The Obstacle Avoiding Rectilinear Steiner Minimum Tree (OARSMT) problem, which seeks the shortest interconnection of a given number of terminals in a rectilinear plane while avoiding obstacles, is a critical task in integrated circuit design, network optimization, and robot path planning. Since OARSMT is NP-hard, exact algorithms scale poorly with the number of terminals, leading practical solvers to sacrifice accuracy for large problems. We propose MazeNet, a deep learning-based method that learns to solve the OARSMT from data. MazeNet reframes OARSMT as a maze-solving task that can be addressed with a recurrent convolutional neural network (RCNN). A key hallmark of MazeNet is its scalability: we only need to train the RCNN blocks on mazes with a small number of terminals; larger mazes can be solved by replicating the same pre-trained blocks to create a larger network. Across a wide range of experiments, MazeNet achieves perfect OARSMT-solving accuracy, significantly reduces runtime compared to classical exact algorithms, and can handle more terminals than state-of-the-art approximate algorithms.