PolyARBerNN: A Neural Network Guided Solver and Optimizer for Bounded Polynomial Inequalities

Constraints solvers play a significant role in the analysis, synthesis, and formal verification of complex embedded and cyber-physical systems. In this paper, we study the problem of designing a scalable constraints solver for an important class of constraints named polynomial constraint inequalities (also known as non-linear real arithmetic theory). In this paper, we introduce a solver named PolyARBerNN that uses convex polynomials as abstractions for highly nonlinear polynomials. Such abstractions were previously shown to be powerful to prune the search space and restrict the usage of sound and complete solvers to small search spaces. Compared with the previous efforts on using convex abstractions, PolyARBerNN provides three main contributions namely (i) a neural network guided abstraction refinement procedure that helps selecting the right abstraction out of a set of pre-defined abstractions, (ii) a Bernstein polynomial-based search space pruning mechanism that can be used to compute tight estimates of the polynomial maximum and minimum values which can be used as an additional abstraction of the polynomials, and (iii) an optimizer that transforms polynomial objective functions into polynomial constraints (on the gradient of the objective function) whose solutions are guaranteed to be close to the global optima. These enhancements together allowed the PolyARBerNN solver to solve complex instances and scales more favorably compared to the state-of-art non-linear real arithmetic solvers while maintaining the soundness and completeness of the resulting solver. In particular, our test benches show that PolyARBerNN achieved 100X speedup compared with Z3 8.9, Yices 2.6, and NASALib (a solver that uses Bernstein expansion to solve multivariate polynomial constraints) on a variety of standard test benches

Learning-Based Communication Systems

Connecting people offers opportunities to build communities of any size and consequently, brings the world closer together. Conventionally, the connectivity has happened through traditional radio-frequency communication methods. However, the ever-increasing demand for higher data-rate communications and the explosion of advanced wireless applications such as virtual reality, augmented reality, and internet of things, reduce the effectiveness of these method. Therefore, developing next-generation technologies, such as learning-based communication systems, that can satisfy the large data and ultra-high rate communication requirements would be of interest. To address the challenging problem of connectivity, our research focuses on developing a learning-based framework for the next-generation communication systems. These systems can proactively adapt their communication and networking strategies to the dynamic of the environment, thereby maximizing their end-to-end performance in terms of data-rates, energy-efficiency, and link-reliability. Toward this goal, first information-theoretical tools are used to establish the fundamental limits (including bounds on the end-to-end performance). These performance limits are the keys for building reliable and efficient systems. Then, powerful machine learning techniques, such as deep learning, are employed for the implementation of such systems. In particular, a simple and cost-effective system with near-optimal performance can be implemented by merely taking off-the-shelf deep learning models, applying them to communication design problems, and tuning them based on the training data.masters, M.S., Electrical and Computer Engineering -- University of Idaho - College of Graduate Studies, 2019-0