LEVIS: Large Exact Verifiable Input Spaces for Neural Networks

The robustness of neural networks is paramount in safety-critical applications. While most current robustness verification methods assess the worst-case output under the assumption that the input space is known, identifying a verifiable input space $\mathcal{C}$, where no adversarial examples exist, is crucial for effective model selection, robustness evaluation, and the development of reliable control strategies. To address this challenge, we introduce a novel framework, $\texttt{LEVIS}$, comprising $\texttt{LEVIS}$-$\alpha$ and $\texttt{LEVIS}$-$\beta$. $\texttt{LEVIS}$-$\alpha$ locates the largest possible verifiable ball within the central region of $\mathcal{C}$ that intersects at least two boundaries. In contrast, $\texttt{LEVIS}$-$\beta$ integrates multiple verifiable balls to encapsulate the entirety of the verifiable space comprehensively. Our contributions are threefold: (1) We propose $\texttt{LEVIS}$ equipped with three pioneering techniques that identify the maximum verifiable ball and the nearest adversarial point along collinear or orthogonal directions. (2) We offer a theoretical analysis elucidating the properties of the verifiable balls acquired through $\texttt{LEVIS}$-$\alpha$ and $\texttt{LEVIS}$-$\beta$. (3) We validate our methodology across diverse applications, including electrical power flow regression and image classification, showcasing performance enhancements and visualizations of the searching characteristics.

Physics-Informed Heterogeneous Graph Neural Networks for DC Blocker Placement

The threat of geomagnetic disturbances (GMDs) to the reliable operation of the bulk energy system has spurred the development of effective strategies for mitigating their impacts. One such approach involves placing transformer neutral blocking devices, which interrupt the path of geomagnetically induced currents (GICs) to limit their impact. The high cost of these devices and the sparsity of transformers that experience high GICs during GMD events, however, calls for a sparse placement strategy that involves high computational cost. To address this challenge, we developed a physics-informed heterogeneous graph neural network (PIHGNN) for solving the graph-based dc-blocker placement problem. Our approach combines a heterogeneous graph neural network (HGNN) with a physics-informed neural network (PINN) to capture the diverse types of nodes and edges in ac/dc networks and incorporates the physical laws of the power grid. We train the PIHGNN model using a surrogate power flow model and validate it using case studies. Results demonstrate that PIHGNN can effectively and efficiently support the deployment of GIC dc-current blockers, ensuring the continued supply of electricity to meet societal demands. Our approach has the potential to contribute to the development of more reliable and resilient power grids capable of withstanding the growing threat that GMDs pose.

Globally Optimal Boresight Alignment of UAV-LiDAR Systems

In airborne light detection and ranging (LiDAR) systems, misalignments between the LiDAR-scanner and the inertial navigation system (INS) mounted on an unmanned aerial vehicle (UAV)'s frame can lead to inaccurate 3D point clouds. Determining the orientation offset, or boresight error is key to many LiDAR-based applications. In this work, we introduce a mixed-integer quadratically constrained quadratic program (MIQCQP) that can globally solve this misalignment problem. We also propose a nested spatial branch and bound (nsBB) algorithm that improves computational performance. The nsBB relies on novel preprocessing steps that progressively reduce the problem size. In addition, an adaptive grid search (aGS) allowing us to obtain quick heuristic solutions is presented. Our algorithms are open-source, multi-threaded and multi-machine compatible.

Ising Processing Units: Potential and Challenges for Discrete Optimization

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, presents new opportunities for hybrid-optimization algorithms that leverage these kinds of specialized hardware. In this work, we propose the idea of an Ising processing unit as a computational abstraction for these emerging tools. Challenges involved in using and benchmarking these devices are presented, and open-source software tools are proposed to address some of these challenges. The proposed benchmarking tools and methodology are demonstrated by conducting a baseline study of established solution methods to a D-Wave 2X adiabatic quantum computer, one example of a commercially available Ising processing unit.