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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., Comment: Paper is accepted by PSCC 2024

We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and entanglement. The equilibrium asset pricing solution is a quantum state. We introduce quantum decision-theoretic foundations of ambiguity and model/parameter uncertainty to deal with model selection., Comment: 51 pages, 4 figures

We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving liner systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher precision quantum estimates of the eigenvalues relevant to the linear system, and an enhanced classical processing step to guide the eigenvalue inversion part of Hybrid HHL. We show that eigenvalue estimates with just two extra bits of precision results in tighter error bounds for our Enhanced Hybrid HHL compared to HHL. We also show that our enhancement reduces the error of Hybrid HHL by an average of 57 percent on an ideal quantum processor for a representative sample of 2x2 systems. On IBM Hanoi and IonQ Aria-1 hardware, we see that the error of Enhanced Hybrid HHL algorithm is on average 13 percent and 20 percent (respecitvely) less than that of HHL for a similar set of 2x2 systems. Finally, we use simulated eigenvalue estimates to perform an inversion of a 4x4 matrix on IonQ Aria-1 with a fidelity of 0.61. To our knowledge this is the largest HHL implementation with a fidelity greater than 0.5., Comment: 9 pages, 4 figures, submitted to QCE24

For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other conservative schemes. However, our work reveals a more fundamental culprit: the smooth Heaviside and delta functions inherent to the standard formulation. Even if reinitialization is done exactly, i.e., the zero contour interface remains stationary, the use of smooth functions lead to violation of mass conservation. We propose a novel approach using variational analysis to incorporate a mass conservation constraint. This introduces a Lagrange multiplier that enforces overall mass balance. Notably, as the delta function sharpens, i.e., approaches the Dirac delta limit, the Lagrange multiplier approaches zero. However, the exact Lagrange multiplier method disrupts the signed distance property of the level set function. This motivates us to develop an approximate version of the Lagrange multiplier that preserves both overall mass and signed distance property of the level set function. Our framework even recovers existing mass-conserving level set methods, revealing some inconsistencies in prior analyses. We extend this approach to three-phase flows for fluid-structure interaction (FSI) simulations. We present variational equations in both immersed and non-immersed forms, demonstrating the convergence of the former formulation to the latter when the body delta function sharpens. Rigorous test problems confirm that the FSI dynamics produced by our simple, easy-to-implement immersed formulation with the approximate Lagrange multiplier method are accurate and match state-of-the-art solvers.