arXiv subjects

Brian Kiedrowski

Publications and source records attributed to Brian Kiedrowski.

3 recordsLinked to original sources

arXiv2026

The Method of Simultaneous Solutions Applied to Neutron Transport and Heat Conduction

This paper provides an initial description of the Method of Simultaneous Solutions, a Monte Carlo approach that simultaneously solves multiple Boltzmann-transport-like phenomena. Here, it is used to simultaneously solve the neutron transport and heat conduction equations. Analytically-derived weighting factors are tracked through a neutron transport-governed random walk to tally statistical estimators that can be used to calculate the temperature distribution. In this initial presentation, the method is readily applicable to neutron-heat multiphysics problems where the heat source and neutron source are identically distributed spatially. The primary theoretical benefit of MOSS lies in the reduction of computational cost that occurs from the removal of a dedicated routine to solve the heat conduction equation. Practically, branching processes required to capture the disparate boundary conditions associated with these separate physical phenomena can lead to large computational times dedicated to a single physics. In addition, this correlated sampling-based method can suffer from infinite variance associated with statistical estimators if the stochastic processes being tracked are too different. The final drawback demonstrated in this paper is that the approximation of heat conduction as a Boltzmann transport-governed process leads to errors in calculated temperatures. The paper explores these drawbacks on two demonstration problems, a problem consisting of slab geometry and a problem consisting of a hexagonal pin cell.

physics.comp-ph↗

arXiv2026

Quantum Algorithms for Heterogeneous PDEs: The Neutron Diffusion Eigenvalue Problem

We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with piecewise constant coefficients, describing a problem in a heterogeneous medium. We apply uniform finite elements and show that the quantum algorithm provides significant polynomial end-to-end speedup over its classical counterparts. This speedup leverages recent advances in quantum linear systems -- fast inversion and quantum preconditioning -- and uses Hamiltonian simulation as a subroutine. Our results suggest that quantum algorithms may provide speedups for heterogeneous PDEs, though the extent of this advantage over the fastest classical algorithm depends on the effectiveness of other classical approaches such as nonuniform or adaptive meshing for a given problem instance.

quant-ph↗

arXiv2025

Tensor Network Structure Search Via Canonical Dimension Tree Enumeration

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network structure search a challenging problem. Existing solutions typically rely on sampling and compressing numerous candidate structures; these procedures are computationally expensive and therefore limiting for practical applications. We address this challenge by decoupling topology enumeration from rank assignment search. We first represent the search space using canonical dimension trees, which encode potential network topology through nested index partitions and inherently rule out redundant and suboptimal topologies by construction. To mitigate the assessment bottleneck, we introduce a mechanism powered by the precomputation of a singular value map. By archiving the singular values of all feasible tensor matricizations, we transform the evaluation of any candidate dimension tree into a constraint-solving problem. This formulation yields an empirically near-optimal rank assignment via simple metadata lookups, allowing us to compute structural costs and bypass expensive tensor decompositions for all but the final selected candidate. Experimental results show that our approach accelerates the structure search by up to 10x while achieving highly competitive compression ratios, outperforming standard tensor trains and hierarchical tuckers by up to 10x, and matching or exceeding state-of-the-art structure search tools. Notably, our approach scales to larger tensors that are unattainable by prior work. Furthermore, the discovered topologies generalize well to similar data; they achieve compression ratios up to 2.4x better than tensor trains or hierarchical tuckers, while maintaining a search time of approximately 110 seconds for 6D tensors of 1-2GB disk size.

cs.CE↗