Behnaz Moradi-Jamei

Heman Shakeri, Behnaz Moradi-Jamei, Aram Vajdi et al.

Non-Markovian (renewal) epidemic simulation on multi-million-node contact networks is essential for realistic forecasting under general age-dependent holding-time distributions (log-normal, Weibull, Erlang, and similar), but the age-dependent hazard forces dense per-step updates that render the sparse event-queue strategies of standard CPU methods ineffective. We present FlashSpread, a GPU framework that consolidates the per-step renewal pipeline (CSR traversal, numerically stable erfcx-based hazard evaluation, Bernoulli tau-leaping, state transition, and next-step infectivity write-back) into a single fused Triton kernel whose intermediates never leave streaming-multiprocessor registers, with block-scalar skips that preserve CUDA Graph capture and a degree-aware CSR dispatch (thread / warp / edge-merge) that keeps the peak throughput on scale-free graphs. On an NVIDIA A100 the fused CUDA-Graph engine reaches 8.09 Giga-NUPS at N = 10^6 on a uniform-degree graph, a 217x strict hardware speedup over optimised CPU tau-leaping at the same N; on a Barabasi-Albert graph of the same size the merge-based dispatch recovers 4.5x (0.45 to 2.0 Giga-NUPS) over the default kernel, and the framework scales to N = 10^8 on a single A100 (40 GB), with a mixed-precision storage path that extends the L2-reachable scale by roughly 3x and delivers a 1.15x throughput lift at the far bandwidth-bound end. Validation against an exact non-Markovian Gillespie reference shows a structural-bias floor of approximately 6% on peak infection and approximately 7% on final attack rate that does not detectably decrease as epsilon nears 0 across two decades of tolerance, comfortably within typical epidemiological parameter uncertainty. Code: https://github.com/Shakeri-Lab/FlashSpread.

Ali Tavasoli, Behnaz Moradijamei, Heman Shakeri

This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman operator, which provides a linear, infinite-dimensional representation of the nonlinear dynamics, and approximate a finite version that remains robust against spectral pollutions due to truncation. By computing $ε$-approximate Koopman eigenfunctions using dynamics-adapted kernels in delay coordinates, we decompose the load dynamics into coherent spatiotemporal patterns that evolve quasi-independently. Our approach captures temporal coherent patterns due to seasonal changes and finer time scales, such as time of day and day of the week. This method allows for a more nuanced understanding of the complex interactions within power grids and their response to various exogenous factors. We assess our method using a large-scale dataset from a renewable power system in the continental European electricity system. The results indicate that our Koopman-based method surpasses a separately optimized deep learning (LSTM) architecture in both accuracy and computational efficiency, while providing deeper insights into the underlying dynamics of the power grid\footnote{The code is available at \href{https://github.com/Shakeri-Lab/Power-Grids}{github.com/Shakeri-Lab/Power-Grids}.

Behnaz Moradi-Jamei, Heman Shakeri, Pietro Poggi-Corradini et al.

A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local "richness" of the cyclic structure. In this paper, we introduce renewal non-backtracking random walks (RNBRW) as a way of quantifying this structure. RNBRW gives a weight to each edge equal to the probability that a non-backtracking random walk completes a cycle with that edge. Hence, edges with larger weights may be thought of as more important to the formation of cycles. Of note, since separate random walks can be performed in parallel, RNBRW weights can be estimated very quickly, even for large graphs. We give simulation results showing that pre-weighting edges through RNBRW may substantially improve the performance of common community detection algorithms. Our results suggest that RNBRW is especially efficient for the challenging case of detecting communities in sparse graphs.