Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2311.10850

Scaling laws of failure dynamics on complex networks

G. Pál·Zs. Danku·A. Batool·V. Kádár·N. Yoshioka·N. Ito·G. Ódor·F. Kun
View original source ↗Read source document ↗Export metadata ↓

Abstract

The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

Explore related subjects

cond-mat.dis-nn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

G. Pál, Zs. Danku, A. Batool, V. Kádár, N. Yoshioka, N. Ito, G. Ódor, F. Kun. 2023-11-17. Scaling laws of failure dynamics on complex networks. https://doi.org/10.1038/s41598-023-47152-2

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The critical slowing down in training diffusion models

Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control over when and why they succeed. Here we provide such insight for diffusion models---a class of generative schemes highly effective in practice---by analyzing their application to the $O(n)$ model of statistical field theory in the Gaussian limit $n \to \infty$. In this analytically tractable setting, we show that training a score model with a one-layer network architecture matching the exact solution exhibits a form of critical slowing down in parameter learning. This slowing down also impacts the generation process, indicating that the well-known difficulties of sampling near criticality persist even for learned generative models. To overcome this bottleneck, we consider the power of architectural depth. We find that using a two-layer architecture drastically reduces the critical slowing down, with the training time scaling logarithmically rather than quadratically with system size. Using a Fourier implementation of the architecture, we further show that this acceleration in training time can be achieved without drastically increasing operational complexity. Taken together, these results demonstrate that diffusion models can overcome the critical slowing down through appropriate architectural design, and establish a controlled framework for understanding and improving learned sampling methods in statistical physics and beyond.

cond-mat.dis-nn↗
arXiv2026

Switching diffusivity selects Pareto tail exponent in random growth with redistribution

Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-Mézard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes, where volatility (diffusivity) is often fluctuating. We replace the constant noise intensity by a switching diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with switching diffusivity, the long-time Gaussian limit holds when the redraw law has finite mean and variance. The asymptotic variance retains a contribution from diffusivity persistence. With redistribution and a general redraw law, the stationary large-wealth problem is characterized by a spectral condition for admissible algebraic modes. For a two-state diffusivity, an exact tail analysis gives a Pareto exponent interpolating between the high-diffusivity slow-refresh limit and the mean-diffusivity fast-refresh Bouchaud-Mézard limit.

cond-mat.dis-nn↗
arXiv2026

Extreme-Scale Ising Machines with Cluster Mean-Field Theory

Scaling analog and digital Ising machines to larger problems requires overcoming finite device capacity and the cost of communication between devices. We present cluster mean-field theory (CMFT), a framework that partitions a large interaction graph into clusters sized to fit available hardware. Each cluster performs local updates independently, while interactions across cluster boundaries enter through periodically updated effective biases computed from boundary-spin averages. To reduce the error introduced by fixed cluster boundaries, we introduce dynamic partitioning, which cycles through multiple partitions so that interactions approximated by mean fields at one stage can act through instantaneous spins at another. On three-dimensional spin glasses and planted Pegasus instances, dynamic CMFT exhibits power-law decay of residual energy over sweep budgets. This shows that solution quality continues to improve with computational effort despite the mean-field approximation. An automated graph partitioner combined with a weighted recovery ratio provides a practical heuristic for selecting partition combinations on graphs without natural cut directions. We demonstrate CMFT on four GPUs with approximately four million p-bits, reaching comparable energy densities up to 15 times faster than a single-GPU implementation of the full graph. By coupling locally evolving clusters through programmable effective biases, CMFT provides a route to extreme-scale Ising machines on both analog and digital hardware.

cond-mat.dis-nn↗