Evolutionary Discovery of Sequence Acceleration Methods for Slab Geometry Neutron Transport

• URL: http://arxiv.org/abs/2512.24559v1
• Date: Wed, 31 Dec 2025 01:53:34 GMT
• Title: Evolutionary Discovery of Sequence Acceleration Methods for Slab Geometry Neutron Transport
• Abstract summary: We present a genetic programming approach to automatically discover convergence acceleration methods for discrete ordinates solutions of neutron transport problems.<n>We evolved mathematical formulas specifically tailored to SN convergence characteristics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a genetic programming approach to automatically discover convergence acceleration methods for discrete ordinates solutions of neutron transport problems in slab geometry. Classical acceleration methods such as Aitken's delta-squared and Wynn epsilon assume specific convergence patterns and do not generalize well to the broad set of transport problems encountered in practice. We evolved mathematical formulas specifically tailored to SN convergence characteristics in this work. The discovered accelerator, featuring second differences and cross-product terms, achieved over 75 percent success rate in improving convergence compared to raw sequences - almost double that observed for classical techniques for the problem set considered. This work demonstrates the potential for discovering novel numerical methods in computational physics via genetic programming and attempts to honor Prof. Ganapol's legacy of advancing experimental mathematics applied to neutron transport.

Related papers

• Nesterov acceleration in optimizing over probability measures [2.1838525584229362]
  Motivated by Nesterov's accelerated method in Euclidean space, we develop Heavy-ball and Nesterov acceleration methods over the probability measure space.<n>We establish non-asymptotic convergence guarantees that match their Euclidean counterparts.
  arXiv  Detail & Related papers  (2026-07-25T02:53:53Z)
• The Glider Equation for Asymptotic Lenia [0.764671395172401]
  Asymptotic Lenia is a continuous extension of Conway's Game of Life that exhibits rich pattern formations.<n>We analytically derive the conditions for glider patterns, which we term the Glider Equation''
  arXiv  Detail & Related papers  (2025-08-06T07:47:24Z)
• Riemannian Neural Geodesic Interpolant [15.653104625330062]
  Differential interpolants are efficient generative models that bridge two arbitrary probability density functions in finite time.<n>These models are primarily developed in Euclidean space, and are therefore limited in their application to many distribution learning problems.<n>We introduce the Riemannian Geodesic Interpolant (RNGI) model, which interpolates between two probability densities.
  arXiv  Detail & Related papers  (2025-04-22T09:28:29Z)
• Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods [0.0]
  This thesis develops advanced Network (TN) methods to address Hamiltonian Lattice Theories (LGTs)<n>A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields.<n>These advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.
  arXiv  Detail & Related papers  (2025-01-19T17:09:57Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Adaptive Federated Learning Over the Air [108.62635460744109]
  We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. Our analysis shows that the AdaGrad-based training algorithm converges to a stationary point at the rate of $mathcalO( ln(T) / T 1 - frac1alpha ).
  arXiv  Detail & Related papers  (2024-03-11T09:10:37Z)
• A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples [5.581859462239914]
  We show the theoretical results for the frequently-used smoothers, i.e. Richardson (damped Jacobi) and Gauss-Seidel. As a meshless acceleration method, it is provided with enormous potentials for practice applications.
  arXiv  Detail & Related papers  (2024-02-11T11:02:25Z)
• Reweighted Interacting Langevin Diffusions: an Accelerated Sampling Methodfor Optimization [28.25662317591378]
  We propose a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the connection between posterior distribution sampling and optimization with Langevin dynamics.
  arXiv  Detail & Related papers  (2023-01-30T03:48:20Z)
• A Discrete Variational Derivation of Accelerated Methods in Optimization [68.8204255655161]
  We introduce variational which allow us to derive different methods for optimization. We derive two families of optimization methods in one-to-one correspondence. The preservation of symplecticity of autonomous systems occurs here solely on the fibers.
  arXiv  Detail & Related papers  (2021-06-04T20:21:53Z)
• Acceleration Methods [57.202881673406324]
  We first use quadratic optimization problems to introduce two key families of acceleration methods. We discuss momentum methods in detail, starting with the seminal work of Nesterov. We conclude by discussing restart schemes, a set of simple techniques for reaching nearly optimal convergence rates.
  arXiv  Detail & Related papers  (2021-01-23T17:58:25Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
  We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
  arXiv  Detail & Related papers  (2020-06-11T18:49:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.