Optimising 4th-Order Runge-Kutta Methods: A Dynamic Heuristic Approach for Efficiency and Low Storage

• URL: http://arxiv.org/abs/2506.21465v1
• Date: Thu, 26 Jun 2025 16:51:22 GMT
• Title: Optimising 4th-Order Runge-Kutta Methods: A Dynamic Heuristic Approach for Efficiency and Low Storage
• Authors: Gavin Lee Goodship, Luis Miralles-Pechuan, Stephen O'Sullivan,
• Abstract summary: Genetic Algorithm (GA) and Reinforcement Learning (RL) approach for automated discovery, optimising low-storage Runge-Kutta methods.<n>GA-driven mutations for search-space exploration and an RL-inspired state transition mechanism to refine selection dynamically.<n>Best-performing Genetic Algorithm achieves a 25% reduction in IPOPT compared to traditional ESRK optimisation processes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Extended Stability Runge-Kutta (ESRK) methods are crucial for solving large-scale computational problems in science and engineering, including weather forecasting, aerodynamic analysis, and complex biological modelling. However, balancing accuracy, stability, and computational efficiency remains challenging, particularly for high-order, low-storage schemes. This study introduces a hybrid Genetic Algorithm (GA) and Reinforcement Learning (RL) approach for automated heuristic discovery, optimising low-storage ESRK methods. Unlike traditional approaches that rely on manually designed heuristics or exhaustive numerical searches, our method leverages GA-driven mutations for search-space exploration and an RL-inspired state transition mechanism to refine heuristic selection dynamically. This enables systematic parameter reduction, preserving fourth-order accuracy while significantly improving computational efficiency.The proposed GA-RL heuristic optimisation framework is validated through rigorous testing on benchmark problems, including the 1D and 2D Brusselator systems and the steady-state Navier-Stokes equations. The best-performing heuristic achieves a 25\% reduction in IPOPT runtime compared to traditional ESRK optimisation processes while maintaining numerical stability and accuracy. These findings demonstrate the potential of adaptive heuristic discovery to improve resource efficiency in high-fidelity simulations and broaden the applicability of low-storage Runge-Kutta methods in real-world computational fluid dynamics, physics simulations, and other demanding fields. This work establishes a new paradigm in heuristic optimisation for numerical methods, opening pathways for further exploration using Deep RL and AutoML-based heuristic search

Related papers

• Preference Optimization for Combinatorial Optimization Problems [54.87466279363487]
  Reinforcement Learning (RL) has emerged as a powerful tool for neural optimization, enabling models learns that solve complex problems without requiring expert knowledge.<n>Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast action spaces.<n>We propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling.
  arXiv  Detail & Related papers  (2025-05-13T16:47:00Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Constrained Hybrid Metaheuristic Algorithm for Probabilistic Neural Networks Learning [0.3686808512438362]
  This study investigates the potential of hybrid metaheuristic algorithms to enhance the training of Probabilistic Neural Networks (PNNs)<n>Traditional learning methods, such as gradient-based approaches, often struggle to optimise high-dimensional and uncertain environments.<n>We propose the constrained Hybrid Metaheuristic (cHM) algorithm, which combines multiple population-based optimisation techniques into a unified framework.
  arXiv  Detail & Related papers  (2025-01-26T19:49:16Z)
• Synergistic Development of Perovskite Memristors and Algorithms for Robust Analog Computing [53.77822620185878]
  We propose a synergistic methodology to concurrently optimize perovskite memristor fabrication and develop robust analog DNNs.<n>We develop "BayesMulti", a training strategy utilizing BO-guided noise injection to improve the resistance of analog DNNs to memristor imperfections.<n>Our integrated approach enables use of analog computing in much deeper and wider networks, achieving up to 100-fold improvements.
  arXiv  Detail & Related papers  (2024-12-03T19:20:08Z)
• Enhancing Stochastic Optimization for Statistical Efficiency Using ROOT-SGD with Diminishing Stepsize [13.365997574848759]
  This paper revisits textsfROOT-SGD, an innovative method for optimization to bridge the gap between optimization and statistical efficiency. The proposed method enhances the performance and reliability of textsfROOT-SGD by integrating a carefully designed emphdiminishing stepsize strategy.
  arXiv  Detail & Related papers  (2024-07-15T17:54:03Z)
• Comparative Evaluation of Metaheuristic Algorithms for Hyperparameter Selection in Short-Term Weather Forecasting [0.0]
  This paper explores the application of metaheuristic algorithms, namely Genetic Algorithm (GA), Differential Evolution (DE) and Particle Swarm Optimization (PSO) We evaluate their performance in weather forecasting based on metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE)
  arXiv  Detail & Related papers  (2023-09-05T22:13:35Z)
• Optimization of Rocker-Bogie Mechanism using Heuristic Approaches [0.0]
  This paper focuses on the Rocker Bogie mechanism, a standard suspension methodology associated with foreign terrains. This paper presents extensive tests on Simulated Annealing, Genetic Algorithms, Swarm Intelligence techniques, Basin Hoping and Differential Evolution.
  arXiv  Detail & Related papers  (2022-09-14T21:02:01Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization [85.84019017587477]
  Distributionally robust supervised learning is emerging as a key paradigm for building reliable machine learning systems for real-world applications. Existing algorithms for solving Wasserstein DRSL involve solving complex subproblems or fail to make use of gradients. We revisit Wasserstein DRSL through the lens of min-max optimization and derive scalable and efficiently implementable extra-gradient algorithms.
  arXiv  Detail & Related papers  (2021-04-27T16:56:09Z)
• Reinforcement Learning with Fast Stabilization in Linear Dynamical Systems [91.43582419264763]
  We study model-based reinforcement learning (RL) in unknown stabilizable linear dynamical systems. We propose an algorithm that certifies fast stabilization of the underlying system by effectively exploring the environment. We show that the proposed algorithm attains $tildemathcalO(sqrtT)$ regret after $T$ time steps of agent-environment interaction.
  arXiv  Detail & Related papers  (2020-07-23T23:06:40Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Online Hyperparameter Search Interleaved with Proximal Parameter Updates [9.543667840503739]
  We develop a method that relies on the structure of proximal gradient methods and does not require a smooth cost function. Such a method is applied to Leave-one-out (LOO)-validated Lasso and Group Lasso. Numerical experiments corroborate the convergence of the proposed method to a local optimum of the LOO validation error curve.
  arXiv  Detail & Related papers  (2020-04-06T15:54:03Z)

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.