ANN-based modeling of third order runge kutta method

Dehghanpour, Mehdi; Rahati, A.; Dehghanian, E.

doi:10.14419/jacst.v4i1.4365

Cited by 3 publications

(1 citation statement)

References 14 publications

(12 reference statements)

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“…To learn the coefficients in RK-4, [54] construct the loss function by the scaled distance between true and approximation value. [1] and [8] are respectively concerned with the RK-2 and RK-3 method and augment the loss function to penalize deviation of the coefficients from the equations that are required for an RK method. However, the present method differs in a number of ways.…”

Section: Introductionmentioning

confidence: 99%

Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators

Guo,

Dietrich,

Bertalan

et al. 2021

Preprint

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We study the meta-learning of numerical algorithms for scientific computing, which combines the mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a departure from the classical approaches in numerical analysis, which typically do not feature such learning-based adaptations. As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture. By combining neural network approximations and meta-learning, we show that we can obtain highorder integrators for targeted families of differential equations without the need for computing integrator coefficients by hand. Moreover, we demonstrate that in certain cases we can obtain superior performance to classical RK methods. This can be attributed to certain properties of the ODE families being identified and exploited by the approach. Overall, this work demonstrates an effective, learning-based approach to the design of algorithms for the numerical solution of differential equations, an approach that can be readily extended to other numerical tasks.

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Section: Introductionmentioning

confidence: 99%

Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators

Guo,

Dietrich,

Bertalan

et al. 2021

Preprint

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Personalized Algorithm Generation: A Case Study in Learning ODE Integrators

Guo¹,

Dietrich²,

Bertalan³

et al. 2022

SIAM J. Sci. Comput.

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Classification of Marine Mammals Using the Trained Multilayer Perceptron Neural Network with the Whale Algorithm Developed with the Fuzzy System

Takhti

Saffari²,

Martín

et al. 2022

Computational Intelligence and Neuroscience

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The existence of various sounds from different natural and unnatural sources in the deep sea has caused the classification and identification of marine mammals intending to identify different endangered species to become one of the topics of interest for researchers and activist fields. In this paper, first, an experimental data set was created using a designed scenario. The whale optimization algorithm (WOA) is then used to train the multilayer perceptron neural network (MLP-NN). However, due to the large size of the data, the algorithm has not determined a clear boundary between the exploration and extraction phases. Next, to support this shortcoming, the fuzzy inference is used as a new approach to developing and upgrading WOA called FWOA. Fuzzy inference by setting FWOA control parameters can well define the boundary between the two phases of exploration and extraction. To measure the performance of the designed categorizer, in addition to using it to categorize benchmark datasets, five benchmarking algorithms CVOA, WOA, ChOA, BWO, and PGO were also used for MLPNN training. The measured criteria are concurrency speed, ability to avoid local optimization, and the classification rate. The simulation results on the obtained data set showed that, respectively, the classification rate in MLPFWOA, MLP-CVOA, MLP-WOA, MLP-ChOA, MLP-BWO, and MLP-PGO classifiers is equal to 94.98, 92.80, 91.34, 90.24, 89.04, and 88.10. As a result, MLP-FWOA performed better than other algorithms.

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ANN-based modeling of third order runge kutta method

Cited by 3 publications

References 14 publications

Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators

Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators

Personalized Algorithm Generation: A Case Study in Learning ODE Integrators

Classification of Marine Mammals Using the Trained Multilayer Perceptron Neural Network with the Whale Algorithm Developed with the Fuzzy System

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