Parameter estimation of partial differential equations using artificial neural network

Jamili, Elnaz; Dua, Vivek

doi:10.1016/j.compchemeng.2020.107221

Cited by 7 publications

(3 citation statements)

References 26 publications

(38 reference statements)

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“…In this case, bayesian learning is connected to regularization since the regularization problem coincides with the maximization of the likelihood of the parameters given the observations Bishop (1995) . Therefore, Machine Learning techniques have been proposed to take advantage of the capability of the models to discover hidden relationships between the input data and the final estimation Jamili and Dua (2021) . Most of those models use the fact that the samples are given in advance.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Estimating spatio-temporal fields through reinforcement learning

et al. 2022

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Prediction and estimation of phenomena of interest in aquatic environments are challenging since they present complex spatio-temporal dynamics. Over the past few decades, advances in machine learning and data processing contributed to ocean exploration and sampling using autonomous robots. In this work, we formulate a reinforcement learning framework to estimate spatio-temporal fields modeled by partial differential equations. The proposed framework addresses problems of the classic methods regarding the sampling process to determine the path to be used by the agent to collect samples. Simulation results demonstrate the applicability of our approach and show that the error at the end of the learning process is close to the expected error given by the fitting process due to added noise.

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Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Estimating spatio-temporal fields through reinforcement learning

et al. 2022

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“…In contrast to traditional statistical models, such as the Bayesian approach [2], maximum likelihood estimation [3], modern artificial neural network [4], and machine learning methods [5], which usually need many samples, the grey model requires less data modelling [1]. It makes full use of the limited data from a small sample and excavates more useful information from the data.…”

Section: Introductionmentioning

confidence: 99%

“…The inversion of the fractional-order accumulative generation convolution sequence can be calculated directly by assigning the minus fractional order, without demanding a round number order (compare with [8] (p. 1780)). (4) According to model fitting error, the fractional accumulation grey model can dynamically adjust the order to model and predict the system behaviour data better.…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Accumulative Generation with Discrete Convolution Transformation

Chen

2023

Fractal Fract

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A new fractional accumulation technique based on discrete sequence convolution transform was developed. The accumulation system, whose unit impulse response is the accumulation convolution sequence, was constructed; then, the order was extended to fractional orders. The fractional accumulative convolution grey forecasting model GMr*(1,1) was established on the sequence convolution. From the viewpoint of sequence convolution, we can better understand the mechanism of accumulative generation. Real cases were used to verify the validity and effectiveness of the fractional accumulative convolution method.

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Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network

Noorani¹,

Mehrdoust²

2022

Chaos, Solitons & Fractals

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Parameter estimation of partial differential equations using artificial neural network

Cited by 7 publications

References 26 publications

Estimating spatio-temporal fields through reinforcement learning

Estimating spatio-temporal fields through reinforcement learning

Fractional-Order Accumulative Generation with Discrete Convolution Transformation

Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network

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