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Optimization free neural network approach for solving ordinary and partial differential equations

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Abstract

Current work introduces a fast converging neural network-based approach for solution of ordinary and partial differential equations. Proposed technique eliminates the need of time-consuming optimization procedure for training of neural network. Rather, it uses the extreme learning machine algorithm for calculating the neural network parameters so as to make it satisfy the differential equation and associated boundary conditions. Various ordinary and partial differential equations are treated using this technique, and accuracy and convergence aspects of the procedure are discussed.

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Acknowledgements

We express our sincere thanks to editor in chief, editor and reviewers for their valuable suggestions to revise this manuscript.

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  1. Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004, Uttar Pradesh, India

    Shagun Panghal & Manoj Kumar

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  1. Shagun Panghal
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  2. Manoj Kumar
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Correspondence to Manoj Kumar.

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Panghal, S., Kumar, M. Optimization free neural network approach for solving ordinary and partial differential equations. Engineering with Computers 37, 2989–3002 (2021). https://doi.org/10.1007/s00366-020-00985-1

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