Version 1
: Received: 27 April 2024 / Approved: 28 April 2024 / Online: 29 April 2024 (10:25:10 CEST)
How to cite:
Kabi-Nejad, P. Investigating Effective Factors in Solving Partial Differential Equations using Deep Learning Techniques. Preprints2024, 2024041884. https://doi.org/10.20944/preprints202404.1884.v1
Kabi-Nejad, P. Investigating Effective Factors in Solving Partial Differential Equations using Deep Learning Techniques. Preprints 2024, 2024041884. https://doi.org/10.20944/preprints202404.1884.v1
Kabi-Nejad, P. Investigating Effective Factors in Solving Partial Differential Equations using Deep Learning Techniques. Preprints2024, 2024041884. https://doi.org/10.20944/preprints202404.1884.v1
APA Style
Kabi-Nejad, P. (2024). Investigating Effective Factors in Solving Partial Differential Equations using Deep Learning Techniques. Preprints. https://doi.org/10.20944/preprints202404.1884.v1
Chicago/Turabian Style
Kabi-Nejad, P. 2024 "Investigating Effective Factors in Solving Partial Differential Equations using Deep Learning Techniques" Preprints. https://doi.org/10.20944/preprints202404.1884.v1
Abstract
Partial Differential Equations (PDEs) constitute a fundamental framework for modeling various physical phenomena across diverse fields such as physics, engineering, and finance. Solving PDEs accurately and efficiently remains a significant challenge, particularly when dealing with complex systems or high-dimensional data. In this paper, we present a novel approach based on deep learning techniques to investigate the effective factors in solving PDEs. Our methodology leverages the expressive power of deep neural networks to learn and represent the underlying relationships between input parameters and the solutions of PDEs. By incorporating domain knowledge into the network architecture and training process, our approach aims to provide insights into the key factors influencing the solution of PDEs. We demonstrate the effectiveness of our method through numerical experiments on various PDEs, showcasing its capability to identify important features and improve predictive accuracy. Our findings suggest that deep learning techniques offer a promising avenue for understanding and analyzing the complex dynamics inherent in PDEs, paving the way for enhanced computational methods in scientific and engineering applications.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
