Advances in Solving Differential Equations and Large-Scale Systems with Machine Learning-Based Numerical Methods
Keywords:
Numerical Methods, Machine Learning, Differential EquationAbstract
In this work, we apply machine learning-based strategies by investigating the use ofneural networks to directly approximate solutions of ordinary and partial differentialequations and physics-based neural networks (PINNs) that embed the governing equations in the training process
References
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707.
Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63(1), 208–228.
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Published
2025-08-30
How to Cite
Mohammed Hassan Harjan. (2025). Advances in Solving Differential Equations and Large-Scale Systems with Machine Learning-Based Numerical Methods. Journal of Computational Analysis and Applications (JoCAAA), 34(8), 205–217. Retrieved from https://www.eudoxuspress.com/index.php/pub/article/view/3609
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