Mathematics is often called the language of the Universe and differential equations are its grammar, shaping how systems evolve across physics, chemistry, mechanics, electromagnetism, and beyond. Yet, traditional numerical methods to solve them can be time-consuming and computationally intensive.
To address this, Ms Shilpa Dey and Prof. Shruti Dubey from the Department of Mathematics, IIT Madras, explored the use of neural networks to solve differential equations with implicit boundary conditions โ a class of problems frequently arising in fluid mechanics, heat transfer, and electromagnetics.
Their study proposes an Orthogonal Polynomial-based Neural Network (ONN) that integrates Legendre, Laguerre, Chebyshev, and Hermite polynomials within a feed-forward architecture, trained using the Extreme Learning Machine (ELM) algorithm. The results demonstrate higher accuracy, efficiency, and analytic closed-form solutions compared to conventional numerical methods.
This neural approach eliminates the need for derivative discretisation and enhances generalisation, making it a robust framework for solving complex boundary conditions.
Building on this foundation, the authors plan to extend their approach to delay and fractional differential equations, pushing the boundaries of neural network-based scientific computing.
Read here:
tech-talk.iitm.ac.in/defer-dโฆ.
Read the full study here:
emerald.com/hff/article/doi/โฆ.
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