A Machine Learning-Based Data-Driven Optimisation Approach for Solving Differential Equations
Mariyam AhmedKalinga University,Department of Management,Raipur,IndiaYusufjanovUlugbekJavlonUgliTuran International University,Faculty of Humanities & Pedagogy,Namangan,UzbekistanK.S. BhuvaneshwariKarpagam College of Engineering,Department of Artificial Intelligence and Data Science,Coimbatore,641032ZaedBalasmCollege of Technical Engineering, Islamic University in Najaf,Department of Computer Techniques Engineering,Najaf,IraqAnkita AggarwalSchool of Engineering and Technology (SET), CGC University,Mohali,Punjab,India,140307Arulmozhiyal RSona College of Technology,Department of EEE,Salem
2025
ABI
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The research presents a Machine Learning (ML) system to expedite numerical calculations of time-dependent Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE). The approach involves reformulating current numerical methods as Artificial Neural Networks (ANNs) using trainable parameters. These variables are learned offline by minimising appropriate (potentially non-convex) loss functions using (stochastic) gradient descent methods. The suggested approach is intended to maintain consistency with the fundamental DE at all times. Numerical simulations involving linear and nonlinear ODE and PDE models achieve substantial computational speedups compared to conventional numerical methods.
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