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Author

C. Ogbonna

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Open access 2026

Adaptive Weighting Strategies and Loss Balancing For Physics Informed Neural Network Solution of the Monge Ampere Partial Differential Equation

In this research we present a comprehensive computational framework for solving the nonlinear Monge-Ampère equation using an adaptive Physics-Informed Neural Network (PINN) approach. The Monge-Ampère equation is a fully nonlinear second-order partial differential equation which plays a fundamental role in optimal trans...

C. Ogbonna, Maliki Olaniyi S, Nkem Ogbonna · 0 citations
Open access 2026

A Physics-Informed Neural Network Approach for Solving the Monge-Ampère Partial Differential Equation

This paper presents a comparative study of classical numerical and machine learning techniques for solving the nonlinear Monge–Ampère Equation (MAE). A finite difference method (FDM) implemented in MATLAB is first validated using a quadratic exact solution on a square domain. Two neural network approaches are then inve...

C. Ogbonna, Maliki Olaniyi S, Nkem Ogbonna · 0 citations

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