Solving Inverse PDE Problems using Minimization Methods and AI
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential equations, contrasting well-established numerical methods with new AI-based techniques, specifically Physics-Informed Neural Networks (PINNs). We first analyze the logistic differential equation, using its closed-form solution to verify numerical schemes and validate PINN performance. We then address the Porous Medium Equation (PME), a nonlinear partial differential equation with no general closed-form solution, building strong solvers of the direct problem a...
| Authors | Noura Al Helwani, Sophie Moufawad, Georges Sakr |
|---|---|
| Primary category | math.NA |
| Published | 2 March 2026 |
| Last updated at source | 3 March 2026 |
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