Solving the Monge-Ampère equation via Poisson series physics-informed neural networks and its convergence analysis

Key Points

• Solving the Monge-Ampère equation yields significant results for numerical applications in higher dimensions.
• Key evidence includes a convergence metric indicating success in reaching accurate solutions with neural networks.
• Analysis employs physics-informed neural networks to model the Monge-Ampère equation effectively.
• Implications highlight the need for advanced computational techniques in complex mathematical physics models.