Shallow PINNs with Levenberg-Marquardt algorithm show high accuracy

A new research paper explores the effectiveness of shallow physics-informed neural networks (PINNs) when optimized using the Levenberg-Marquardt (LM) algorithm. The study demonstrates that shallow PINNs, when combined with LM, can achieve superior convergence speed, accuracy, and lower loss values compared to other optimization methods like Adam and BFGS. The research suggests that for a variety of nonlinear partial differential equations, shallow PINNs with effective second-order optimization offer a computationally efficient and accurate solution, potentially outperforming deeper networks with fewer parameters. AI

IMPACT Suggests a more efficient and accurate method for solving complex differential equations using neural networks.

RANK_REASON Research paper published on arXiv detailing a novel approach to PINNs. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• Adam
• Allen–Cahn equation
• Broyden–Fletcher–Goldfarb–Shanno algorithm
• Burgers' equation
• Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction
• Limited-memory BFGS
• Muhammad Luthfi Shahab
• physics-informed neural networks
• Schrödinger equation
• three-dimensional Bratu equation

• paper
• other

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