New research guarantees convergence for physics-informed neural networks trained with SGD

Researchers have established the linear convergence of stochastic gradient descent (SGD) for training over-parameterized two-layer physics-informed neural networks (PINNs) when solving the Poisson equation. This analysis extends previous work by considering the dynamic randomness introduced by stochastic optimization methods, providing convergence guarantees for PINNs trained with SGD. The key to this analysis involves ensuring the positive definiteness of specific Gram matrices during the training process. AI

IMPACT Provides theoretical guarantees for training physics-informed neural networks, potentially improving their reliability in solving complex scientific problems.

RANK_REASON Academic paper published on arXiv detailing convergence guarantees for a specific type of neural network. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• arXiv
• Bangti Jin
• partial differential equations
• physics-informed neural networks
• Poisson's equation
• stochastic gradient descent
• Stochastic Gradient Methods for Distributionally Robust Optimization with f-divergences
• Two-Layer Physics-Informed Neural Networks

• paper
• other

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