A Stochastic Ensemble Physics-Informed Neural Networks via Bagging and Monte Carlo Dropout

Key Points

• The aim is to enhance the solution methods for differential equations using stochastic ensemble techniques in neural networks.
• Developed an ensemble model combining physics-informed neural networks with bagging techniques.
• Implemented Monte Carlo dropout for uncertainty estimation during training.
• Evaluated the model's performance in solving ordinary and partial differential equations.
• Demonstrated significantly improved accuracy in solving differential equations compared to traditional methods.
• Achieved lower error rates with the ensemble approach, leading to more reliable solutions.
• Quantified the impact of stochastic methods on computational efficiency and stability of solutions.