מושגי ליבה
The author proposes an innovative approach using Ensemble Kalman Inversion for efficient uncertainty quantification in DeepONets, addressing challenges of noisy and limited data.
תקציר
The content discusses the importance of uncertainty quantification in DeepONets, introducing a novel method using Ensemble Kalman Inversion. It highlights the challenges faced in practical applications and showcases the effectiveness of the proposed methodology through various benchmark problems. The approach leverages EKI's advantages to efficiently train ensembles of DeepONets while providing informative uncertainty estimates for mission-critical applications with limited and noisy data.
סטטיסטיקה
EKI offers numerous advantages such as being derivative-free, noise-robust, highly parallelizable.
The training output data is generated at 100 equally spaced locations along x ∈ [0, 1] for each corresponding output function s.
For EKI, J = 5000 ensemble members are utilized.
The mean relative error shows a 0.9% error in the mean prediction and a corresponding 1.4% uncertainty.
On average, 98.5% of each truth sample fall within the two standard deviation confidence interval.