From the 1 of 9 linked papers with an AI index.
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A Physics-informed Multi-resolution Neural Operator
Sumanta Roy, Bahador Bahmani, Ioannis G. Kevrekidis +1
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial am…
Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators
Ponkrshnan Thiagarajan, Tamer A. Zaki, Michael D. Shields
Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demandi…
Neural Chaos: A Spectral Stochastic Neural Operator
Bahador Bahmani, Ioannis G. Kevrekidis, Michael D. Shields
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties,…
Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards
Somdatta Goswami, Dimitris G. Giovanis, Bowei Li +2
Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on…