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math.NA2024
Laplace-based strategies for Bayesian optimal experimental design with nuisance uncertainty
Arved Bartuska, Luis Espath, Raúl Tempone
Finding the optimal design of experiments in the Bayesian setting typically requires estimation and optimization of the expected information gain functional. This functional consis…
math.NA2024
Deep NURBS -- Admissible Physics-informed Neural Networks
Hamed Saidaoui, Luis Espath, Rául Tempone
In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs…
math.OC2024
Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization
Andre Carlon, Luis Espath, Raul Tempone
Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditi…