79 citations · 91 across the 12 of their papers we have counts for
15 papers
Efficient Stochastic BFGS methods Inspired by Bayesian Principles
André Carlon, Luis Espath, Raúl Tempone
Quasi-Newton methods are ubiquitous in deterministic local search due to their efficiency and low computational cost. This class of methods uses the history of gradient evaluations…
Multilevel randomized quasi-Monte Carlo estimator for nested integration
Arved Bartuska, André Gustavo Carlon, Luis Espath +2
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantificat…
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…
Scalable method for Bayesian experimental design without integrating over posterior distribution
Vinh Hoang, Luis Espath, Sebastian Krumscheid +1
We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations…
Physics-informed Spectral Learning: the Discrete Helmholtz--Hodge Decomposition
Luis Espath, Pouria Behnoudfar, Raul Tempone
In this work, we further develop the Physics-informed Spectral Learning (PiSL) by Espath et al. \cite{Esp21} based on a discrete projection to solve the discrete Hodge--Helmh…
Double-loop randomized quasi-Monte Carlo estimator for nested integration
Arved Bartuska, André Gustavo Carlon, Luis Espath +2
Nested integration of the form $\int f\left(\int g(\bs{y},\bs{x})\di{}\bs{x}\right)\di{}\bs{y}$, characterized by an outer integral connected to an inner integral through a nonline…
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…
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…
Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty
Arved Bartuska, Luis Espath, Raúl Tempone
Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters,…
On the equivalence of different adaptive batch size selection strategies for stochastic gradient descent methods
Luis Espath, Sebastian Krumscheid, Raúl Tempone +1
In this study, we demonstrate that the norm test and inner product/orthogonality test presented in \cite{Bol18} are equivalent in terms of the convergence rates associated with Sto…
Statistical Learning for Fluid Flows: Sparse Fourier divergence-free approximations
Luis Espath, Dmitry Kabanov, Jonas Kiessling +1
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf)…
Multi-Iteration Stochastic Optimizers
Andre Carlon, Luis Espath, Rafael Lopez +1
We introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic methods that control the relative error using successive control variates along th…
Multilevel Double Loop Monte Carlo and Stochastic Collocation Methods with Importance Sampling for Bayesian Optimal Experimental Design
Joakim Beck, Ben Mansour Dia, Luis F. R. Espath +1
An optimal experimental set-up maximizes the value of data for statistical inferences and predictions. The efficiency of strategies for finding optimal experimental set-ups is part…
Nesterov-aided Stochastic Gradient Methods using Laplace Approximation for Bayesian Design Optimization
Andre Gustavo Carlon, Ben Mansour Dia, Luis FR Espath +2
Finding the best setup for experiments is the primary concern for Optimal Experimental Design (OED). Here, we focus on the Bayesian experimental design problem of finding the setup…
Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain
Joakim Beck, Ben Mansour Dia, Luis FR Espath +2
In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number…