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Scalable Method for Bayesian Experimental Design without Integrating over Posterior Distribution (2025)
Journal Article
Hoang, V., Espath, L., Krumscheid, S., & Tempone, R. (2025). Scalable Method for Bayesian Experimental Design without Integrating over Posterior Distribution. SIAM/ASA Journal on Uncertainty Quantification, 13(1), 114-139. https://doi.org/10.1137/23m1603364

We address the computational efficiency of finding the A-optimal Bayesian experimental design, where the observation map is based on partial differential equations and thus computationally expensive to evaluate. A-optimality is a widely used and easi... Read More about Scalable Method for Bayesian Experimental Design without Integrating over Posterior Distribution.

Laplace-based strategies for Bayesian optimal experimental design with nuisance uncertainty (2024)
Journal Article
Bartuska, A., Espath, L., & Tempone, R. (2025). Laplace-based strategies for Bayesian optimal experimental design with nuisance uncertainty. Statistics and Computing, 35(1), Article 12. https://doi.org/10.1007/s11222-024-10544-z

Finding the optimal design of experiments in the Bayesian setting typically requires estimation and optimization of the expected information gain functional. This functional consists of one outer and one inner integral, separated by the logarithm fun... Read More about Laplace-based strategies for Bayesian optimal experimental design with nuisance uncertainty.

Deep NURBS—admissible physics-informed neural networks (2024)
Journal Article
Saidaoui, H., Espath, L., & Tempone, R. (2024). Deep NURBS—admissible physics-informed neural networks. Engineering with Computers, 40, 4007-4021. https://doi.org/10.1007/s00366-024-02040-9

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solutions for partial differential equations (PDEs) in case of arbitrary geometries while strongly enforcing Dirichlet... Read More about Deep NURBS—admissible physics-informed neural networks.

Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization (2024)
Journal Article
Carlon, A. G., Espath, L., & Tempone, R. (2024). Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization. Optimization Methods and Software, 39(6), 1352-1382. https://doi.org/10.1080/10556788.2024.2339226

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-conditioning noisy gradient observations tend to amplify the noise. We propos... Read More about Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization.

A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness (2024)
Journal Article
Boschman, A., Espath, L., & van der Zee, K. G. (2024). A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness. Physica D: Nonlinear Phenomena, 460, Article 134055. https://doi.org/10.1016/j.physd.2024.134055

In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surface materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a bulk-surface dynamics,... Read More about A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness.

Corrigendum to “Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty” [Comput. Methods Appl. Mech. Engrg. 399 (2022) 115320] (Computer Methods in Applied Mechanics and Engineering (2022) 399, (S0045782522004194), (10.1016/j.cma.2022.115320)) (2023)
Journal Article
Bartuska, A., Espath, L., & Tempone, R. (2023). Corrigendum to “Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty” [Comput. Methods Appl. Mech. Engrg. 399 (2022) 115320] (Computer Methods in Applied Mechanics and Engineering (2022) 399, (S0045782522004194), (10.1016/j.cma.2022.115320)). Computer Methods in Applied Mechanics and Engineering, 410, Article 115995. https://doi.org/10.1016/j.cma.2023.115995

The authors regret that because of the condensed notation in Eq. (21), we failed to keep track of the dependence of the correction term [Formula presented] on the parameters of interest [Formula presented] entering through [Formula presented] in Sect... Read More about Corrigendum to “Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty” [Comput. Methods Appl. Mech. Engrg. 399 (2022) 115320] (Computer Methods in Applied Mechanics and Engineering (2022) 399, (S0045782522004194), (10.1016/j.cma.2022.115320)).

The effects of chemical and mechanical interactions on the thermodynamic pressure for mineral solid solutions (2023)
Journal Article
Clavijo, S. P., Espath, L., & Calo, V. M. (2023). The effects of chemical and mechanical interactions on the thermodynamic pressure for mineral solid solutions. Continuum Mechanics and Thermodynamics, 35, 1821-1840. https://doi.org/10.1007/s00161-023-01200-4

We use a coupled thermodynamically consistent framework to model reactive chemo-mechanical responses of solid solutions. Specifically, we focus on chemically active solid solutions that are subject to mechanical effects due to heterogeneous stress di... Read More about The effects of chemical and mechanical interactions on the thermodynamic pressure for mineral solid solutions.

A continuum framework for phase field with bulk-surface dynamics (2022)
Journal Article
Espath, L. (2023). A continuum framework for phase field with bulk-surface dynamics. Partial Differential Equations and Applications, 4, Article 1. https://doi.org/10.1007/s42985-022-00218-8

This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer et al. (Phys Rev Lett 79:893, 1997), Goldstein et al. (Phys D Nonlinear Phenom 240:754–766, 2011), and Knopf et al... Read More about A continuum framework for phase field with bulk-surface dynamics.