New article: Romero, I. and Ortiz, M. (2026). Identification of optimal history variables and corresponding hereditary laws in linear viscoelasticity, Computer Methods in Applied Mechanics and Engineering, 461, 119122. (link).

In this article, we develop an operator-theoretic formulation of linear hereditary constitutive models and characterize optimal finite-rank internal-variable approximations in the sense of Kolmogorov 𝑁-widths. The history operator is shown to be compact under natural assumptions on the relaxation kernel, thereby admitting optimal low-rank approximations. The resulting reduced models inherit thermodynamic consistency, stability, and provable approximation bounds. An analysis clarifies the structural relation between hereditary representations and internal-variable theories and provides a rigorous basis for reduced-order modelling in computational mechanics. Selected numerical examples showcase optimal convergence of approximations with respect to rank and sampling.

New article: Schenk, C. and Romero, I. (2026). A Framework for the Bayesian Calibration of Complex and Data-Scarce Models in Applied Sciences, Archives of Computational Methods in Engineering. (link).

In this review article, we present a unified framework for the Bayesian calibration of computational models, with particular emphasis on applications involving computationally expensive simulations and scarce experimental data. The article describes four calibration strategies of increasing complexity — covering simple and expensive models, with and without model discrepancy — and introduces ACBICI, a new open-source Python library that implements all of them. The library supports single- and multi-output calibration with Gaussian process surrogates, MCMC and variational inference, and provides practical guidelines for reliable Bayesian calibration in engineering and applied sciences.

New article: - Kaleem, A. and Gebhardt, C. and Romero, I. (2026). On the pure traction problem of linear elasticity: A regularized formulation and its robust approximation, Computer Methods in Applied Mechanics and Engineering, 459, 119105. link

An old-standing problem in elasticity and other variational problems is finding a solution when only Neumann (traction) boundary conditions are imposed on the solution domain. Traditionally, this very common problem has been solved by selecting some special nodes and imposing special boundary conditions on them to remove the rigid body motions. Alternatively, Lagrange multipliers can be employed for the same purpose, at a much higher cost.

New article: Romero, I. and Ortiz, M. (2026). A note on data-driven methods for mechanical problems with non-unique solutions, Meccanica, 61. (link).

In this article, we show that most of the usual machine learning models have a serious drawback when employed in nonlinear mechanics: they can not predict the bifurcation of solutions and therefore might incur in serious misrepresentations, even for the simplest problem.

New article: Portillo, D. and Romero, I. (2026). Embedding structures in continua: linear models and finite element discretizations, /Computer Methods in Applied Mechanics and Engineering/, 451, 118683. (link).

In this article, we present a /model/ for the embedding of arbitrary deformable structural models inside continua. Additionally, we introduce convergent finite element discretizations of the proposed model. Applications include: reinforced concrete, materials with inclusions, materials with fibers, etc.

New article: Castillón, M. and Romero, I. and Segurado, J. (2026). A phase-ield approach to fracture and fatigue analysis: bridging theory and simulation, International Journal of Fatigue, 205, 109397. (link)

New article from the group: Cantón-Sánchez, R. and Romero, I. (2025). Fluid-structure interaction between dimensionally-reduced nonlinear dragged solids and incompressible flows, Computer Methods in Applied Mechanics and Engineering, 446, 118211 (link)

In this article, we propose a new framework that allows the coupling of structural models (beams, shells, etc.) with incompressible flows based on the Navier-Stokes equations. The idea is based on leveraging standard ALE fluid/solid interaction methods with new operators that transfer the structural kinematics to surrogate solids that enclose the latter. Numerical examples illustrate these ideas.

New article: E. Bell-Navas, D. Portillo, I. Romero (2025). A fully variational numerical method for structural topology optimization based on a Cahn-Hilliard model. Computer Methods in Applied Mechanics and Engineering (445) (link)

New article from the group: Romero, I. and Ortiz, M. (2025). An energy-stepping Markov Monte Carlo method. Meccanica (60), pg. 1411-1436 (link)

We have a new article on the modelling of mass diffusion with particle methods based on optimal transport theory.

New article from the group: Ortiz-Toranzo, Á. and Romero, I. (2024). Finite Element Discretization of the Thermo-Diffusive-Mechanical Problem with Large Deformations, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 40. (link)

Check our new article describing new numerical methods for the simulation of hydrogen diffusion in metals. The method, extremely robust and efficient, will be the starting point for future studies of the effect of hydrogen in metals.

Check our new article based on the collaboration with IMDEA Materials: Model-based reinforcement learning control of reaction-diffusion problems (2024) Christina Schenk, Aditya Vasudevan, Maciej Haranczyk, Ignacio Romero in the Journal of Optimal Control, Application and Methods.