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Celia Reina

Celia Reina contributes to research discovery and scholarly infrastructure.

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Published work

4 published item(s)

preprint2026arXiv

Nonlinear GENERIC Informed Neural Networks (N-GINNs): learning GENERIC dynamics with non-quadratic dissipation potentials

We introduce Nonlinear GENERIC Informed Neural Networks (N-GINNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium Reversible-Irreversible Coupling). Such systems exhibit coupled conservative and dissipative dynamics, and can be described via the superposition of a Hamiltonian flow and a generalized gradient flow. In contrast to existing approaches, our formulation incorporates generalized gradient flows via convex dissipation potentials, enabling the identification of a broader class of thermodynamically consistent dynamics, including systems with non-quadratic dissipation potentials. Thermodynamic structure is strongly enforced by construction through suitable reparameterizations of both the bivector operator and the dissipation potential, ensuring exact compliance with the first and second laws of thermodynamics. We validate the proposed approach on three representative examples: a harmonic oscillator coupled to a heat bath, an idealized chemical motor, and a one-dimensional viscoplastic model of Perzyna type. These results demonstrate the method's ability to accurately infer thermodynamically consistent models from data for systems incorporating both conservative and nonlinear dissipative dynamics.

preprint2025arXiv

Integrated Experiment and Simulation Co-Design: A Key Infrastructure for Predictive Mesoscale Materials Modeling

The design of structural & functional materials for specialized applications is being fueled by rapid advancements in materials synthesis, characterization, manufacturing, with sophisticated computational materials modeling frameworks that span a wide spectrum of length & time scales in the mesoscale between atomistic & continuum approaches. This is leading towards a systems-based design methodology that will replace traditional empirical approaches, embracing the principles of the Materials Genome Initiative. However, several gaps remain in this framework as it relates to advanced structural materials:(1) limited availability & access to high-fidelity experimental & computational datasets, (2) lack of co-design of experiments & simulation aimed at computational model validation,(3) lack of on-demand access to verified and validated codes for simulation and for experimental analyses, & (4) limited opportunities for workforce training and educational outreach. These shortcomings stifle major innovations in structural materials design. This paper describes plans for a community-driven research initiative that addresses current gaps based on best-practice recommendations of leaders in mesoscale modeling, experimentation & cyberinfrastructure obtained at an NSF-sponsored workshop dedicated to this topic. The proposal is to create a hub for Mesoscale Experimentation and Simulation co-Operation (hMESO)-that will (I) provide curation and sharing of models, data, & codes, (II) foster co-design of experiments for model validation with systematic uncertainty quantification, & (III) provide a platform for education & workforce development. It will engage experimental & computational experts in mesoscale mechanics and plasticity, along with mathematicians and computer scientists with expertise in algorithms, data science, machine learning, & large-scale cyberinfrastructure initiatives.

preprint2021arXiv

Predicting the unobserved: a statistical mechanics framework for non-equilibrium material response with quantified uncertainty

Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible in principle for systems governed by stochastic differential equations, thanks to a set of exact relations between probability densities for trajectories derived from the path integral formalism [1, 2, 3]. In this article, we systematically investigate inferences (in the form of ensemble-averages) drawn on system/process S based on stochastic trajectory data of system/process S~, with quantified uncertainty, to directly address the aforementioned questions. Interestingly, such inferences and their associated uncertainty do not require any simulations or experiments of S. The results are exemplified over two illustrative examples by means of numerical simulations: a one-dimensional system as a prototype for polymers and biological macromolecules, and a two-dimensional glassy system. In principle, the approach can be pushed to the extreme case where S~ is simply comprised of Brownian trajectories, i.e., equilibrium non-interacting particles, and S is a complex interacting system driven far from equilibrium. In practice, however, the "further" S~ is from S, the greater the uncertainty in the predictions, for a fixed number of realizations of system S~.

preprint2021arXiv

Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential. Specifically, these two potentials are learned from spatio-temporal measurements of macroscopic observables via proposed neural network architectures that strongly enforce the satisfaction of the second law of thermodynamics. The method is applied to three distinct physical processes aimed at highlighting the robustness and versatility of the proposed approach. These include (i) the phase transformation of a coiled-coil protein, characterized by a non-convex free-energy density; (ii) the one-dimensional dynamic response of a three-dimensional viscoelastic solid, which leverages the variational formulation as a tool for obtaining reduced order models; and (iii) linear and nonlinear diffusion models, characterized by a lack of uniqueness of the free energy and dissipation potentials. These illustrative examples showcase the possibility of learning partial differential equations through their variational action density (i.e., a function instead), by leveraging the thermodynamic structure intrinsic to mechanical and multiphysics problems.