Tikhonov regularization as a nonparametric method for uncertainty quantification in aggregate data problems

Simple item page
dc.contributor.authorVillalon, Elena
dc.contributor.authorYang, Qian
dc.contributor.authorLong, Carlos A. Sing
dc.date.accessioned2025-01-20T16:14:37Z
dc.date.available2025-01-20T16:14:37Z
dc.date.issued2024
dc.description.abstractDynamical systems are widely used in mathematical models in engineering and in the applied sciences. However, the parameters of these systems are usually unknown and they must be estimated from measured data. Performing parameter estimation and quantifying the uncertainty in these estimates becomes critical to realize the predictive power of dynamical systems. In some applications, only measurements about the states of an ensemble of systems are available, where each one evolves according to the same model but for different parameter values, leading to aggregate data problems. In this case, an approach proposed in the literature is to estimate a density that is consistent with some estimates of the expected value of some quantities of interest. To solve the problem in practice, the density is discretized and, to solve the resulting ill-posed problem, Tikhonov regularization is used. In this work, we propose a Bayesian model that shows this approach can be interpreted as a maximum a posteriori estimate for the density. We show that the infinite-dimensional problem defining the MAP can be reformulated as a finite-dimensional problem that does not require discretizing the density. In several cases of interest, this problem is convex, unconstrained, and the objective function is smooth. Thus, it can be solved using algorithms with optimal convergence rates. The trade -off is that the objective is defined by an integral. However, our results characterize the regularity of the integrand, allowing the use of tailored numerical schemes to approximate it. Furthermore, our theoretical results characterize the form of the optimal density, whereas our numerical results illustrate the performance of our method and confirm our theoretical findings.
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.jcp.2024.113141
dc.identifier.eissn1090-2716
dc.identifier.issn0021-9991
dc.identifier.urihttps://doi.org/10.1016/j.jcp.2024.113141
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90451
dc.identifier.wosidWOS:001255456400001
dc.language.isoen
dc.revistaJournal of computational physics
dc.rightsacceso restringido
dc.subjectUncertainty quantification
dc.subjectDynamical systems
dc.subjectConvex optimization
dc.subjectAggregate data problems
dc.subjectRegularization
dc.subjectNonparametric methods
dc.titleTikhonov regularization as a nonparametric method for uncertainty quantification in aggregate data problems
dc.typeartículo
dc.volumen513
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
Files
Collections
Artículos de revistas