My research activity focuses on:
| Methods & Applications | Projects |
|---|---|
| Reduced-order models | LocalROM, BackUQ, ROMES |
| Machine learning | ROMES |
| Uncertainty quantification | BackUQ |
| Cardiac electrophysiology | LocalROM |
Local reduced-order models
Local ROMs enable to better approximate the solution of parametrized (nonlinear) time-dependent problems in a lower-dimensional subspace generated by local basis vectors, rather than in a unique subspace spanned by global basis vectors. In our work, we have performed several numerical tests dealing with the monodomain equation coupled with the Aliev-Panfilov ionic model in several parameter-dependent scenarios. In particular, we have compared a local ROM built through a k-means clustering in the state space of the snapshots with three alternative local ROMs (time-, parameter- and state-based).
Material
- Paper
- Test case 1D code LocalROM
- Slides from a part of my talk at IV ECCOMAS YOUNG INVESTIGATOR CONFERENCE - YIC2017 - Politecnico di Milano (Italy)
Inverse (backward UQ) problems
A growing number of applications in computational science and engineering are bringing new challenges dealing with the integration of high-dimensional and complex data (possibly affected by uncertainty) within mathematical models built on partial differential equations. Backward uncertainty quantification (UQ) problems involve parameter (and state) estimation and data assimilation in view of both model calibration and personalization. In this context, Bayesian methods provide a rigorous framework for the solution of backward UQ problems: sampling algorithms, such as the Markov chain Monte Carlo (MCMC) or the (ensemble) Kalman filter, enable to estimate the distribution of quantities of interest (model parameters, state of a system) from noisy measurements. Adopting Bayesian methods is much costly compared to deterministic optimization procedure, which however neglect the presence of uncertainties. To apply them to complex full-order models with possibly large parameter space, new efficient reduction methods, combining statistical and numerical tools, have been developed in our works.
Material
Reduced-order model error surrogates
A statistical closure model for reduced-order models (ROMs) based on the ROMES technique aims to construct a statistical model for the state error of stationary systems; it achieves this by constructing statistical models for the generalized coordinates characterizing both the in-plane error (i.e., error in the trial subspace) and a low-dimensional approximation of the out-of-plane error. The former can be considered a closure model, as it models the error in the state variables preserved by the ROM. Because any quantity of interest can be computed as a functional of the state, the proposed approach enables the error in any quantity of interest to be statistically quantified a posteriori, as the closure model for the state error can be propagated through the associated quantity-of-interest functional.
Material
Forward uncertainty quantification
Under construction
Sensitivity analysis
Under construction