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A digital twin is formally defined as “a set of virtual information constructs that mimics the structure, context, and behavior of a natural, engineered, or social system (or system-of-systems), is dynamically updated with data from its physical twin, has a predictive capability, and informs decisions that realize value. The bidirectional interaction between the virtual and the physical is central to the digital twin” [1].
We develop numerical methods to enable the creation of scalable predictive digital twins.
[1] National Academies of Sciences, Engineering, and Medicine. (2024). Foundational research gaps and future directions for digital twins. Washington, D.C.: The National Academies Press.
Model order reduction (MOR) aims at reducing the computational complexity of mathematical models in numerical simulations. It is a computational technique to reduce the order of dynamical systems or parameterized PDEs discretized in a computational mesh.
MOR enables the efficient solution of high-dimensional problems thus opening new routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, and optimization, which are ubiquitous challenges in computational sciences and engineering.
In the early design phase of cruise ship hulls the designers are tasked with ensuring the structural resilience of the ship against extreme waves while reducing steel usage and respecting safety and manufacturing constraints. The ship's geometry is already finalized and the designer can choose the thickness of the primary structural elements, such as decks, bulkheads, and the shell.
We integrated reduced order modeling and black-box optimization techniques into a structural optimization pipeline to reduce the use of expensive finite element analysis and validate only the most promising configurations, thanks to the efficient exploration of the domain of decision variables.
Parameter space reduction is a dimensionality reduction method that identifies a low-dimensional structure for functions varying primarily on a low-dimensional subspace of the high-dimensional input space. Such low-dimensional structures are present in many engineering models. Parameter space reduction techniques proved to be crucial tools to speed-up the execution of many numerical tasks such as optimization, inverse problems resolution, sensitivity analysis, and surrogate models’ design, especially when in presence of high-dimensional parametrized systems.
We developed many techniques stemming from the active subspaces (AS) method, a gradient-based method to perform linear dimensionality reduction. We leveraged localization techniques to develop local AS and reproducing kernel Hilbert spaces for kernel-based AS. We also integrated AS into genetic algorithms to speed-up the optimization of high-dimensional functions.
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