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A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
Low-Rank Adaptation (LoRA) has proven effective in reducing computational costs while maintaining performance comparable to fully fine-tuned foundation models across various tasks. However, its fixed low-rank structure restricts its…
We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a model-free extremum seeking (ES) dither-based…
State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…
This paper presents an H2-optimal model order reduction (MOR) method for linear systems with quadratic outputs based on Riemannian optimization. The H2-optimal MOR is formulated as an optimization problem in which the optimization variables…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
Model order reduction (MOR) techniques have always struggled in compressing information for advection dominated problems. Their linear nature does not allow to accelerate the slow decay of the Kolmogorov $N$--width of these problems. In the…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to…
Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…
The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the…
One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on…
Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads,…
We consider the problem of learning an inner approximation of the region of attraction (ROA) of an asymptotically stable equilibrium point without an explicit model of the dynamics. Rather than leveraging approximate models with bounded…
The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…