Related papers: Subdomain POD-TPWL with Local Parameterization for…

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

Nowadays, the shipbuilding industry is facing a radical change towards solutions with a smaller environmental impact. This can be achieved with low emissions engines, optimized shape designs with lower wave resistance and noise generation,…

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Despite the success, the process of fine-tuning large-scale PLMs brings prohibitive adaptation costs. In fact, fine-tuning all the parameters of a colossal model and retaining separate instances for different tasks are practically…

Hard parameter sharing in multi-domain learning (MDL) allows domains to share some of the model parameters to reduce storage cost while improving prediction accuracy. One common sharing practice is to share the bottom layers of a deep…

Large pre-trained models have been vital in recent advancements in domains like language and vision, making model training for individual downstream tasks more efficient and provide superior performance. However, tackling time-series…

Deep learning has achieved state-of-the-art performance on several computer vision tasks and domains. Nevertheless, it still has a high computational cost and demands a significant amount of parameters. Such requirements hinder the use in…

Embedded controllers for cyber-physical systems are often parameterized by look-up maps representing discretizations of continuous functions on metric spaces. For example, a non-linear control action may be represented as a table of…

Task specific hyperparameter tuning in reservoir computing is an open issue, and is of particular relevance for hardware implemented reservoirs. We investigate the influence of directly including externally controllable task specific…

Reduced-order models (ROMs) are often used to accelerate the simulation of large physical systems. However, traditional ROM techniques, such as those based on proper orthogonal decomposition (POD), often struggle with advection-dominated…

Parameter space reduction has been proved to be a crucial tool to speed-up the execution of many numerical tasks such as optimization, inverse problems, sensitivity analysis, and surrogate models' design, especially when in presence of…

Hyperparameter tuning can dramatically impact training stability and final performance of large-scale models. Recent works on neural network parameterisations, such as $\mu$P, have enabled transfer of optimal global hyperparameters across…

Deep learning models trained on large data sets have been widely successful in both vision and language domains. As state-of-the-art deep learning architectures have continued to grow in parameter count so have the compute budgets and times…

Local Fourier analysis is a commonly used tool for the analysis of multigrid and other multilevel algorithms, providing both insight into observed convergence rates and predictive analysis of the performance of many algorithms. In this…

We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local…

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers…

Deep learning models often struggle to maintain performance when deployed on data distributions different from their training data, particularly in real-world applications where environmental conditions frequently change. While Multi-source…