Related papers: Offline-Enhanced Reduced Basis Method through adap…

We seek to understand what facilitates sample-efficient learning from historical datasets for sequential decision-making, a problem that is popularly known as offline reinforcement learning (RL). Further, we are interested in algorithms…

Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

This paper proposes and tests the first-ever reduced basis warm-start iterative method for the parametrized linear systems, exemplified by those discretizing the parametric partial differential equations. Traditional iterative methods are…

Gradient-based attacks are important methods for evaluating model robustness. However, since the proposal of APGD, it has been difficult for such methods to achieve significant breakthroughs. To achieve such an effect, we first analyze the…

The performance of the existing sparse Bayesian learning (SBL) methods for off-gird DOA estimation is dependent on the trade off between the accuracy and the computational workload. To speed up the off-grid SBL method while remain a…

We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an…

Offline reinforcement learning (RL) defines the task of learning from a fixed batch of data. Due to errors in value estimation from out-of-distribution actions, most offline RL algorithms take the approach of constraining or regularizing…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized…

Online social networks have been one of the most effective platforms for marketing and advertising. Through "word of mouth" effects, information or product adoption could spread from some influential individuals to millions of users in…

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

In this work, we analyse space-time reduced basis methods for the efficient numerical simulation of hemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while…

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…

Restricted Boltzmann Machine (RBM) is a generative stochastic energy-based model of artificial neural network for unsupervised learning. Recently, RBM is well known to be a pre-training method of Deep Learning. In addition to visible and…

We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…

Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent…

A novel machine learning optimization process coined Restrictive Federated Model Selection (RFMS) is proposed under the scenario, for example, when data from healthcare units can not leave the site it is situated on and it is forbidden to…