相关论文: A New Two-dimensional Model-based Subspace Method …

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…

In this paper, we analyze the accuracy of gradient estimates obtained by linear interpolation when the underlying function is subject to bounded measurement noise. The total gradient error is decomposed into a deterministic component…

We present MeshODE, a scalable and robust framework for pairwise CAD model deformation without prespecified correspondences. Given a pair of shapes, our framework provides a novel shape feature-preserving mapping function that continuously…

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…

Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…

Surgical navigation based on multimodal image registration has played a significant role in providing intraoperative guidance to surgeons by showing the relative position of the target area to critical anatomical structures during surgery.…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this…

The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…

Many real world scientific and industrial applications require optimizing multiple competing black-box objectives. When the objectives are expensive-to-evaluate, multi-objective Bayesian optimization (BO) is a popular approach because of…

We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…

Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP),…

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential…

In this paper, we focus on the nonconvex-strongly-convex bilevel optimization problem (BLO). In this BLO, the objective function of the upper-level problem is nonconvex and possibly nonsmooth, and the lower-level problem is smooth and…

This paper presents a novel and lightweight hyperparameter optimization (HPO) method, MOdular FActorial Design (MOFA). MOFA pursues several rounds of HPO, where each round alternates between exploration of hyperparameter space by factorial…

High-dimensional Bayesian Optimization (BO) has attracted significant attention in recent research. However, existing methods have mainly focused on optimizing in continuous domains, while combinatorial (ordinal and categorical) and mixed…

The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale…