Related papers: New Approaches to Inverse Structural Modification …
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…
Aerodynamic inverse design can improve vehicle and aircraft efficiency, but practical design rarely seeks performance alone: vehicle refinement must reduce drag while preserving visual features linked to design language, brand recognition…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies…
While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
The objective of this Philosophiae Doctor (Ph.D) thesis is to propose an efficient approach for optimizing a multidisciplinary black-box model when the optimization problem is constrained and involves a large number of mixed integer design…
Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…
Simultaneous optimization of multiple quantum objectives is often considered a demanding task. However, a special circumstance arises when a primary objective is pitted against a set of secondary objectives, which we show leads to invariant…
Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…
Grokking -- the delayed transition from memorization to generalization in small algorithmic tasks -- remains poorly understood. We present a geometric analysis of optimization dynamics in transformers trained on modular arithmetic. PCA of…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…
With more efficient structures, last trends in aeronautics have witnessed an increased flexibility of wings, calling for adequate design and optimization approaches. To correctly model the coupled physics, aerostructural optimization has…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…