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Theoretical guarantees for the robust solution of inverse problems have important implications for applications. To achieve both guarantees and high reconstruction quality, we propose learning a pixel-based ridge regularizer with a…
World models aim to capture the states and dynamics of an environment in a compact latent space. Moreover, using Boolean state representations is particularly useful for search heuristics and symbolic reasoning and planning. Existing…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
In Part I of this paper we have presented a simple model capable of describing the localized failure of a massive structure. In this part, we discuss the identification of the model parameters from two kinds of experiments: a uniaxial…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
It is broadly known that deep neural networks are susceptible to being fooled by adversarial examples with perturbations imperceptible by humans. Various defenses have been proposed to improve adversarial robustness, among which adversarial…
We study a simple and tractable model of many-body localization. The main idea is to take a renormalization group perspective in which local entanglement is removed to reach a product state. The model is built from a random local unitary…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the…
We numerically study the single particle localization and delocalization phenomena of an initially localized wave packet in the kicked Harper model (KHM) and Harper model subjected to quasi-periodic perturbation composed of $M-$modes. Both…
We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation…
We describe a generic technique for fault localization independent from the nature of the object or the specification language used to declare its expected properties. This technique is based on the concept of "repair", a minimal set of…
Distribution shifts are ubiquitous in real-world machine learning applications, posing a challenge to the generalization of models trained on one data distribution to another. We focus on scenarios where data distributions vary across…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
We investigate dynamic crack propagation and fragmentation with the phase-field fracture approach. The method was chosen for its ability to yield crack paths that are independent of the underlying mesh, thanks to the damage regularization…
The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…
Through the lense of multilevel model (MLM) specification and regularization, this is a connect-the-dots introductory summary of Small Area Estimation, e.g. small group prediction informed by a complex sampling design. While a comprehensive…
In many reinforcement learning (RL) applications, the observation space is specified by human developers and restricted by physical realizations, and may thus be subject to dramatic changes over time (e.g. increased number of observable…
A novel phase-field for ductile fracture model is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling…