Related papers: Model Boundary Approximation Method as a Unifying …
It is a challenging problem that solving the \textit{multivariate linear model} (MLM) $\mathbf{A}\mathbf{x}=\mathbf{b}$ with the $\ell_1 $-norm approximation method such that $||\mathbf{A}\mathbf{x}-\mathbf{b}||_1$, the $\ell_1$-norm of the…
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…
Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate…
Accurate spatiotemporal calibration is a prerequisite for multisensor fusion. However, sensors are typically asynchronous, and there is no overlap between the fields of view of cameras and LiDARs, posing challenges for intrinsic and…
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 show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate…
This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the…
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…
Time series forecasting is a long-standing and highly challenging research topic. Recently, driven by the rise of large language models (LLMs), research has increasingly shifted from purely time series methods toward harnessing textual…
This paper proposes a novel robust Model Predictive Control (MPC) scheme for linear discrete-time systems affected by model uncertainty described by interval matrices. The key feature of the proposed method is a bound on the uncertainty…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an…
An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase space methods…
Prompting and in-context learning (ICL) have become efficient learning paradigms for large language models (LLMs). However, LLMs suffer from prompt brittleness and various bias factors in the prompt, including but not limited to the…
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…
Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the…
Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…