Related papers: Iterative Cut-Based PWA Approximation of Multi-Dim…
This paper presents a method to approximate regions of attraction of unknown nonlinear dynamical systems from data. Assuming point-wise evaluations of the vector field and known Lipschitz bounds, a polyhedral uncertainty set of admissible…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…
Capturing nonlinear relationships without sacrificing interpretability remains a persistent challenge in regression modeling. We introduce SplitWise, a novel framework that enhances stepwise regression. It adaptively transforms numeric…
Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…
Partial-wave analyses (PWA) are an essential tool for studying resonance structures in decays with hadronic multi-body final states. For several years, more model-independent approaches to such analyses have been used for various decay…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
In this paper, we describe a novel framework for digital predistortion (DPD) based linearization of strongly nonlinear millimeter-wave active antenna arrays. Specifically, we formulate a piecewise (PW) closed-loop (CL) DPD solution and…
Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
Piecewise linearization is a key technique for solving nonlinear problems in transportation network design and other optimization fields, in which generating breakpoints is a fundamental task. This paper proposes an optimal breakpoint…
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…
Binary Convolutional Neural Networks (CNNs) can significantly reduce the number of arithmetic operations and the size of memory storage, which makes the deployment of CNNs on mobile or embedded systems more promising. However, the accuracy…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
Invariant-based models for incompressible isotropic hyperelasticity are typically formulated as functions of the first and second invariants, $W = W(\bar{I}_1, \bar{I}_2)$. A widely used class of models employs separable representations of…
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…
We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($\epsilon$-PLA) has emerged…
We study piecewise affine policies for multi-stage adjustable robust optimization (ARO) problems with non-negative right-hand side uncertainty. First, we construct new dominating uncertainty sets and show how a multi-stage ARO problem can…