相关论文: Hyper-reduction for parametrized transport dominat…

We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration…

Computational efficiency is an important consideration for deploying machine learning models for time series prediction in an online setting. Machine learning algorithms adjust model parameters automatically based on the data, but often…

Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we…

In this work, we propose and analyze a residual-minimization strategy for the numerical solution of nonlinear PDEs posed in Banach spaces. Given a finite-dimensional trial space and a suitably enriched discrete test space (of higher…

We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…

This paper proposes online sampling in the parameter space of a neural network for GPU-accelerated motion planning of autonomous vehicles. Neural networks are used as controller parametrization since they can handle nonlinear non-convex…

This paper presents an adaptive online distributed optimal control approach that is applicable to optimal planning for very-large-scale robotics systems in highly uncertain environments. This approach is developed based on the optimal mass…

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…

We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular prediction rules, modeled by Besov spaces $B\_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s >…

Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and…

In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…

In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent…

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…

Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…

Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…

Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…