Related papers: Optimal renormalization of multi-scale systems
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…
Magnetizable piezoelectric beams exhibit strong couplings between mechanical, electric, and magnetic fields, significantly affecting their high-frequency vibrational behavior. Ensuring exponential stability under boundary feedback…
In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
We consider low-order controller design for large-scale linear time-invariant dynamical systems with inputs and outputs. Model order reduction is a popular technique, but controllers designed for reduced-order models may result in unstable…
In this paper we address the class of Sequential Decision Making (SDM) problems that are characterized by time-varying parameters. These parameter dynamics are either pre-specified or manipulable. At any given time instant the decision…
This paper applies Benders decomposition to two-stage stochastic problems for energy planning under climate uncertainty, a key problem for the design of renewable energy systems. To improve performance, we adapt various refinements for…
The inviscid Burgers equation is one of the simplest nonlinear hyperbolic conservation law which provides a variety examples for many topics in nonlinear partial differential equations such as wave propagation, shocks and perturbation, and…
In this paper, we focus on model reduction of biomolecular systems with multiple time-scales, modeled using the Linear Noise Approximation. Considering systems where the Linear Noise Approximation can be written in singular perturbation…
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…
We consider the problem of locating a nearest descriptor system of prescribed reduced order to a descriptor system with large order with respect to the ${\mathcal L}_\infty$ norm. Widely employed approaches such as the balanced truncation…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
In this work, we focus on reduced order modeling (ROM) techniques for hyperbolic conservation laws with application in uncertainty quantification (UQ) and in conjunction with the well-known Monte Carlo sampling method. Because we are…
We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…
This paper presents a novel methodology for tractably solving optimal control and offline reinforcement learning problems for high-dimensional systems. This work is motivated by the ongoing challenges of safety, computation, and optimality…
Recurrent neural network (RNN)'s architecture is a key factor influencing its performance. We propose algorithms to optimize hidden sizes under running time constraint. We convert the discrete optimization into a subset selection problem.…
The modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained optimal control problems by introducing surrogate models for PDE…
Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…