Related papers: Deep Reinforcement Learning for Adaptive Mesh Refi…
We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the…
Although in recent years reinforcement learning has become very popular the number of successful applications to different kinds of operations research problems is rather scarce. Reinforcement learning is based on the well-studied dynamic…
In neuroscience, one of the key behavioral tests for determining whether a subject of study exhibits model-based behavior is to study its adaptiveness to local changes in the environment. In reinforcement learning, however, recent studies…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
Many challenging real-world problems require the deployment of ensembles multiple complementary learning models to reach acceptable performance levels. While effective, applying the entire ensemble to every sample is costly and often…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
Adaptive Mixed-Criticality (AMC) is a fixed-priority preemptive scheduling algorithm for mixed-criticality hard real-time systems. It dominates many other scheduling algorithms for mixed-criticality systems, but does so at the cost of…
One of the main goals of reinforcement learning (RL) is to provide a~way for physical machines to learn optimal behavior instead of being programmed. However, effective control of the machines usually requires fine time discretization. The…
We propose policy gradient algorithms which learn risk-sensitive policies in a reinforcement learning (RL) framework. Our proposed algorithms maximize the distortion risk measure (DRM) of the cumulative reward in an episodic Markov decision…
Deep reinforcement learning is an increasingly popular technique for synthesising policies to control an agent's interaction with its environment. There is also growing interest in formally verifying that such policies are correct and…
Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…
In this paper, we present substantial evidence that a deep neural network will intrinsically learn the appropriate way to discretize the ideal continuous reconstruction filter. Currently, the Ram-Lak filter or heuristic filters which impose…
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical…
I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…
Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…
We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks. The field solution on each…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
We study the setting of \emph{performative reinforcement learning} where the deployed policy affects both the reward, and the transition of the underlying Markov decision process. Prior work~\parencite{MTR23} has addressed this problem…