Related papers: Deep Reinforcement Learning for Adaptive Mesh Refi…

This paper presents novel refinement sensors for the application to adaptive mesh and algorithm refinement (AMAR) with kinetic models, such as discrete velocity and lattice Boltzmann methods. While refinement criteria for AMAR based on…

Adaptive mesh refinement (AMR) is widely used to efficiently resolve localized features in time-dependent partial differential equations (PDEs) by selectively refining and coarsening the mesh. However, in long-horizon simulations, repeated…

The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…

We present on-line policy gradient algorithms for computing the locally optimal policy of a constrained, average cost, finite state Markov Decision Process. The stochastic approximation algorithms require estimation of the gradient of the…

Deep reinforcement learning (RL) algorithms can learn complex policies to optimize agent operation over time. RL algorithms have shown promising results in solving complicated problems in recent years. However, their application on…

Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…

Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…

Several applications in the scientific simulation of physical systems can be formulated as control/optimization problems. The computational models for such systems generally contain hyperparameters, which control solution fidelity and…

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…

Numerical evolution of the spherically symmetric, massive Klein-Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…

We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, their performance heavily relies on the strategy used to select training points. Conventional adaptive…

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…

A Markov Decision Process (MDP) is a popular model for reinforcement learning. However, its commonly used assumption of stationary dynamics and rewards is too stringent and fails to hold in adversarial, nonstationary, or multi-agent…

Reinforcement learning (RL) is a central problem in artificial intelligence. This problem consists of defining artificial agents that can learn optimal behaviour by interacting with an environment -- where the optimal behaviour is defined…