Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers

• URL: http://arxiv.org/abs/2407.19000v2
• Date: Fri, 4 Oct 2024 11:49:30 GMT
• Title: Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers
• Authors: David Huergo, Martín de Frutos, Eduardo Jané, Oscar A. Marino, Gonzalo Rubio, Esteban Ferrer,
• Abstract summary: We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p using Reinforcement Learning (RL) We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. We derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors.
• Score: 0.37109226820205005
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. In addition, we derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors. The proposed methodology is agnostic to both the computational mesh and the partial differential equation to be solved. The application of RL to mesh adaptation offers several benefits. It enables automated and adaptive mesh refinement, reducing the need for manual intervention. It optimizes computational resources by dynamically allocating high-order polynomials where necessary and minimizing refinement in stable regions. This leads to computational cost savings while maintaining the accuracy of the solution. Furthermore, RL allows for the exploration of unconventional mesh adaptations, potentially enhancing the accuracy and robustness of simulations. This work extends our original research, offering a more robust, reproducible, and generalizable approach applicable to complex three-dimensional problems. We provide validation for laminar and turbulent cases: circular cylinders, Taylor Green Vortex and a 10MW wind turbine to illustrate the flexibility of the proposed approach.

Related papers

• Adaptive $Q$-Network: On-the-fly Target Selection for Deep Reinforcement Learning [18.579378919155864]
  We propose Adaptive $Q$Network (AdaQN) to take into account the non-stationarity of the optimization procedure without requiring additional samples. AdaQN is theoretically sound and empirically validate it in MuJoCo control problems and Atari $2600 games.
  arXiv  Detail & Related papers  (2024-05-25T11:57:43Z)
• Learning Constrained Optimization with Deep Augmented Lagrangian Methods [54.22290715244502]
  A machine learning (ML) model is trained to emulate a constrained optimization solver. This paper proposes an alternative approach, in which the ML model is trained to predict dual solution estimates directly. It enables an end-to-end training scheme is which the dual objective is as a loss function, and solution estimates toward primal feasibility, emulating a Dual Ascent method.
  arXiv  Detail & Related papers  (2024-03-06T04:43:22Z)
• QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power Flow Solutions Under Constraints [4.1920378271058425]
  We propose an innovated computational learning ACOPF, where the input is mapped to the ACOPF network in a computationally efficient manner. We show through simulations that our proposed method achieves superior feasibility rate and cost in situations where the existing-based approaches fail.
  arXiv  Detail & Related papers  (2024-01-11T20:17:44Z)
• A reinforcement learning strategy for p-adaptation in high order solvers [0.0]
  Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the order in the computational mesh when using high-order solvers.
  arXiv  Detail & Related papers  (2023-06-14T07:01:31Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching [55.28394191394675]
  We develop an adaptive inexact Newton method for equality-constrained nonlinear, nonIBS optimization problems. We demonstrate the superior performance of our method on benchmark nonlinear problems, constrained logistic regression with data from LVM, and a PDE-constrained problem.
  arXiv  Detail & Related papers  (2023-05-28T06:33:37Z)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• Reinforcement Learning for Adaptive Mesh Refinement [63.7867809197671]
  We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning to train refinement policies directly from simulation. The model sizes of these policy architectures are independent of the mesh size and hence scale to arbitrarily large and complex simulations.
  arXiv  Detail & Related papers  (2021-03-01T22:55:48Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications [5.660384137948734]
  The proposed algorithm converges to the correct distribution with a controllable bias under mild conditions. We show that the proposed algorithm canally converge to the correct distribution with a controllable bias under mild conditions.
  arXiv  Detail & Related papers  (2020-06-29T20:57:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.