Dynamically configured physics-informed neural network in topology optimization applications

• URL: http://arxiv.org/abs/2312.06993v1
• Date: Tue, 12 Dec 2023 05:35:30 GMT
• Title: Dynamically configured physics-informed neural network in topology optimization applications
• Authors: Jichao Yin and Ziming Wen and Shuhao Li and Yaya Zhanga and Hu Wang
• Abstract summary: The physics-informed neural network (PINN) can avoid generating enormous amounts of data when solving forward problems. A dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed. The accuracy of the displacement prediction and optimization results indicate that the DCPINN-TO method is effective and efficient.
• Score: 4.403140515138818
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Integration of machine learning (ML) into the topology optimization (TO) framework is attracting increasing attention, but data acquisition in data-driven models is prohibitive. Compared with popular ML methods, the physics-informed neural network (PINN) can avoid generating enormous amounts of data when solving forward problems and additionally provide better inference. To this end, a dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed. The DCPINN is composed of two subnetworks, namely the backbone neural network (NN) and the coefficient NN, where the coefficient NN has fewer trainable parameters. The designed architecture aims to dynamically configure trainable parameters; that is, an inexpensive NN is used to replace an expensive one at certain optimization cycles. Furthermore, an active sampling strategy is proposed to selectively sample collocations depending on the pseudo-densities at each optimization cycle. In this manner, the number of collocations will decrease with the optimization process but will hardly affect it. The Gaussian integral is used to calculate the strain energy of elements, which yields a byproduct of decoupling the mapping of the material at the collocations. Several examples with different resolutions validate the feasibility of the DCPINN-TO method, and multiload and multiconstraint problems are employed to illustrate its generalization. In addition, compared to finite element analysis-based TO (FEA-TO), the accuracy of the displacement prediction and optimization results indicate that the DCPINN-TO method is effective and efficient.

Related papers

• RoPINN: Region Optimized Physics-Informed Neural Networks [66.38369833561039]
  Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) This paper proposes and theoretically studies a new training paradigm as region optimization. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm.
  arXiv  Detail & Related papers  (2024-05-23T09:45:57Z)
• Hallmarks of Optimization Trajectories in Neural Networks: Directional Exploration and Redundancy [75.15685966213832]
  We analyze the rich directional structure of optimization trajectories represented by their pointwise parameters. We show that training only scalar batchnorm parameters some while into training matches the performance of training the entire network.
  arXiv  Detail & Related papers  (2024-03-12T07:32:47Z)
• Model-Based Control with Sparse Neural Dynamics [23.961218902837807]
  We propose a new framework for integrated model learning and predictive control. We show that our framework can deliver better closed-loop performance than existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-12-20T06:25:02Z)
• Towards Hyperparameter-Agnostic DNN Training via Dynamical System Insights [4.513581513983453]
  We present a first-order optimization method specialized for deep neural networks (DNNs), ECCO-DNN. This method models the optimization variable trajectory as a dynamical system and develops a discretization algorithm that adaptively selects step sizes based on the trajectory's shape.
  arXiv  Detail & Related papers  (2023-10-21T03:45:13Z)
• A Multi-Head Ensemble Multi-Task Learning Approach for Dynamical Computation Offloading [62.34538208323411]
  We propose a multi-head ensemble multi-task learning (MEMTL) approach with a shared backbone and multiple prediction heads (PHs) MEMTL outperforms benchmark methods in both the inference accuracy and mean square error without requiring additional training data.
  arXiv  Detail & Related papers  (2023-09-02T11:01:16Z)
• Orthogonal Stochastic Configuration Networks with Adaptive Construction Parameter for Data Analytics [6.940097162264939]
  randomness makes SCNs more likely to generate approximate linear correlative nodes that are redundant and low quality. In light of a fundamental principle in machine learning, that is, a model with fewer parameters holds improved generalization. This paper proposes orthogonal SCN, termed OSCN, to filtrate out the low-quality hidden nodes for network structure reduction.
  arXiv  Detail & Related papers  (2022-05-26T07:07:26Z)
• NTopo: Mesh-free Topology Optimization using Implicit Neural Representations [35.07884509198916]
  We present a novel machine learning approach to tackle topology optimization problems. We use multilayer perceptrons (MLPs) to parameterize both density and displacement fields. As we show through our experiments, a major benefit of our approach is that it enables self-supervised learning of continuous solution spaces.
  arXiv  Detail & Related papers  (2021-02-22T05:25:22Z)
• A Dynamical View on Optimization Algorithms of Overparameterized Neural Networks [23.038631072178735]
  We consider a broad class of optimization algorithms that are commonly used in practice. As a consequence, we can leverage the convergence behavior of neural networks. We believe our approach can also be extended to other optimization algorithms and network theory.
  arXiv  Detail & Related papers  (2020-10-25T17:10:22Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Self-Directed Online Machine Learning for Topology Optimization [58.920693413667216]
  Self-directed Online Learning Optimization integrates Deep Neural Network (DNN) with Finite Element Method (FEM) calculations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 5 orders of magnitude compared with directly using methods, and outperformed all state-of-the-art algorithms tested in our experiments.
  arXiv  Detail & Related papers  (2020-02-04T20:00:28Z)

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.