Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processes

• URL: http://arxiv.org/abs/2408.03490v1
• Date: Wed, 7 Aug 2024 01:01:35 GMT
• Title: Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processes
• Authors: Amin Yousefpour, Shirin Hosseinmardi, Carlos Mora, Ramin Bostanabad,
• Abstract summary: Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. We develop a new class of TO methods based on the framework of Gaussian processes (GPs) whose mean functions are parameterized via deep neural networks. To test our method against conventional TO approaches implemented in commercial software, we evaluate it on four problems involving the minimization of dissipated power in Stokes flow.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of existing TO approaches leverage numerical solvers for design evaluations during the optimization and hence have a nested nature and rely on discretizing the design variables. Contrary to these approaches, herein we develop a new class of TO methods based on the framework of Gaussian processes (GPs) whose mean functions are parameterized via deep neural networks. Specifically, we place GP priors on all design and state variables to represent them via parameterized continuous functions. These GPs share a deep neural network as their mean function but have as many independent kernels as there are state and design variables. We estimate all the parameters of our model in a single for loop that optimizes a penalized version of the performance metric where the penalty terms correspond to the state equations and design constraints. Attractive features of our approach include $(1)$ having a built-in continuation nature since the performance metric is optimized at the same time that the state equations are solved, and $(2)$ being discretization-invariant and accommodating complex domains and topologies. To test our method against conventional TO approaches implemented in commercial software, we evaluate it on four problems involving the minimization of dissipated power in Stokes flow. The results indicate that our approach does not need filtering techniques, has consistent computational costs, and is highly robust against random initializations and problem setup.

Related papers

• Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks [3.0468934705223774]
  We propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. We show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs.
  arXiv  Detail & Related papers  (2023-02-14T18:55:21Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Parameter Tuning Strategies for Metaheuristic Methods Applied to Discrete Optimization of Structural Design [0.0]
  This paper presents several strategies to tune the parameters of metaheuristic methods for (discrete) design optimization of reinforced concrete (RC) structures. A novel utility metric is proposed, based on the area under the average performance curve.
  arXiv  Detail & Related papers  (2021-10-12T17:34:39Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders [1.0124625066746595]
  A robust topology optimization (RTO) problem identifies a design with the best average performance. A neural network method is proposed that offers computational efficiency. Numerical application of the method is shown on the robust design of L-bracket structure with single point load as well as multiple point loads.
  arXiv  Detail & Related papers  (2021-07-19T20:40:51Z)
• Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation [101.22379613810881]
  We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive process. We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
  arXiv  Detail & Related papers  (2021-02-16T06:04:27Z)
• An AI-Assisted Design Method for Topology Optimization Without Pre-Optimized Training Data [68.8204255655161]
  An AI-assisted design method based on topology optimization is presented, which is able to obtain optimized designs in a direct way. Designs are provided by an artificial neural network, the predictor, on the basis of boundary conditions and degree of filling as input data.
  arXiv  Detail & Related papers  (2020-12-11T14:33:27Z)
• Recent Theoretical Advances in Non-Convex Optimization [56.88981258425256]
  Motivated by recent increased interest in analysis of optimization algorithms for non- optimization in deep networks and other problems in data, we give an overview of recent results of theoretical optimization algorithms for non- optimization.
  arXiv  Detail & Related papers  (2020-12-11T08:28:51Z)
• Objective-Sensitive Principal Component Analysis for High-Dimensional Inverse Problems [0.0]
  We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching.
  arXiv  Detail & Related papers  (2020-06-02T18:51:17Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)
• Bayesian optimization of variable-size design space problems [0.0]
  Two alternative Bayesian Optimization-based approaches are proposed in order to solve this type of optimization problems. The first approach consists in a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables.
  arXiv  Detail & Related papers  (2020-03-06T16:30:44Z)

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.