Aug 2026· AIP Advances· Vol 16· 0 citations· 32 references
TL;DR
A machine learning-assisted inverse parameter prediction framework that couples a Random Forest-based inverse surrogate model with compliance-minimization topology optimization and suggests that the framework may serve as a rapid design initialization tool for lightweight structural applications.
Abstract
Structural topology optimization for lightweight design faces two major challenges: the high computational cost of iterative finite-element analysis and the limited capacity of conventional surrogate models to solve inverse design problems. To address these issues, this paper introduces a machine learning-assisted inverse parameter prediction framework that couples a Random Forest (RF)-based inverse surrogate model with compliance-minimization topology optimization. The approach inverts the conventional input–output relationship by constructing a direct mapping from deformation response to design parameters. The methodology proceeds in three stages: first, the topology optimization procedure is parameterized to generate a representative sample database; second, an RF model is trained to capture the inverse regression between deformation responses and geometric and optimization parameters; third, engineering-viable solutions are obtained through a compliance-oriented refinement optimization. The proposed inverse surrogate model g1, trained on SIMP-based data, achieves approximately a twofold reduction in computational cost relative to the conventional SIMP approach. By contrast, model g2, trained on level-set-based data, incurs longer computational times, a consequence of the higher cost of level-set sample generation. Load-induced deformation errors are maintained within 5% of the reference value, and prediction accuracy exceeds 95% across repeated trials. These results suggest that the framework may serve as a rapid design initialization tool for lightweight structural applications.
Optimizing lattice structures for energy absorption and load-bearing applications necessitates accurately capturing their nonlinear mechanical response under large deformation. However, traditional nonlinear finite element analysis (NL-FEA) can often fail, particularly at higher compression, which creates numerical gaps in the design space, hindering gradient-based optimization algorithms, ultimately resulting in suboptimal designs. We propose here a neural network (NN) surrogate model that is trained on data generated using Abaqus, a commercial FEA solver. A unique feature of the model is that it exploits both fully and partially successful NL-FEA simulations. This significantly improves the surrogate model’s accuracy and predictive coverage across the design space. The resulting model enables efficient, gradient-driven optimization of lattice structures to match a desired force-displacement response. By replacing expensive NL-FEA evaluations, the surrogate model substantially reduces computational cost while maintaining a coefficient of determination (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document}) of 0.98 in prediction. The effectiveness and versatility of this framework are demonstrated by successfully optimizing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 \times 3$$\end{document} lattice structures under 40% compression, with the lattice radii as design variables.
Akshay Kumar, S. Sridhara, Krishnan Suresh· Engineering computations· 0 citations
Topology optimization provides innovative solutions for lightweight structural design by rationally arranging material distribution. It enhances structural performance while reducing material consumption and structural weight, thereby significantly lowering production and operational costs and generating enormous economic benefits. In the development of topology optimization, the density-based method has gained widespread adoption due to its easy-to-understand principles. However, this method still faces the following challenges when applied to engineering applications. First, the geometric models generated by topology optimization lack explicit parameter descriptions, leading to data interaction barriers with Computer Aided Design (CAD) systems. Second, due to element discretization and density penalty mechanisms, structural boundaries exhibit rough and blurred characteristics. These problems severely constrain the iterative efficiency of structural design and manufacturing feasibility. To address these issues, this paper proposes a strategy for geometric reconstruction and shape optimization of topology optimization results. The reconstruction process begins with extracting isolines from the density field as a set of contour points. These points are subsequently interpolated with B-spline curves to explicitly represent the geometric boundaries. Shape optimization is then carried out by adjusting the positions of the B-spline control points. Compared to post-processing methods based on graphics techniques for topology optimization, which ignore the volume constraint and performance loss, the structures reconstructed in this paper exhibits the following advantages: structural boundaries are smoothed and characterized with explicit parameters, reducing performance loss caused by geometric reconstruction while satisfying volume constraints. This paper successfully establishes compatibility between topology optimization and CAD systems, facilitating the transition from conceptual design to manufacturing.
Yuting Tang, Yu Li, Jiaxiang Luo et al.· SAE technical paper series· 0 citations
Engineering shape optimization faces challenges in both expert-dependent problem setup and surrogate-model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers, while surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape-optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization. We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty-estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment. Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of $1.16\%$ and a trend-prediction accuracy of $94.34\%$, outperforming the best baseline results of $1.52\%$ and $90.34\%$, respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately $4\%$ to $10\%$.
Wenhao Fan, Yuanwei Bin, Jianghang Gu et al.· 0 citations
This work evaluates surrogate-assisted optimization of a seven-parameter current-excited coil--core benchmark subject to geometric, manufacturing, and separate core and copper mass constraints. A Python--MPh--COMSOL workflow couples a two-dimensional axisymmetric finite-element method (FEM) model to a Matern 5/2 Gaussian-process (GP) probabilistic surrogate. Here, physics-constrained denotes a design problem evaluated by a governing-equation FEM model and restricted by explicit physical, geometric, manufacturing, and material-allocation constraints; it does not denote a physics-informed GP architecture. Sequential Bayesian optimization (BO) ranks candidates using expected improvement (EI), and every reported incumbent is verified by FEM. Five paired runs show that optimizer ranking depends on the available FEM-evaluation budget: EI--BO improves rapidly at small continuation budgets, COBYLA is stronger at the earliest checkpoint, and BOBYQA attains the highest mean terminal response. A retrospective finite-pool study further finds no robust endpoint advantage of EI over posterior-mean ranking on this smooth response surface. The broader result is that early progress, terminal response, information use, and wall-clock cost can favor different methods in simulation-driven design. A selected-design check at a common total current preserves the observed BOBYQA--COBYLA--EI-BO ordering. The conclusions nevertheless remain conditional on this axisymmetric benchmark and do not establish a fixed-current optimum, fixed-power performance, or electrical-efficiency superiority.
With the advance of high-end manufacturing and the rise of green design, lightweight structures have become a central concern in aerospace. Topology optimization offers a principled route to shed mass while preserving performance, yet most additive manufacturing (AM) studies still emphasize process tuning and new materials rather than structural layouts constrained by AM realities. This work targets a representative wing rib from a specific unmanned aerial vehicle (UAV) and formulates a multi-objective topology optimization that explicitly embeds AM constraints. Using the Solid Isotropic Material with Penalization (SIMP) variable-density framework, we couple static stiffness and strength measures with modal objectives so that the optimized rib not only resists deformation and limits stress but also improves the first three natural frequencies, thereby mitigating adverse vibration interactions at the wing level. A compromise-programming strategy balances these competing objectives under volume and manufacturability requirements, including AM-driven minimum feature scales and related geometric restrictions. Finite-element analyses are used throughout the loop to evaluate displacement, von Mises stress, and eigenfrequencies, ensuring that the emerging material distribution is both efficient and physically meaningful. The resulting topology exhibits clearer load paths and smoother stress flow, reduces peak displacements, and delivers a marked rise in the first three natural frequencies. Overall mass is lowered by approximately 55% while meeting all imposed constraints, achieving the dual aims of structural optimization and lightweighting. The study demonstrates that integrating AM constraints directly into the optimization stage yields designs that are performance-robust and fabrication-ready, and it provides a reusable workflow for thin-walled aerospace components such as wing ribs where stiffness, strength, and vibration behavior must be jointly considered.
Fei Zhao, Heran Zhang, Xiaoting Li et al.· SAE technical paper series· 0 citations
We present a topology optimization framework for anisotropic elastoplastic structures based on a new deformation plasticity formulation derived directly from Hill’s yield criterion. Conventional incremental elastoplastic approaches in topology optimization, while accurate, are computationally demanding due to their path-dependent nature and the need to store internal variables over multiple load steps. The proposed Hill-based deformation plasticity formulation enables single-step loading and direct computation of the final equilibrium state, thereby eliminating path dependence and substantially reducing computational cost and memory requirements. The formulation is embedded within a density-based topology optimization framework with stiffness maximization as the design objective. Numerical examples demonstrate the effectiveness of the proposed approach, validate the proportional loading assumption, and illustrate its applicability to realistic structural design problems. The results establish the Hill-based deformation plasticity formulation as a computationally efficient and robust alternative to conventional incremental elastoplastic methods.
Sobhan Dar, Zacharia N’Dao, M. Ristinmaa et al.· Structural And Multidiscipli...· 0 citations