A direct-adjoint Lattice-Boltzmann solver for turbulent fluid-structure interaction and shape optimization

Accelerated simulation and design optimization of elastic rod networks with a spline-based least-squares formulation

ABSTRACT Bathymetric contour mapping in inland waterway systems presents significant challenges in balancing data simplification, feature preservation, and visual quality. Traditional single-stage methods address individual aspects but fail to meet comprehensive hydrographic surveying requirements. This study proposes a dual-stage BCPO+FRO algorithm framework that combines Boundary Control Point Optimization and Fluctuation Reduction Optimization. The BCPO stage performs global shape optimization through control point calculation, polygon construction, and iterative smoothing. This process reduces line complexity while preserving bathymetric accuracy. The FRO stage identifies and suppresses local fluctuation features using terrain-weighted indicators and dynamic parameter adjustment mechanisms. This approach improves visual quality without compromising critical underwater terrain characteristics. Experimental validation was conducted on diverse terrain types in the Yangtze River inland waterway navigation channel. Results demonstrate superior performance with substantial turning point reductions, minimal horizontal deviations, and high terrain feature preservation rates. This research provides practical applications for inland waterway management, navigation safety, and hydraulic engineering, and provides technical reference for research on China’s smart water conservancy construction.

An optimal pillow minimizes cervical symptoms. This study aims to investigate the personalized pillow shape involving body dimensions, and develop a shape-adjustable smart pillow. The optimal pillow shape, defined as best maintaining the natural standing cervical curvature in supine position, was evaluated among 14 subjects across varying pillow heights (4-10cm) and neck support heights (flat-2cm). Spearman correlation analysis verified significant positive monotonic associations between optimal pillow shape parameters and body dimensions, from which descriptive equations were derived. Muscle fatigue of optimal pillow was evaluated via electromyography of neck muscles on 7 subjects. Body height showed a significant positive monotonic association with optimal pillow height. Similarly, the ratio of body height to cervical eminence showed a significant positive monotonic association with optimal neck support height. This personalized pillow shape induced the highest median frequency slope in neck muscles. Pneumatic-driven smart pillow with adjustable pillow height and neck support height was subsequently developed for body dimension adaption, and the cervical curvatures in supine position were tested among 13 subjects. It exhibited superior ability in maintaining natural cervical curvature than latex pillow and polyester fiber pillow. In conclusion, body height and cervical eminence are associated with the optimal pillow shape for cervical curvature preservation. This pillow shape benefits relieving neck muscle fatigue. The developed smart pillow preserves physiological cervical curvature more effectively in the supine position than latex and polyester fiber pillows.

The determination of sex morphs and the optimization of fruit shape are key challenges in cucumber cultivation and breeding, with ethylene recognized as a crucial regulatory factor in both processes. Ethylene is synthesized through the coordinated actions of 1-aminocyclopropane-1-carboxylate (ACC) synthase (ACS) and ACC oxidase (ACO). While previous studies have highlighted the significant role of CsACSs in cucumber sex determination, investigations on CsACOs remain limited. In this study, we generated mutants of all members of the ACO gene family involved in ethylene synthesis during cucumber flower development and systematically analyzed their functions. Our results demonstrate that CsACO2 plays a dual role: it is involved in the early induction of carpel initiation during flower development and subsequently regulates ovary elongation. Mutations in CsACO2 affect ovary elongation, as evidenced by the shorter ovaries of female flowers in the cswip1/csaco2 double mutants. In developing female buds, after carpel initiation, we identified CsACO3 as the core regulatory gene responsible for stamen arrest, in cooperation with either CsACO2 or CsACO4. Notably, the cswip1/csaco2/csaco3 triple mutants produce hermaphrodite flowers with shorter ovaries. In contrast, the cswip1/csaco3/csaco4 triple mutants exhibit hermaphrodite flowers with normal ovaries and fruit shapes, and more importantly, their fruit-setting ability is comparable to that of the subgynoecious control. Our results enrich the ethylene regulatory network of cucumber female/hermaphrodite flower development and fruit shape, and provide an optional breeding pathway for high-yield varieties.

Reducing the flow resistance of local components in building transmission and distribution systems is a key pathway to building energy conservation. Here we propose a novel low-resistance optimization method applied to U-bend shape design, with the minor axis a, major axis b, and offset c defined as shape features. The sample size is 150, and the parameter ranges are as follows: [50 mm, 150 mm] for a, [50 mm, 150 mm] for b, and [-30 mm, 30 mm] for c. On this basis, five representative machine learning regression modeling paradigms, including ridge regression, support vector regression, random forest, multilayer perceptron, and Gaussian process regression, are systematically compared, and the model with the best predictive performance is selected as the surrogate model for U-bend optimization. The proposed method is validated through full-scale experiments, numerical simulations, and turbulent energy dissipation. The results show that within a Reynolds number range of 1.0 × 105 to 2.4 × 105, the optimized U-bend achieves a resistance reduction rate of 13-24% relative to the traditional circular U-bend. This study provides a reference for the low-resistance design and energy-saving optimization of building transmission and distribution systems.

ABSTRACT This study investigates the effect of sacrificial piles on the anti-scouring performance of the sea-crossing bridge foundations under combined wave–current action through three-dimensional numerical simulation. The numerical wave flume model and local scour model were first validated by comparing with results of previous experiments to ensure the accuracy of the numerical method. Second, for the monopile of a cross-sea bridge, the optimal pile spacing of the sacrificial pile under constant flow conditions was studied, and the effects of a single sacrificial pile and the combined action of the sacrificial pile and protective ring were compared to obtain a better protective measure. Then the optimal spacing of the sacrificial pile under the combined action of wave and current was determined. The influence of different cross-sectional shapes of the sacrificial pile on anti-scouring was investigated to obtain the optimal cross-sectional shape under the combined action of wave and current. Under steady flow conditions, the sacrificial pile with a diameter of 0.25D and a pile center spacing of 1.5D has the best anti-scouring effect. It is shown that the sacrificial pile with a rhombic cross-section shape has the best anti-scouring performance.

Large-eddy simulation enhanced by machine learning: space-time correlations, wall models, and shape optimization

• A novel SPH framework built around differentiability and for Machine Learning • The application of our framework to inverse problems and optimization • A novel approach to address particle-shifting using differentiable SPH operators • Easy integration with neural networks for hybrid solver-network solutions • A unified framework for compressible, weakly-compressible and incompressible fluids We present diffSPH , a novel open-source differentiable Smoothed Particle Hydrodynamics (SPH) framework developed entirely in PyTorch with GPU acceleration. diffSPH is designed centrally around differentiation to facilitate optimization and machine learning (ML) applications in Computational Fluid Dynamics (CFD), including solving inverse problems and the development of hybrid models. Its differentiable SPH core, and schemes for compressible (with shock capturing and multi-phase flows), weakly compressible (with boundary handling and free-surface flows), and incompressible physics, enable a broad range of applications. We demonstrate the framework’s unique capabilities through several applications, including addressing particle shifting via a novel, target-oriented approach by minimizing physical and regularization loss terms, a task often intractable in traditional solvers. Further examples include optimizing initial conditions and physical parameters to match target trajectories, shape optimization, implementing a solver-in-the-loop setup to emulate higher-order integration, and demonstrating gradient propagation through hundreds of simulation steps. Prioritizing readability, usability, flexibility, and extensibility, this work offers a foundational platform for the CFD community to develop and deploy novel neural networks and adjoint optimization applications. Our differentiable SPH framework is available at https://github.com/tum-pbs/diffSPH .

Abstract We establish a quantitative version of the isoperimetric inequality for the torsional rigidity of multiply connected domains, among sets with given area and with given joint area of the holes. Since the optimal shape is the annulus, we study how a domain approaches an annular configuration when its torsional rigidity is close to optimal. Our result shows that when the torsional rigidity is nearly optimal, the domain $$\Omega $$ Ω must be close to an annulus.

Fruit growth has long been described using single- or double-sigmoid curves; however, these temporal models cannot fully capture the spatial heterogeneity that ultimately shapes a fruit. Here, we present a three-dimensional analysis pipeline that non-destructively tracks spatial fruit growth dynamics from field-collected imagery. Surface landmarks were drawn, and video recordings were taken throughout development for three pome fruits, apple (Malus × domestica), Japanese pear (Pyrus pyrifolia) and European pear (Pyrus communis), and two drupe fruits, peach (Prunus persica) and Japanese apricot (Prunus mume), to track their motion. Using 3D Gaussian splatting, we successfully reconstructed 3D models of the fruits, and the landmark displacement could be measured with high accuracy, with R2 ≥ 0.98 when compared to manual recordings. We found a common spatial growth gradient in the longitudinal growth shared in the pomes and drupes of the Rosaceae; proximal (stem-end) regions exhibited more pronounced growth than the distal (stylar) end. An exception was found in European pear 'Bartlett,' which showed relatively vigorous growth in the distal region, explaining its distinct shape with expanded distal end. Transverse expansion varied far less than longitudinal expansion, with a possible association with initial fruit morphology. Inter-fruit growth variability peaked in the fastest-growing regions, particularly in the distal area of the European pear, highlighting the link between growth vigor and phenotypic variance. These results provide foundational insights into the developmental dynamics of both pome and drupe fruits of the Rosaceae family, contributing to the optimization of fruit size, shape, and uniformity.

Surrogate-based optimization using neural networks (NNs) reduces computational costs in engineering design but depends heavily on systematic hyperparameter optimization (HPO). This study compares HPO methods—including grid search, random search, Bayesian optimization (BO), hyperband (HB), and BOHB—using analytical functions and aerodynamic shape optimization (ASO). The study first explores HPO in a one-shot method where NNs are trained with datasets of different sample sizes. The analysis then extends to adaptive HPO approaches within an efficient global optimization (EGO) framework using NNs, which employs sequential sampling. Under this framework, static HPO (maintaining initially optimized HPs), periodic HPO (adjusting HPs every five infill points), and dynamic HPO (adjusting HPs after each infill point) are compared. In ASO with a one-shot method, BOHB achieves a drag coefficient (Cd) of 117 drag counts (d.c.)—close to BO’s 115 d.c.—while requiring only 30.5% of BO’s computational time with 500 samples. Additionally, in ASO with sequential sampling, periodic HPO effectively balances performance and computational efficiency by achieving a Cd of 119 d.c. with 25 initial samples and 50 infills. Dynamic HPO reduces Cd to 113 d.c. but at a higher cost compared to periodic HPO, which offers a balance between drag reduction and computational expense.

This research introduces a novel approach to rapidly estimate the nonlinear buckling behaviour of concrete thin-shells, using Multi-Fidelity deep learning. The prediction speed of these models could potentially be used to improve design space exploration during the structural shape optimisation phase. Indeed, the use of nonlinear Finite Element (FE) analysis for estimating the buckling factor is unpractical in such settings because of its high computational cost. This research considers the use of Multi-Fidelity models to mitigate the computational cost required to constitute a sufficiently large dataset for training deep learning models. Two datasets – a low-fidelity dataset and a high-fidelity dataset – that contain concrete thin-shells with various shapes and material properties were therefore generated. The buckling factor of the 20,000 thin-shells in the low-fidelity dataset were obtained through linear eigenvalue FE analysis, which has a low computational cost. Additionally, the buckling factors of the 5,000 thin-shells in the high-fidelity dataset were obtained using computationally expensive nonlinear FE analyses. These datasets were used to train Multi-Fidelity Multilayer Perceptrons in two different approaches: using several sequentially connected models, and using Transfer Learning. These two approaches were also compared to a Single-Fidelity baseline. It was found that the models were able to make highly accurate predictions of the nonlinear buckling factor (Mean Absolute Errors are consistently below 0.65%), while being more than 97,000 times quicker than the average time required for a nonlinear FE analysis. Additionally, the Multi-Fidelity approaches were found to be beneficial when the amount of high-fidelity data is limited. • Deep learning can be used to predict the nonlinear buckling of concrete shells. • Multi-Fidelity approaches are beneficial when computational resources are limited. • The models are more than 97,000 times faster than nonlinear Finite Element analysis.

Shape optimisation of metal additive manufacturing connections in lightweight steel structures

Cross-sectional shape optimization of flow channels in all-vanadium redox flow batteries: A comparative performance study

Multiobjective shape optimization of TPMS-based compact heat exchangers through RBF-FD meshless simulations

Retraction notice to "Minimization of energy consumption by building shape optimization using an improved Manta-ray foraging optimization algorithm" [Energ. Rep., 7 (2021) 1068–1078

A hierarchical optimization strategy based on cluster characteristics for aerodynamic shape optimization

Blade shape optimization of floating offshore vertical axis wind turbines for maximum power coefficient under platform pitch motion

On the robustness of adjoint shape optimization method when applied to the optimal design of vortex generators: The impact of the Reynolds number