Topology Optimization

Design of antenna structures for Internet of Things (IoT) applications is a challenging problem. Contemporary radiators are often subject to a number of electric and/or radiation-related requirements, but also constraints imposed by specifics of IoT systems and/or intended operational environments. Conventional approaches to antenna design typically involve manual development of topology intertwined with its tuning. Although proved useful, the approach is prone to errors and engineering bias. Alternatively, geometries can be generated and optimized without supervision of the designer. The process can be controlled by suitable algorithms to determine and then adjust the antenna geometry according to the specifications. Unfortunately, automatic design of IoT radiators is associated with challenges such as determination of desirable geometries or high optimization cost. In this work, a variable-fidelity framework for performance-oriented development of free-form antennas represented using the generic simulation models is proposed. The method employs a surrogate-assisted classifier capable of identifying a suitable radiator topology from a set of automatically generated (and stored for potential re-use) candidate designs. The obtained geometry is then subject to a bi-stage tuning performed using a gradient-based optimization engine. The presented framework is demonstrated based on six numerical experiments concerning unsupervised development of bandwidth-enhanced patch antennas dedicated to work within 5 GHz to 6 GHz and 6 GHz to 7 GHz bands, respectively. Extensive benchmarks of the method, as well as the generated topologies are also performed.

Despite topology optimization producing high-performance structures, late-stage localized revisions remain brittle: direct density-space edits (e.g., warping pixels, inserting holes, swapping infill) can sever load paths and sharply degrade compliance, while re-running optimization is slow and may drift toward a qualitatively different design. We present TopoEdit, a fast post-optimization editor that demonstrates how structured latent embeddings from a pre-trained topology foundation model (OAT) can be repurposed as an interface for physics-aware engineering edits. Given an optimized topology, TopoEdit encodes it into OAT's spatial latent, applies partial noising to preserve instance identity while increasing editability, and injects user intent through an edit-then-denoise diffusion pipeline. We instantiate three edit operators: drag-based topology warping with boundary-condition-consistent conditioning updates, shell-infill lattice replacement using a lattice-anchored reference latent with updated volume-fraction conditioning, and late-stage no-design region enforcement via masked latent overwrite followed by diffusion-based recovery. A consistency-preserving guided DDIM procedure localizes changes while allowing global structural adaptation; multiple candidates can be sampled and selected using a compliance-aware criterion, with optional short SIMP refinement for warps. Across diverse case studies and large edit sweeps, TopoEdit produces intention-aligned modifications that better preserve mechanical performance and avoid catastrophic failure modes compared to direct density-space edits, while generating edited candidates in sub-second diffusion time per sample.

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in handling complex physics. These limitations become more pronounced in multi-material, multi-physics problems whose objective or constraint functions are not self-adjoint. To address these challenges, we propose a framework based on physics-informed Gaussian processes (PIGPs). In our approach, the primary, adjoint, and design variables are represented by independent GP priors whose mean functions are parametrized via neural networks whose architectures are particularly beneficial for surrogate modeling of PDE solutions. We estimate all parameters of our model simultaneously by minimizing a loss that is based on the objective function, multi-physics potential energy functionals, and design-constraints. We demonstrate the capability of the proposed framework on benchmark TO problems such as compliance minimization, heat conduction optimization, and compliant mechanism design under single- and multi-material settings. Additionally, we leverage thermo-mechanical TO with single- and multi-material options as a representative multi-physics problem. We also introduce differentiation and integration schemes that dramatically accelerate the training process. Our results demonstrate that the proposed PIGP framework can effectively solve coupled multi-physics and design problems simultaneously -- generating super-resolution topologies with sharp interfaces and physically interpretable material distributions. We validate these results using open-source codes and the commercial software package COMSOL.

Typically, heuristic/trial-based approaches are used to design soft pneumatic grippers (SPGs). This paper presents a systematic topology optimization framework for developing SPGs. The design-dependent nature of actuating load is modeled using Darcy's law with an added drainage term. A 2D soft arm unit is then optimized as a compliant mechanism under pneumatic loading. To ensure the design is robust and manufacturable, the problem is formulated as a min-max optimization, where output deformations of blueprint and eroded designs are considered. A volume constraint is imposed on the blueprint part, while a strain-energy constraint is enforced on the eroded part. The Method of Moving Asymptotes is employed to solve optimization problems. The optimized 2D part is extruded suitably to generate a 3D unit. Ten such 3D units are assembled to create a gripper arm. Both the optimized 2D unit and the corresponding gripper arm outperform their conventional rectangular designs under pneumatic loading, demonstrating the efficacy of the proposed approach. The arms are fabricated using the SLA printing technique. Numerical and experimental results are compared at different pneumatic loads. Four 3D-printed arms are integrated with a supporting structure to form the SPG. The gripping action of the SPG is demonstrated on objects with different weights, sizes, structures, stiffnesses, and shapes.