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1. Exploring FPGA Optimizations in OpenCL for Breadth-First Search on Sparse Graph Datasets

   https://doi.org/10.1109/FPL50879.2020.00032  

   Gondhalekar, Atharva; Feng, Wu-Chun (August 2020, 30th International Conference on Field-Programmable Logic and Applications)

   Breath-first search (BFS) is a fundamental building block in many graph-based applications. It is challenging to optimize due to its irregular memory-access pattern. Prior work, based on hardware description languages (HDLs) and high-level synthesis (HLS), address the memory-access bottleneck by using techniques such as edge-centric traversal, data alignment, and compute-unit (CU) replication. While these optimizations work well for dense graph datasets, optimizing BFS on sparse graphs remains a significant challenge due to the kernel launch overhead and poor workload distribution across processing elements. As a complement to the prior work, we present and evaluate optimizations in OpenCL for BFS on sparse graphs. Specifically, we explore application-specific and architecture-aware optimizations aimed at mitigating the irregular global-memory access bottleneck in sparse graphs. In our kernel design, we consider factors such as choice of data structure between queue and array, number of memory banks, and kernel launch configuration. We evaluate the impact of proposed optimizations on a diverse set of sparse graphs. In comparison with the state-of-the-art OpenCL implementation for FPGA, we achieve 5.7x-22.3x speedup on Stratix 10 SX 2800 FPGA for the graphs that are most sensitive to our optimization scheme. 

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2. Improving Equality Saturation for EDA via Semantic E-Graphs

   https://doi.org/10.1145/3808299  

   Kong, Sijie; Xia, Jingtao; Ruelas-Petrisko, Daniel; Sisco, Zachary D; Balkind, Jonathan; Smith, Gus Henry (June 2026, Proceedings of the ACM on Programming Languages)

   Equality saturation (eqsat) is a program optimization technique that uses syntax-based term rewriting to simultaneously explore many possible optimizations of a program, storing equivalent programs efficiently in a data structure called an e-graph. By exploring optimizations simultaneously, eqsat mitigates the phase ordering problem, where the order of optimizations significantly affects quality of results. Eqsat is especially promising for Electronics Design Automation (EDA), whose tools suffer from phase ordering. Previous eqsat-for-EDA efforts have focused on single tool stages; while they demonstrate significant benefits within a stage, they do not address phase ordering between stages. When we investigated the reason for their limited scope, we found that previous works struggle to implement an efficient hardware representation useful in both high-level (e.g. arithmetic optimization) and low-level (e.g. logic synthesis) tasks. The root issue is that such a representation must maintain equivalences between the high- and low-level portions of the language. While these equalities are conceptually simple—e.g., two high-level bitvectors are equal if they contain the same low-level bits—maintaining them using syntax-based rewrites alone proves inefficient in modern eqsat engines. In response, this paper makes two contributions. First, we introduce semantic e-graphs, an enhancement to e-graphs that improves performance of a narrow but highly useful class of semantics-based equalities. Second, we present Nextmap, a new eqsat-based hardware optimization engine whose representation uses semantic e-graphs to efficiently bridge high- and low-level hardware expressions. As a result, Nextmap simultaneously runs more EDA stages than previous eqsat-based works, more effectively mitigating phase ordering and reaching previously inaccessible optimizations. Compared with open-source and commercial tools, Nextmap provides competitive quality of results on a range of designs. 

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3. Data-driven multiphysics modeling and optimization of dual-phase spinodoid metamaterials

   https://doi.org/10.1088/2515-7639/ae409e  

   Yıldız, Saltuk; Ender_Eğer, Z; Acar, Pınar (February 2026, Journal of Physics: Materials)

   Abstract Spinodal topologies (STs), inspired by material phase transition phenomena, exhibit complex geometries generated by Gaussian random fields (GRFs). These dual-phase structures feature smooth transitions and low-curvature designs, offering enhanced mechanical response compared to traditional surface- or strut-based metamaterials. Their flexible design spaces allow both periodic and non-periodic topologies, making them promising candidates for multiphysics applications. This work presents a computationally efficient data-driven framework for optimizing the mechanical and thermal properties of STs. A convolutional neural network (CNN) is trained on homogenized elastic and thermal properties obtained from finite element analyses. Next, the CNN model is coupled with an optimization solver to design dual-phase STs to improve multiphysics objectives. The inherent variations of STs introduced by the GRF formulation limit the ability of gradient-based optimizers to efficiently search for the design space. To overcome this challenge, a gradient-free global optimization algorithm is integrated into the surrogate model to find optimum designs with superior mechanical and thermal performance. 

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4. GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty

   https://doi.org/10.1115/1.4055898  

   Chen, Wei; Lee, Doksoo; Balogun, Oluwaseyi; Chen, Wei (January 2023, Journal of Mechanical Design)

   Abstract Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. The past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the “real-world,” “free-form” uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a generative adversarial network-based design under uncertainty framework (GAN-DUF), which contains a deep generative model that simultaneously learns a compact representation of nominal (ideal) designs and the conditional distribution of fabricated designs given any nominal design. This opens up new possibilities of (1) building a universal uncertainty quantification model compatible with both shape and topological designs, (2) modeling free-form geometric uncertainties without the need to make any assumptions on the distribution of geometric variability, and (3) allowing fast prediction of uncertainties for new nominal designs. We can combine the proposed deep generative model with robust design optimization or reliability-based design optimization for design under uncertainty. We demonstrated the framework on two real-world engineering design examples and showed its capability of finding the solution that possesses better performance after fabrication. 

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5. Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty

   https://doi.org/10.1115/DETC2022-89707  

   Chen, Wei; Lee, Doksoo; Balogun, Oluwaseyi; Chen, Wei (August 2022, American Society of Mechanical Engineers)

   Abstract Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. Past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the “real-world”, “free-form” uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a Generative Adversarial Network-based Design under Uncertainty Framework (GAN-DUF), which contains a deep generative model that simultaneously learns a compact representation of nominal (ideal) designs and the conditional distribution of fabricated designs given any nominal design. This opens up new possibilities of 1) building a universal uncertainty quantification model compatible with both shape and topological designs, 2) modeling free-form geometric uncertainties without the need to make any assumptions on the distribution of geometric variability, and 3) allowing fast prediction of uncertainties for new nominal designs. We can combine the proposed deep generative model with robust design optimization or reliability-based design optimization for design under uncertainty. We demonstrated the framework on two real-world engineering design examples and showed its capability of finding the solution that possesses better performances after fabrication. 

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