Hadi Keramati

Hadi Keramati, Feridun Hamdullahpur

Generative design has been growing across the design community as a viable method for design space exploration. Thermal design is more complex than mechanical or aerodynamic design because of the additional convection-diffusion equation and its pertinent boundary interaction. We present a generative thermal design using cooperative multi-agent deep reinforcement learning and continuous geometric representation of the fluid and solid domain. The proposed framework consists of a pre-trained neural network surrogate model as an environment to predict heat transfer and pressure drop of the generated geometries. The design space is parameterized by composite Bezier curve to solve multiple fin shape optimization. We show that our multi-agent framework can learn the policy for design strategy using multi-objective reward without the need for shape derivation or differentiable objective function.

Hadi Keramati, Feridun Hamdullahpur

We present surrogate models for heat transfer and pressure drop prediction of complex fin geometries generated using composite Bezier curves. Thermal design process includes iterative high fidelity simulation which is complex, computationally expensive, and time-consuming. With the advancement in machine learning algorithms as well as Graphics Processing Units (GPUs), we can utilize the parallel processing architecture of GPUs rather than solely relying on CPUs to accelerate the thermo-fluid simulation. In this study, Convolutional Neural Networks (CNNs) are used to predict results of Computational Fluid Dynamics (CFD) directly from topologies saved as images. The case with a single fin as well as multiple morphable fins are studied. A comparison of Xception network and regular CNN is presented for the case with a single fin design. Results show that high accuracy in prediction is observed for single fin design particularly using Xception network. Increasing design freedom to multiple fins increases the error in prediction. This error, however, remains within three percent for pressure drop and heat transfer estimation which is valuable for design purpose.

Hadi Keramati, Morteza Sadeghi, Rajeev K. Jaiman

This study presents a generative optimization framework based on a guided denoising diffusion probabilistic model (DDPM) that leverages surrogate gradients to generate heat sink designs minimizing pressure drop while maintaining surface temperatures below a specified threshold. Geometries are represented using boundary representations of multiple fins, and a multi-fidelity approach is employed to generate training data. Using this dataset, along with vectors representing the boundary representation geometries, we train a denoising diffusion probabilistic model to generate heat sinks with characteristics consistent with those observed in the data. We train two different residual neural networks to predict the pressure drop and surface temperature for each geometry. We use the gradients of these surrogate models with respect to the design variables to guide the geometry generation process toward satisfying the low-pressure and surface temperature constraints. This inference-time guidance directs the generative process toward heat sink designs that not only prevent overheating but also achieve lower pressure drops compared to traditional optimization methods such as CMA-ES. In contrast to traditional black-box optimization approaches, our method is scalable, provided sufficient training data is available. Unlike traditional topology optimization methods, once the model is trained and the heat sink world model is saved, inference under new constraints (e.g., temperature) is computationally inexpensive and does not require retraining. Samples generated using the guided diffusion model achieve pressure drops up to 10 percent lower than the limits obtained by traditional black-box optimization methods. This work represents a step toward building a foundational generative model for electronics cooling.

Hadi Keramati, Patrick Kirchen, Mohammed Hannan et al.

This study presents a generative optimization framework that builds on a fine-tuned diffusion model and reward-directed sampling to generate high-performance engineering designs. The framework adopts a parametric representation of the design geometry and produces new parameter sets corresponding to designs with enhanced performance metrics. A key advantage of the reward-directed approach is its suitability for scenarios in which performance metrics rely on costly engineering simulations or surrogate models (e.g. graph-based, ensemble models, or tree-based) are non-differentiable or prohibitively expensive to differentiate. This work introduces the iterative use of a soft value function within a Markov decision process framework to achieve reward-guided decoding in the diffusion model. By incorporating soft-value guidance during both the training and inference phases, the proposed approach reduces computational and memory costs to achieve high-reward designs, even beyond the training data. Empirical results indicate that this iterative reward-directed method substantially improves the ability of the diffusion models to generate samples with reduced resistance in 3D ship hull design and enhanced hydrodynamic performance in 2D airfoil design tasks. The proposed framework generates samples that extend beyond the training data distribution, resulting in a greater 25 percent reduction in resistance for ship design and over 10 percent improvement in the lift-to-drag ratio for the 2D airfoil design. Successful integration of this model into the engineering design life cycle can enhance both designer productivity and overall design performance.

Hadi Keramati, Samaneh Jazayeri

We present a reinforcement learning (RL)-driven framework for optimizing block-preconditioner sizes in iterative solvers used in portfolio optimization and option pricing. The covariance matrix in portfolio optimization or the discretization of differential operators in option pricing models lead to large linear systems of the form $\mathbf{A}\textbf{x}=\textbf{b}$. Direct inversion of high-dimensional portfolio or fine-grid option pricing incurs a significant computational cost. Therefore, iterative methods are usually used for portfolios in real-world situations. Ill-conditioned systems, however, suffer from slow convergence. Traditional preconditioning techniques often require problem-specific parameter tuning. To overcome this limitation, we rely on RL to dynamically adjust the block-preconditioner sizes and accelerate iterative solver convergence. Evaluations on a suite of real-world portfolio optimization matrices demonstrate that our RL framework can be used to adjust preconditioning and significantly accelerate convergence and reduce computational cost. The proposed accelerated solver supports faster decision-making in dynamic portfolio allocation and real-time option pricing.