Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework

We introduce copresheaf topological neural networks (CTNNs), a powerful and unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data: including images, point clouds, graphs, meshes, and topological manifolds. While deep learning has profoundly impacted domains ranging from digital assistants to autonomous systems, the principled design of neural architectures tailored to specific tasks and data types remains one of the field's most persistent open challenges. CTNNs address this gap by grounding model design in the language of copresheaves, a concept from algebraic topology that generalizes and subsumes most practical deep learning models in use today. This abstract yet constructive formulation yields a rich design space from which theoretically sound and practically effective solutions can be derived to tackle core challenges in representation learning: long-range dependencies, oversmoothing, heterophily, and non-Euclidean domains. Our empirical results on structured data benchmarks demonstrate that CTNNs consistently outperform conventional baselines, particularly in tasks requiring hierarchical or localized sensitivity. These results underscore CTNNs as a principled, multi-scale foundation for the next generation of deep learning architectures.

Advancing Fluid-Based Thermal Management Systems Design: Leveraging Graph Neural Networks for Graph Regression and Efficient Enumeration Reduction

In this research, we developed a graph-based framework to represent various aspects of optimal thermal management system design, with the aim of rapidly and efficiently identifying optimal design candidates. Initially, the graph-based framework is utilized to generate diverse thermal management system architectures. The dynamics of these system architectures are modeled under various loading conditions, and an open-loop optimal controller is employed to determine each system's optimal performance. These modeled cases constitute the dataset, with the corresponding optimal performance values serving as the labels for the data. In the subsequent step, a Graph Neural Network (GNN) model is trained on 30% of the labeled data to predict the systems' performance, effectively addressing a regression problem. Utilizing this trained model, we estimate the performance values for the remaining 70% of the data, which serves as the test set. In the third step, the predicted performance values are employed to rank the test data, facilitating prioritized evaluation of the design scenarios. Specifically, a small subset of the test data with the highest estimated ranks undergoes evaluation via the open-loop optimal control solver. This targeted approach concentrates on evaluating higher-ranked designs identified by the GNN, replacing the exhaustive search (enumeration-based) of all design cases. The results demonstrate a significant average reduction of over 92% in the number of system dynamic modeling and optimal control analyses required to identify optimal design scenarios.