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1. Performance-Portable Graph Coarsening for Efficient Multilevel Graph Analysis

   https://doi.org/10.1109/IPDPS49936.2021.00030  

   Gilbert, Michael S.; Acer, Seher; Boman, Erik G.; Madduri, Kamesh; Rajamanickam, Sivasankaran (May 2021, 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS))

   null (Ed.)

   The multilevel heuristic is an effective strategy for speeding up graph analytics, and graph coarsening is an integral step of multilevel methods. We perform a comprehensive study of multilevel coarsening in this work. We primarily focus on the graphics processing unit (GPU) parallelization of the Heavy Edge Coarsening (HEC) method executed in an iterative setting. We present optimizations for the two phases of coarsening, a fine-to-coarse vertex mapping phase, and a coarse graph construction phase. We also express several other coarsening algorithms using the Kokkos framework and discuss their parallelization. We demonstrate the efficacy of parallelized HEC on an NVIDIA Turing GPU and a 32-core AMD Ryzen processor using multilevel spectral graph partitioning as the primary case study. 

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2. Learning From Mistakes: A Multilevel Optimization Framework

   Zhang, Li; Garg, Bhanu; Sridhara, Pradyumna; Hosseini, Ramtin; Xie, Pengtao (January 2025, IEEE transactions on artificial intelligence)

   Bi-level optimization methods in machine learning are popularly effective in subdomains of neural architecture search, data reweighting, etc. However, most of these methods do not factor in variations in learning difficulty, which limits their performance in real-world applications. To address the above problems, we propose a framework that imitates the learning process of humans. In human learning, learners usually focus more on the topics where mistakes have been made in the past to deepen their understanding and master the knowledge. Inspired by this effective human learning technique, we propose a multilevel optimization framework, learning from mistakes (LFM), for machine learning. We formulate LFM as a three-stage optimization problem: 1) the learner learns, 2) the learner relearns based on the mistakes made before, and 3) the learner validates his learning. We develop an efficient algorithm to solve the optimization problem. We further apply our method to differentiable neural architecture search and data reweighting. Extensive experiments on CIFAR-10, CIFAR-100, ImageNet, and other related datasets powerfully demonstrate the effectiveness of our approach. The code of LFM is available at: https://github.com/importZL/LFM. 

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3. Cyclic and multilevel causation in evolutionary processes

   https://doi.org/10.1007/s10539-020-09753-3  

   Warrell, Jonathan; Gerstein, Mark (October 2020, Biology & Philosophy)

   null (Ed.)

   Abstract Many models of evolution are implicitly causal processes. Features such as causal feedback between evolutionary variables and evolutionary processes acting at multiple levels, though, mean that conventional causal models miss important phenomena. We develop here a general theoretical framework for analyzing evolutionary processes drawing on recent approaches to causal modeling developed in the machine-learning literature, which have extended Pearls do-calculus to incorporate cyclic causal interactions and multilevel causation. We also develop information-theoretic notions necessary to analyze causal information dynamics in our framework, introducing a causal generalization of the Partial Information Decomposition framework. We show how our causal framework helps to clarify conceptual issues in the contexts of complex trait analysis and cancer genetics, including assigning variation in an observed trait to genetic, epigenetic and environmental sources in the presence of epigenetic and environmental feedback processes, and variation in fitness to mutation processes in cancer using a multilevel causal model respectively, as well as relating causally-induced to observed variation in these variables via information theoretic bounds. In the process, we introduce a general class of multilevel causal evolutionary processes which connect evolutionary processes at multiple levels via coarse-graining relationships. Further, we show how a range of fitness models can be formulated in our framework, as well as a causal analog of Prices equation (generalizing the probabilistic Rice equation), clarifying the relationships between realized/probabilistic fitness and direct/indirect selection. Finally, we consider the potential relevance of our framework to foundational issues in biology and evolution, including supervenience, multilevel selection and individuality. Particularly, we argue that our class of multilevel causal evolutionary processes, in conjunction with a minimum description length principle, provides a conceptual framework in which identification of multiple levels of selection may be reduced to a model selection problem. 

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4. Multilevel Decision Support Framework for the Simultaneous Design Exploration of Material Structures and Processes

   https://doi.org/10.1115/DETC2024-146330  

   Digonta, H_M_Dilshad Alam; Nellippallil, Anand Balu; Baby, Mathew (August 2024, American Society of Mechanical Engineers)

   Abstract Traditional manufacturing, such as steel manufacturing, involves a series of processes to realize the final product. The properties and performance of the final product depend on the material processing history and the microstructure generated at each of the processes. Realizing target product performance requires the simultaneous design exploration of the material microstructure and processing, taking into account the multilevel interactions between the material, product, and manufacturing processes. This demands the capability to co-design, which involves sharing a ranged set of solutions through design exploration across multilevel and providing design decision support. In this paper, we present a co-design exploration framework for multilevel decision support. Using the framework, we model the interactions and couplings between the levels and facilitate simultaneous decision-based design exploration. The framework integrates the coupled compromise Decision Support Problem (c-cDSP) construct with interpretable Self-Organizing Maps (iSOM) to facilitate (i) the formulation of the multilevel decision support problems taking into account the interactions and couplings between levels, (ii) the simultaneous visualization and exploration of the multilevel design spaces, and (iii) decision-making across levels for multilevel designers. The efficacy of the framework is tested using a hot rod rolling problem focusing on the interactions between the dynamic and metadynamic phases of material recrystallization and the thermo-mechanical processing during the hot rolling process. The framework is generic and supports the co-design exploration of systems characterized by multilevel interactions, couplings, and multidisciplinary designers. 

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5. A Decision Support Framework for Robust Multilevel Co-Design Exploration of Manufacturing Supply Networks

   https://doi.org/10.1115/1.4065369  

   Baby, Mathew; Guptan, Akshay; Broussard, Jacob; Allen, Janet K; Mistree, Farrokh; Nellippallil, Anand Balu (November 2024, Journal of Mechanical Design)

   Abstract The design of a manufacturing supply network (MSN) requires the consideration of decisions made by different groups at multiple levels and their interactions that include potential conflicts. Decisions are typically made based on information from computational simulations that are abstractions of reality and, therefore, embody uncertainty. This necessitates focusing on design space exploration to identify robust satisficing solution sets that are relatively insensitive to uncertainty. Current frameworks that support robust satisficing design space exploration are limited by their capability to support the efficient exploration of multilevel design spaces simultaneously. In this paper, we present the Framework for Robust Multilevel Co-Design Exploration (FRoMCoDE), a decision support framework that allows designers to (i) model decision problems across multiple levels and their interactions, (ii) consider uncertainties in the decision problems, and (iii) visualize and systematically carry out simultaneous exploration of multilevel design spaces, termed co-design exploration. In FRoMCoDE, we combine the coupled-compromise Decision Support Problem construct, where a combination of the Preemptive and Archimedean formulations is used, with robust design constructs and interpretable-Self-Organizing Maps (iSOM)-based visualization to facilitate robust co-design. We use a steel MSN problem with decisions made at two levels to test the framework. Using the problem, we demonstrate FRoMCoDE's efficacy in supporting designers in (i) modeling multilevel decision problems and their interactions, considering the uncertainties, and (ii) the efficient co-design exploration of multilevel design spaces. FRoMCoDE is generic and supports designers in the robust co-design exploration of multilevel systems. 

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