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1. Addressing GPU memory limitations for Graph Neural Networks in High-Energy Physics applications

   https://doi.org/10.3389/fhpcp.2024.1458674  

   Lee, Claire Songhyun; Hewes, V; Cerati, Giuseppe; Wang, Kewei; Aurisano, Adam; Agrawal, Ankit; Choudhary, Alok; Liao, Wei-Keng (September 2024, Frontiers in High Performance Computing)

   IntroductionReconstructing low-level particle tracks in neutrino physics can address some of the most fundamental questions about the universe. However, processing petabytes of raw data using deep learning techniques poses a challenging problem in the field of High Energy Physics (HEP). In the Exa.TrkX Project, an illustrative HEP application, preprocessed simulation data is fed into a state-of-art Graph Neural Network (GNN) model, accelerated by GPUs. However, limited GPU memory often leads to Out-of-Memory (OOM) exceptions during training, due to the large size of models and datasets. This problem is exacerbated when deploying models on High-Performance Computing (HPC) systems designed for large-scale applications. MethodsWe observe a high workload imbalance issue during GNN model training caused by the irregular sizes of input graph samples in HEP datasets, contributing to OOM exceptions. We aim to scale GNNs on HPC systems, by prioritizing workload balance in graph inputs while maintaining model accuracy. Our paper introduces diverse balancing strategies aimed at decreasing the maximum GPU memory footprint and avoiding the OOM exception, across various datasets. ResultsOur experiments showcase memory reduction of up to 32.14% compared to the baseline. We also demonstrate the proposed strategies can avoid OOM in application. Additionally, we create a distributed multi-GPU implementation using these samplers to demonstrate the scalability of these techniques on the HEP dataset. DiscussionBy assessing the performance of these strategies as data loading samplers across multiple datasets, we can gauge their effectiveness in both single-GPU and distributed environments. Our experiments, conducted on datasets of varying sizes and across multiple GPUs, broaden the applicability of our work to various GNN applications that handle input datasets with irregular graph sizes. 

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2. Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond

   Balcan, M.-F.; Prasad, S.; Sandholm, T.; Vitercik, E. (January 2021, ArXivorg)

   null (Ed.)

   Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find optimal solutions. In this paper we prove the first guarantees for learning high-performing cut-selection policies tailored to the instance distribution at hand using samples. We first bound the sample complexity of learning cutting planes from the canonical family of Chvátal-Gomory cuts. Our bounds handle any number of waves of any number of cuts and are fine tuned to the magnitudes of the constraint coefficients. Next, we prove sample complexity bounds for more sophisticated cut selection policies that use a combination of scoring rules to choose from a family of cuts. Finally, beyond the realm of cutting planes for integer programming, we develop a general abstraction of tree search that captures key components such as node selection and variable selection. For this abstraction, we bound the sample complexity of learning a good policy for building the search tree. 

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3. Joint parameter and parameterization inference with uncertainty quantification through differentiable programming

   Qu, Y; Bhouri, M A; Gentine, P (May 2024, ICLR)

   Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations that govern many problems ranging from weather and climate prediction to turbulence simulations. Recent advances have seen machine learning (ML) increasingly applied to model these subgrid processes, resulting in the development of hybrid physics-ML models through the integration with numerical solvers. In this work, we introduce a novel framework for the joint estimation and uncertainty quantification of physical parameters and machine learning parameterizations in tandem, leveraging differentiable programming. Achieved through online training and efficient Bayesian inference within a high-dimensional parameter space, this approach is enabled by the capabilities of differentiable programming. This proof of concept underscores the substantial potential of differentiable programming in synergistically combining machine learning with differential equations, thereby enhancing the capabilities of hybrid physics-ML modeling. 

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4. Performance of a geometric deep learning pipeline for HL-LHC particle tracking

   https://doi.org/10.1140/epjc/s10052-021-09675-8  

   Ju, Xiangyang; Murnane, Daniel; Calafiura, Paolo; Choma, Nicholas; Conlon, Sean; Farrell, Steven; Xu, Yaoyuan; Spiropulu, Maria; Vlimant, Jean-Roch; Aurisano, Adam; et al (October 2021, The European Physical Journal C)

   Abstract The Exa.TrkX project has applied geometric learning concepts such as metric learning and graph neural networks to HEP particle tracking. Exa.TrkX’s tracking pipeline groups detector measurements to form track candidates and filters them. The pipeline, originally developed using the TrackML dataset (a simulation of an LHC-inspired tracking detector), has been demonstrated on other detectors, including DUNE Liquid Argon TPC and CMS High-Granularity Calorimeter. This paper documents new developments needed to study the physics and computing performance of the Exa.TrkX pipeline on the full TrackML dataset, a first step towards validating the pipeline using ATLAS and CMS data. The pipeline achieves tracking efficiency and purity similar to production tracking algorithms. Crucially for future HEP applications, the pipeline benefits significantly from GPU acceleration, and its computational requirements scale close to linearly with the number of particles in the event. 

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5. Systematically Differentiating Parametric Discontinuities

   https://doi.org/10.1145/3450626.3459775  

   Bangaru, Sai Praveen; Michel, Jesse; Mu, Kevin; Bernstein, Gilbert; Li, Tzu-Mao; Ragan-Kelley, Jonathan (August 2021, ACM transactions on graphics)

   Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate and optimize parametric discontinuities. These discontinuities appear in object boundaries, occlusion, contact, and sudden change over time. In many domains, such as rendering and physics simulation, we differentiate the parameters of models that are expressed as integrals over discontinuous functions. Ignoring the discontinuities during differentiation often has a significant impact on the optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation. We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. We introduce integration as a language primitive and account for the Dirac delta contribution from differentiating parametric discontinuities in the integrand. We formally define the language semantics and prove the correctness and closure under the differentiation, allowing the generation of gradients and higher-order derivatives. We also build a system, Teg, implementing these semantics. Our approach is widely applicable to a variety of tasks, including image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs. 

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