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SkyFACT: high-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number (∼> 10{sup 5}) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that are motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |ℓ|<90{sup o} and | b |<20{sup o}, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.

79 ASTRONOMY AND ASTROPHYSICS↗

O(N) Quantum Molecular Dynamics (QMD) Algorithms, Code Requirements, Release Notes, and Library Deployment

The Exascale Computing Project (ECP) Co-design Center for Particle Applications (CoPA) is addressing the challenges for particle applications to run on upcoming exascale computing architectures. This includes short- and long-range molecular dynamics (MD), particle-in-cell (PIC), and quantum molecular dynamics (QMD). This document addresses $\mathcal{O}(N)$ QMD. The goal of this CoPA team is to develop $\mathcal{O}(N)$ linear scaling methods for QMD optimized for new and next generation architectures. This will provide the capability to simulate larger systems and run for longer timeframes than is possible today. Focus is initially on the density matrix construction. This requires efficient matrix formats and linear algebra operations for distributed architectures. A significant reduction in the wallclock time for an MD timestep is necessary to achieve practical large scale QMD. Equally challenging is to develop scalable distributed implementations. This requires the exploration of efficient data formats (dense, sparse, etc.), data decomposition and distribution across compute nodes using block- and graph-based methods. Traditional programming models such as MPI/OpenMP, hybrid MPI/OpenMP/Accelerator, as well as asynchronous task-based models will be explored to achieve maximum parallelism. Parallelism at the level of a matrix operation, solver, and/or application needs to be explored to gain the most benefit on new and emerging architectures. This report serves as a “living document” of the additions and enhancements throughout the ECP CoPA project for $\mathcal{O}(N)$ QMD. The following sections address the applications we are working with, the quantum chemistry libraries (BML and PROGRESS), and our co-design exploration through the use of a proxy application.

36 MATERIALS SCIENCE↗

MO-FG-CAMPUS-IeP2-05: Feasibility Demonstration of High-Voltage Clinical CT and Impact On X-Ray Penetration Through Metal Objects

Purpose: To demonstrate the possibility and quantify the impact of operating a clinical CT scanner at exceptionally high x-ray tube voltage for better penetration through metal objects and facilitating metal artifact reduction. Methods: We categorize metal objects according to the data corruption severeness (level of distortion and complete photon starvation fraction). To demonstrate feasibility and investigate the impact of high voltage scanning we modified a commercial GE LightSpeed VCT scanner (generator and software) to enable CT scans with x-ray tube voltages as high as 175 kVp. A 20 cm diameter water phantom with two metal rods (10 mm stainless and 25 mm titanium) and a water phantom with realistic metal object (spine cage) were used to evaluate the data corruption and image artifacts in the absence of any algorithm correction. We also performed simulations to confirm our understanding of the transmitted photon levels through metal objects with different size and composition. Results: The reconstructed images at 175 kVp still have significant dark shading artifacts, as expected since no special scatter correction or beam hardening was performed but show substantially lower noise and photon starvation than at lower kVp due to better beam penetration. Analysis of the raw data shows that the photon starved data is reduced from over 4% at 140 kVp to below 0.2% at 175 kVp. The simulations indicate that for clinically relevant titanium and stainless objects a 175 kVp tube voltage effectively avoids photon starvation. Conclusion: The use of exceptionally high tube voltage on a clinical CT system is a practical and effective solution to avoid photon starvation caused by certain metal implants. Sparse and hybrid high-voltage protocols are being considered to maintain low patient dose. This opens the door to algorithmic physics-based corrections rather than treating the data as missing and relying on missing data algorithms. Some of the authors are employees of General Electric.

60 APPLIED LIFE SCIENCES↗

Parallel beamlet dose calculation via beamlet contexts in a distributed multi‐GPU framework

Purpose Dose calculation is one of the most computationally intensive, yet essential tasks in the treatment planning process. With the recent interest in automatic beam orientation and arc trajectory optimization techniques, there is a great need for more efficient model‐based dose calculation algorithms that can accommodate hundreds to thousands of beam candidates at once. Foundational work has shown the translation of dose calculation algorithms to graphical processing units ( GPU s), lending to remarkable gains in processing efficiency. But these methods provide parallelization of dose for only a single beamlet, serializing the calculation of multiple beamlets and under‐utilizing the potential of modern GPU s. In this paper, the authors propose a framework enabling parallel computation of many beamlet doses using a novel beamlet context transformation and further embed this approach in a scalable network of multi‐ GPU computational nodes. Methods The proposed context‐based transformation separates beamlet‐local density and TERMA into distinct beamlet contexts that independently provide sufficient data for beamlet dose calculation. Beamlet contexts are arranged in a composite context array with dosimetric isolation, and the context array is subjected to a GPU collapsed‐cone convolution superposition procedure, producing the set of beamlet‐specific dose distributions in a single pass. Dose from each context is converted to a sparse representation for efficient storage and retrieval during treatment plan optimization. The context radius is a new parameter permitting flexibility between the speed and fidelity of the dose calculation process. A distributed manager‐worker architecture is constructed around the context‐based GPU dose calculation approach supporting an arbitrary number of worker nodes and resident GPU s. Phantom experiments were executed to verify the accuracy of the context‐based approach compared to Monte Carlo and a reference CPU ‐ CCCS implementation for single beamlets and broad beams composed by addition of beamlets. Dose for representative 4 π beam sets was calculated in lung and prostate cases to compare its efficiency with that of an existing beamlet‐sequential GPU ‐ CCCS implementation. Code profiling was also performed to evaluate the scalability of the framework across many networked GPU s. Results The dosimetric accuracy of the context‐based method displays <1.35% and 2.35% average error from the existing serialized CPU ‐ CCCS algorithm and Monte Carlo simulation for beamlet‐specific PDD s in water and slab phantoms, respectively. The context‐based method demonstrates substantial speedup of up to two orders of magnitude over the beamlet‐sequential GPU ‐ CCCS method in the tested configurations. The context‐based framework demonstrates near linear scaling in the number of distributed compute nodes and GPU s employed, indicating that it is flexible enough to meet the performance requirements of most users by simply increasing the hardware utilization. Conclusions The context‐based approach demonstrates a new expectation of performance for beamlet‐based dose calculation methods. This approach has been successful in accelerating the dose calculation process for very large‐scale treatment planning problems ‐ such as automatic 4 π IMRT beam orientation and VMAT arc trajectory selection, with hundreds of thousands of beamlets ‐ in clinically feasible timeframes. The flexibility of this framework makes it as a strong candidate for use in a variety of other very large‐scale treatment planning tasks and clinical workflows.

Neph, Ryan↗

High-Performance Sparse Matrix-Matrix Products on Intel KNL and Multicore Architectures

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is vastly used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. While many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. We firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting multi- and many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We investigate their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. In conclusion, a critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix.

97 MATHEMATICS AND COMPUTING↗

Ultrafast processing of pixel detector data with machine learning frameworks

Modern photon science performed at high repetition rate free-electron laser (FEL) facilities and beyond relies on 2D pixel detectors operating at increasing frequencies (towards 100 kHz at LCLS-II) and producing rapidly increasing amounts of data (towards TB/s). This data must be rapidly stored for offline analysis and summarized in real time for online feedback to the scientists. While at LCLS all raw data has been stored, at LCLS-II this would lead to a prohibitive cost; instead, enabling real time processing of pixel detector data (dark, gain, common mode, background, charge summing, subpixel position, photon counting, data summarization) allows reducing the size and cost of online processing, offline processing and storage by orders of magnitude while preserving full photon information. This could be achieved by taking advantage of the compressibility of sparse data typical for LCLS-II applications. Faced with a similar big data challenge a decade ago, computer vision stimulated revolutionary advances in machine learning hardware and software. We investigated if these developments are useful in the field of data processing for high speed pixel detectors and found that typical deep learning models and autoencoder architectures failed to yield useful noise reduction while preserving full photon information, presumably because of the very different statistics and feature sets in computer vision and radiation imaging. However, the raw performance of modern frameworks like Tensorflow inspired us to redesign in Tensorflow mathematically equivalent versions of the state-of-the-art, “classical” algorithms used at LCLS. The novel Tensorflow models resulted in elegant, compact and hardware agnostic code, gaining 1 to 2 orders of magnitude faster processing on an inexpensive consumer GPU, reducing by 3 orders of magnitude the projected cost of online analysis and compression without photon loss at LCLS-II. The novel Tensorflow models also enabled ongoing development of a pipelined hardware system expected to yield an additional 3 to 4 orders of magnitude speedup, necessary for meeting the data acquisition and storage requirements at LCLS-II, potentially enabling acquiring every single FEL pulse at full speed. Computer vision a decade ago was dominated by hand-crafted filters; their structure inspired the deep learning revolution resulting in modern deep convolutional networks; similarly, our novel Tensorflow filters provide inspiration for designing future deep learning models for ultrafast and efficient processing and classification of pixel detector images at FEL facilities.

47 OTHER INSTRUMENTATION↗

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗

A universal preconditioner for simulating condensed phase materials

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Compressive Classification for TEM-EELS

Acquiring atomic-resolution images of beam sensitive materials or under dynamic conditions (e.g. operando STEM) is very difficult and requires precise dose fractioning to minimize the dose delivered to the sample and acquire the data more rapidly than dynamics present. Typical methods of low-dose STEM imaging include adjusting the beam current, dwell-time, and probe Scanning transmission electron microscopy (STEM) is used routinely to obtain atomic-resolution images of a small selection of radiation tolerant materials under stable conditions.size. All three of these determine the dose over a spatial area in STEM. Recently, compressive sensing [1] has been applied to electron microscopy. The computational imaging method of inpainting [2] has been proposed as a method to reduce dose and increase acquisition speed for STEM. Inpainting is a technique to recover missing pixels in an image. By skipping pixels (randomly) during acquisition, a fourth dose-control mechanism is realized [3]. A few implementations of randomly-subsampled STEM exist (e.g., [4]). To make the concepts of compressive sensing accessible to the microscopy community we begin with an example using atomic resolution images of a GaAs crystal (see Figure 1). Because the crystal is periodic it has a sparse representation in reciprocal space. In fact, a sparse representation is a key component of compressive sensing. If an image is sub-sampled randomly we find that the Fourier transform remains sparse, but becomes increasing noisy as less and less data is acquired. Yet, by finding the peaks in the reciprocal image and removing the noise it is possible to recover atomic resolution images with only 1% of the pixels. Figure 1 shows the reconstruction process for GaAs sub-sampled at 50%, 10%, 5%, and 1%. Periodic images form a special class for which the optimal sampling approach (according to CS theory) is a random selection of pixels. For non-periodic images, such as those arising in in-situ STEM, methods such as dictionary learning are necessary [2,5]. The data can be compressed in time for TEM [5] or pixels can be skipped randomly for STEM. There are several issues that arise in developing a random scan for STEM [4] and a coded aperture for TEM. The remainder of the talk will address these issues. References: [1] E Candes and M Wakin. Signal Processing Magazine, IEEE. 2(25) (2008), pp. 21. [2] A Stevens, Pu Y, Sun Y, et al. Artificial Intelligence & Statistics (AISTATS), 2017. [3] A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41. [4] L Kovarik, A Stevens, A Liyu et al. Appl. Phys. Lett. 109, 164102 (2016). [5] A Stevens, L Kovarik, P Abellan et al. Adv. Structural and Chemical Imaging 1(10), (2015), pp. 1. [6] Supported by the Chemical Imaging, Signature Discovery, and Analytics in Motion Initiatives at PNNL. PNNL is operated by Battelle Memorial Inst. for the US DOE; contract DE-AC05-76RL01830.

Hao, Weituo↗

Guidelines for Publicly Archiving Terrestrial Model Data to Enhance Usability, Intercomparison, and Synthesis

Scientific communities are increasingly publishing data to evaluate, accredit, and build on published research. However, guidelines for curating data for publication are sparse for model-related research, limiting the usability of archived simulation data. In particular, there are no established guidelines for archiving data related to terrestrial models that simulate land processes and their coupled interactions with climate. Terrestrial modelers have a unique set of challenges when publishing data due to the diversity of scientific domains, research questions, and the types and scales of simulations. Researchers in the U.S. Department of Energy’s (DOE) projects use a variety of multiscale models to advance robust predictions of terrestrial and subsurface ecosystem processes. Here, we synthesize archiving needs for data associated with different DOE models, and provide guidelines for publishing terrestrial model data components following FAIR (Findable, Accessible, Interoperable, Reusable) principles. The guidelines recommend archiving model inputs and testing data used in final simulation runs along with associated codes, workflow scripts, and metadata in public repositories. Researchers should consider archiving model outputs if they are within the storage limits of the repository. We also provide considerations for how to bundle files into different data publications with citable digital object identifiers. Finally, we identify repository features and tools that would enable storage and reuse of model data. Given the diversity of DOE terrestrial models, these guidelines are transferable to other model types and will enable efficient reuse of simulation data for purposes such as model intercomparisons, initialization, benchmarking, synthesis, and comparisons with field observations.

58 GEOSCIENCES↗

Multi-fidelity classification using Gaussian processes: Accelerating the prediction of large-scale computational models

We report that machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational models which typically take days to run, thus hindering the potential of machine learning tools. In this work, we present a novel classifier that takes advantage of lower fidelity models and inexpensive approximations to predict the binary output of expensive computer simulations. We postulate an autoregressive model between the different levels of fidelity with Gaussian process priors. We adopt a fully Bayesian treatment for the hyper-parameters and use Markov Chain Monte Carlo samplers. We take advantage of the probabilistic nature of the classifier to implement active learning strategies. We also introduce a sparse approximation to enhance the ability of the multi-fidelity classifier to handle a large amount of low fidelity samples. We test these multi-fidelity classifiers against their single-fidelity counterpart with synthetic data, showing a median computational cost reduction of 23% for a target accuracy of 90%. In an application to cardiac electrophysiology, the multi-fidelity classifier achieves an F1 score, the harmonic mean of precision and recall, of 99.6% compared to 74.1% of a single-fidelity classifier when both are trained with 50 samples. In general, our results show that the multi-fidelity classifiers outperform their single-fidelity counterpart in terms of accuracy in all cases. Finally, we envision that this new tool will enable researchers to study classification problems that would otherwise be prohibitively expensive. Source code is available at https://github.com/fsahli/MFclass.

97 MATHEMATICS AND COMPUTING↗

FLASH: FPGA-Accelerated Smart Switches with GCN Case Study

Some communication switches, e.g., the Mellanox SHArP and those in the IBM BlueGene clusters, are augmented to process packets at the application level with fixed-function collectives. This approach, however, lacks flexibility, which limits their applicability in diverse and dynamic workloads. Recently, a new type of programmable packet processor, which uses high-level languages, e.g., P4, has emerged as possible candidates. P4-based switches, however, fall short in certain applications, including machine learning, where capabilities not currently supported by P4 are needed. These include more complex calculation, such as sparse computation and fused multiply-accumulate, data-intensive floating point operations, data reuse, and significant memory. The problem addressed here is that such a switch augmentation needs to support: a large amount of state, significant flexible compute capability, and ease of programming, all while maintaining full functionality, including ensuring high throughput, and demonstrating utility. In this work, we propose a programmable look-aside-type accelerator that can be embedded into, or attached to, existing communication switch pipelines and that is capable of processing packets at line-rate. The proposed in-switch accelerator is based on mixing an ISA (subset of RISC-V instructions) with dataflow graphs (found in CGRAs). To augment performance, vector instructions are also supported. To facilitate usability, we have developed a complete toolchain to compile user-provided C/C++ codes to appropriate back-end instructions for configuring the accelerator. While this approach is flexible enough to support various workloads, in this paper, we consider Graph Convolutional Networks (GCNs) as a case study. Experimental results show that this approach considerably improves the performance of distributed GCN applications.

Haghi, Pouya↗

A Communication-Avoiding 3D LU Factorization Algorithm for Sparse Matrices

We propose a new algorithm to improve the strong scalability of right-looking sparse LU factorization on distributed memory systems. Our 3D sparse LU algorithm uses a three-dimensional MPI process grid, aggressively exploits elimination tree parallelism and trades off increased memory for reduced per-process communication. We also analyze the asymptotic improvements for planar graphs (e.g., from 2D grid or mesh domains) and certain non-planar graphs (specifically for 3D grids and meshes). For planar graphs with n vertices, our algorithm reduces communication volume asymptotically in n by a factor of O{log n} and latency by a factor of O{log n}. For non-planar cases, our algorithm can reduce the per-process communication volume by 3× and latency by O{n^1/3} times. In all cases, the memory needed to achieve these gains is a constant factor. We implemented our algorithm by extending the 2D data structure used in superLU. Our new 3D code achieves speedups up to 27× for planar graphs and up to 3.3× for non-planar graphs over the baseline 2D superLU when run on 24,000 cores of a Cray XC30.

Sao, Piyush↗

Inference of bipolar neutrino flavor oscillations near a core-collapse supernova based on multiple measurements at Earth

Neutrinos in compact-object environments, such as core-collapse supernovae, can experience various kinds of collective effects in flavor space, engendered by neutrino-neutrino interactions. These include “bipolar” collective oscillations, which are exhibited by neutrino ensembles where different flavors dominate at different energies. Considering the importance of neutrinos in the dynamics and nucleosynthesis in these environments, it is desirable to ascertain whether an Earth-based detection could contain signatures of bipolar oscillations that occurred within a supernova envelope. To that end, we, in this study, continue examining a cost-function formulation of statistical data assimilation (SDA) to infer solutions to a small-scale model of neutrino flavor transformation. SDA is an inference paradigm designed to optimize a model with sparse data. Our model consists of two monoenergetic neutrino beams with different energies emanating from a source and coherently interacting with each other and with a matter background, with radially varying interaction strengths. We attempt to infer flavor transformation histories of these beams using simulated measurements of the flavor content at locations “in vacuum” (that is, far from the source), which could in principle correspond to Earth-based detectors. Within the scope of this small-scale model, we found that: (i) based on such measurements, the SDA procedure is able to infer whether bipolar oscillations had occurred within the protoneutron star envelope, and (ii) if the measurements sample the full amplitude of the neutrino oscillations in vacuum, then the amplitude of the prior bipolar oscillations is well predicted. This result intimates that the inference paradigm can well complement numerical integration codes, via its ability to infer flavor evolution at physically inaccessible locations.

79 ASTRONOMY AND ASTROPHYSICS↗

Analysis of the Temporal Response of Coupled Asymmetrical Zero-Power Subcritical Bare Metal Reactor Systems

The behavior of symmetrical coupled-core systems has been extensively studied, yet there is a dearth of research on asymmetrical systems due to the increased complexity of the analysis of such systems. In this research, the multipoint kinetics method is applied to asymmetrical zeropower, subcritical, bare metal reactor systems. Existing research on asymmetrical reactor systems assumes symmetry in the neutronic coupling; however, it will be shown that this cannot always be assumed. Deep subcriticality adds another layer of complexity and requires modification of the multipoint kinetics equations to account for the effect of the external neutron source. A modified set of multipoint kinetics equations is derived with this in mind. Subsequently, the Rossi-alpha equations are derived for a two-region asymmetrical reactor system. The predictive capabilities of the radiation transport code MCNP6 for neutron noise experiments are shown in a comparison to the results of a series of Rossi-alpha measurements performed by J. Mihalczo utilizing a coupled set of symmetrical bare highly-enriched uranium (HEU) cylinders. The ptrac option within MCNP6 can generate time-tagged counts in a cell (list-mode data). The list-mode data can then be processed similarly to measured data to obtain values for system parameters such as the dual prompt neutron decay constants observable in a coupled system. The results from the ptrac simulations agree well with the historical measured values. A series of case studies are conducted to study the effects of geometrical asymmetry in the coupling between two bare metal HEU cylinders. While the coupling behavior of symmetrical systems has been reported on extensively, that of asymmetrical systems remains sparse. In particular, it appears that there has been no previous research in obtaining the coupling time constants for asymmetrically-coupled systems. The difficulty in observing such systems is due in part to the inability to determine the individual coupling coefficients from measurement: unlike the symmetrical cases, only the product of the values can be obtained. A method is proposed utilizing MCNP6 tally ratios to separate the coupling coefficients for such systems. This work provides insight into the behavior of asymmetrically-coupled systems as the separation distance between the two cores is changed and also as the asymmetry is increased. As the asymmetry increases, both the slower and the faster observable prompt neutron decay constants increase in magnitude. The coupling time constants are determined from the measured decay constants. As the separation distance increases, both coupling coefficients decrease as expected. Based on these findings, an effective computational method utilizing MCNP6 and the Rossialpha technique can be applied to the prediction of asymmetrical coupled system measurements.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A communication-avoiding 3D algorithm for sparse LU factorization on heterogeneous systems

We propose a new algorithm to improve the strong scalability of right-looking sparse LU factorization on distributed memory systems. Our 3D algorithm for sparse LU uses a three-dimensional MPI process grid, exploits elimination tree parallelism, and trades off increased memory for reduced per-process communication. We also analyze the asymptotic improvements for planar graphs (e.g., those arising from 2D grid or mesh discretizations) and certain non-planar graphs (specifically for 3D grids and meshes). For a planar graph with $n$ vertices, our algorithm reduces communication volume asymptotically in $n$ by a factor of $\mathscr{O}$ $\Big(\sqrt{log \ n}\Big)$ and latency by a factor of $\mathscr{O}$ $(log \ n)$. For nonplanar cases, our algorithm can reduce the per-process communication volume by 3× and latency by $\mathscr{O}$ $\Big(n^\frac13\Big)$ times. In all cases, the memory needed to achieve these gains is a constant factor. We implemented our algorithm by extending the 2D data structure used in SuperLU_DIST. Our new 3D code achieves empirical speedups up to 27× for planar graphs and up to 3.3× for non-planar graphs over the baseline 2D SuperLU_DIST when run on 24,000 cores of a Cray XC30. We extend the 3D algorithm for heterogeneous architectures by adding the Highly Asynchronous Lazy Offload (Halo) algorithm for co-processor offload. On 4096 nodes of a Cray XK7 with 32,768 CPU cores and 4096 Nvidia K20x GPUs, the 3D algorithm achieves empirical speedups up to 24× for planar graphs and 3.5× for non-planar graphs over the baseline 2D SuperLU_DIST with co-processor acceleration.

97 MATHEMATICS AND COMPUTING↗

Onset of Scrambling as a Dynamical Transition in Tunable-Range Quantum Circuits

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior. We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space. This mapping predicts mean-field critical exponents v=–1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that the interpretable nature of language often provides a much richer learning medium for LLMs, compared to policy gradients derived from sparse, scalar rewards. To test this, we introduce GEPA (Genetic-Pareto), a prompt optimizer that thoroughly incorporates natural language reflection to learn high-level rules from trial and error. Given any AI system containing one or more LLM prompts, GEPA samples trajectories (e.g., reasoning, tool calls, and tool outputs) and reflects on them in natural language to diagnose problems, propose and test prompt updates, and combine complementary lessons from the Pareto frontier of its own attempts. As a result of GEPA's design, it can often turn even just a few rollouts into a large quality gain. Across six tasks, GEPA outperforms GRPO by 6% on average and by up to 20%, while using up to 35x fewer rollouts. GEPA also outperforms the leading prompt optimizer, MIPROv2, by over 10% (e.g., +12% accuracy on AIME-2025), and demonstrates promising results as an inference-time search strategy for code optimization. We release our code at https://github.com/gepa-ai/gepa.

97 MATHEMATICS AND COMPUTING↗