This work provides a concrete layered C++ MPI binding using C++20 concepts, with a core extensible layer and adapters for GPU and portability libraries, backed by an open-source implementation.
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Hilfer fractional advection-diffusion equations with power-law initial condition; a Numerical study using variational iteration method
Canonical reference. 92% of citing Pith papers cite this work as background.
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92% of classified citations
abstract
We propose a Hilfer advection-diffusion equation of order $0<\alpha<1$ and type $0\leq\beta\leq1$, and find the power series solution by using variational iteration method. Power series solutions are expressed in a form that is easy to implement numerically and in some particular cases, solutions are expressed in terms of Mittag-Leffler function. Absolute convergence of power series solutions is proved and the sensitivity of the solutions is discussed with respect to changes in the values of different parameters. For power law initial conditions it is shown that the Hilfer advection-diffusion PDE gives the same solutions as the Caputo and Riemann-Liouville advection-diffusion PDE. To leading order, the fractional solution compared to the non-fractional solution increases rapidly with $\alpha$ for $\alpha > 0.7$ at a given time $t$; but for $\alpha<0.7$ this factor is weakly sensitive to $\alpha$. We also show that the truncation errors, arising when using the partial sum as approximate solutions, decay exponentially fast with the number of terms $n$ used. We find that for $\alpha< 0.7$ the number of terms needed is weakly sensitive to the accuracy level and to the fractional order, $n\approx 20$; but for $\alpha>0.7$ the required number of terms increases rapidly with the accuracy level and also with the fractional order $\alpha$.
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representative citing papers
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Simulation study shows cold TLB misses in reverse address translation dominate latency for small collectives in multi-GPU pods, causing up to 1.4x degradation, while larger ones see diminishing returns.
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citing papers explorer
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NCCLZ: Compression-Enabled GPU Collectives with Decoupled Quantization and Entropy Coding
NCCLZ decouples quantization and entropy coding across NCCL stack layers to enable overlapped compression, delivering up to 9.65x speedup over plain NCCL on scientific and training workloads.
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Unfolding an Atomistic World: Atomistic Simulation of Reactor Pressure Vessel Steel Across Year-and-Meter Scales
AtomWorld enables the first direct atomistic simulation of RPV steel at year-and-meter scales, handling ten-quintillion-atom systems and simulating one service year in 1.71 days with 92-97% scaling efficiency on leadership supercomputers.
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Mosaic: Cross-Modal Clustering for Efficient Video Understanding
Mosaic uses cross-modal clusters as the unit for KVCache organization in VLMs to achieve up to 1.38x speedup in streaming long-video understanding.
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NestPipe: Large-Scale Recommendation Training on 1,500+ Accelerators via Nested Pipelining
NestPipe achieves up to 3.06x speedup and 94.07% scaling efficiency on 1,536 workers via dual-buffer inter-batch and frozen-window intra-batch pipelining that overlaps communication with computation.
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Analyzing Reverse Address Translation Overheads in Multi-GPU Scale-Up Pods
Simulation study shows cold TLB misses in reverse address translation dominate latency for small collectives in multi-GPU pods, causing up to 1.4x degradation, while larger ones see diminishing returns.
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Fast MoE Inference via Predictive Prefetching and Expert Replication
Dynamic replication of predicted overloaded experts in MoE models achieves near-100% GPU utilization and up to 3x faster inference while retaining 90-95% of baseline performance.
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Stencil Computations on Cerebras Wafer-Scale Engine
CStencil on the WSE-3 achieves up to 342x speedup for 2D stencils versus an adapted single-precision GPU solver and saturates both compute and on-chip memory bandwidth.
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One Pool, Two Caches: Adaptive HBM Partitioning for Accelerating Generative Recommender Serving
HELM adaptively partitions HBM between EMB and KV caches via a three-layer PPO controller and EMB-KV-aware scheduling, reducing P99 latency by 24-38% while achieving 93.5-99.6% SLO satisfaction on production workloads.
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Matrix-Free 3D SIMP Topology Optimization with Fused Gather-GEMM-Scatter Kernels
A fused gather-GEMM-scatter CUDA kernel achieves 4.6-7.3x end-to-end speedup and 3.2-4.9x lower energy for matrix-free 3D SIMP topology optimization on RTX 4090 compared to three-stage baselines.
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Preserving Clusters in Error-Bounded Lossy Compression of Particle Data
A clustering-aware correction algorithm using spatial partitioning and projected gradient descent preserves single-linkage clusters in lossy-compressed particle data while keeping competitive compression ratios.
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Measurement of Generative AI Workload Power Profiles for Whole-Facility Data Center Infrastructure Planning
High-resolution power profiles for AI workloads on H100 GPUs are measured and scaled to whole-facility energy demand using a bottom-up model, with the dataset made public.