arXiv subjects

Alexandros Nikolaos Ziogas

Publications and source records attributed to Alexandros Nikolaos Ziogas.

At least 19 recordsLinked to original sources

arXiv2026

EmuGEMM: Fused Tensor Core Kernels for Precision Emulation in Matrix Multiplication

Modern GPUs devote an increasing silicon budget to low-precision matrix-multiplication units, widening the precision-throughput gap for scientific computing workloads. Ozaki Schemes I and II offer an alternative by reconstructing high-precision general matrix multiplication (GEMM) from low-precision operations, yet existing implementations leave substantial performance untapped. In particular, intermediate results are repeatedly materialized in global memory, making data movement the dominant bottleneck. We present EmuGEMM, fused integer Tensor Core kernels for NVIDIA Hopper and Blackwell GPUs that eliminate redundant memory round-trips in both Ozaki schemes. Using Scheme I, EmuGEMM sustains up to 1,639 Top/s on Hopper (83% of INT8 peak) and 3,654 Top/s on Blackwell (81%). For large matrices, EmuGEMM surpasses cuBLAS TF32 throughput by up to 1.4x on Hopper and 1.7x on Blackwell, at comparable accuracy. Using Scheme II, EmuGEMM extends to complex arithmetic and outperforms cuBLAS ZGEMM by up to 2.3x on Hopper and 5.5x on Blackwell.

cs.DC↗

arXiv2026

Ab initio Modeling of MoS2/Oxide Device Interfaces with Machine Learned Electronic Structures

We introduce a new ab initio approach to simulate semiconductor devices that integrates scalable machine-learned (ML) electronic structure models with an advanced quantum transport (QT) solver. The developed framework enables 10,000X speedups over density functional theory to produce the Hamiltonian matrix of devices made of >20,000 atoms, while offering high prediction accuracy. We use its unique features to investigate MoS2/oxide samples and single-layer MoS2 field-effect transistors, where the surrounding oxide layers, here, HfO2 or Al2O3, are explicitly included into the QT domain. In particular, we reveal that the presence of undercoordinated metal atoms (Hf or Al) close to the semiconductor-oxide interface significantly affects the magnitude of the electronic current and its propagation through MoS2.

cond-mat.mtrl-sci↗

arXiv2026

MALOQ: Massively Accelerated Learning of Operators for Quantum Transport

Machine-learned (ML) operator models can be trained to predict density functional theory (DFT) Hamiltonian/density matrices at significantly reduced computational cost, thus extending electronic-structure calculations to previously unfeasible scales. Here, we introduce MALOQ (Massively Accelerated Learning of Operators for Quantum Transport), an application built to train on and predict electronic-structure matrices for systems made of few to 100k atoms, described by large basis sets, and covering a wide range of atomic elements. Based on a state-of-the-art, SO(2)-equivariant backbone architecture, MALOQ provides (i) custom data-processing kernels to handle high-rank Hamiltonian matrix data and (ii) a scalable edge-wise distribution of atomic graph(s). Trained on the largest molecular Hamiltonian datasets available today, it reduces time-per-epoch by over 30% compared to a molecule-wise-distributed framework, and enables inference on material graphs of arbitrary size. We demonstrate scalable training and inference for 3,000-12,000 atoms on the Alps supercomputer, up to 192 GPUs and 256 GPUs, respectively.

cs.LG↗

arXiv2026

Optimizing Semiconductor Device Simulations through Low-Precision Arithmetic

Architectural changes in GPUs, especially the promotion of low-precision computational units, pose significant challenges to traditional, FP64-based high-performance computing (HPC) applications, while also presenting opportunities. Adopting reduced-precision data formats is a promising avenue to exploit the increased throughput capabilities. However, straightforward data conversions may lead to degraded accuracy or even erroneous results. For a given application, only an in-depth analysis of its numerical stability can reveal the potential of low-precision arithmetic. In this work, we consider the open-source quatrex package, a quantum transport solver capable of breaking the sustained FP64 Eflop/s barrier, to illustrate trade-offs between accuracy losses and computational speed-ups when moving from high- to low-precision formats. We use three representative benchmark structures to explore the application's numerical properties. Applying the gained insights to a larger, more realistic system, we achieve up to 51% higher throughput while maintaining accurate results, on 40% fewer HPC resources than the FP64 reference.

cs.CE↗

arXiv2026

ADELIA: Automatic Differentiation for Efficient Laplace Inference Approximations

Spatio-temporal Bayesian inference drives environmental and health sciences using latent Gaussian models. Integrated Nested Laplace Approximations (INLA) enable inference for these models at HPC scale but rely on derivative-based optimization over $d$ hyperparameters. State-of-the-art INLA implementations approximate derivatives via central finite differences (FD), requiring $2d{+}1$ evaluations. These evaluations are embarrassingly parallel, but total work and energy grow with $d$, limiting time-to-solution under fixed budgets. Reverse-mode automatic differentiation (AD) computes exact gradients independently of $d$, but its efficient application to INLA's structured-sparse kernels is an open challenge. We present ADELIA, the first AD-enabled INLA implementation with a structure-exploiting multi-GPU backward pass leveraging model sparsity. We evaluate ADELIA on ten benchmark models, including real-world air-pollution monitoring. We achieve $4.2$--$7.9\times$ per-gradient speedups and reliable convergence on production-scale models with up to 1.9M latent variables, where FD struggles. Even when scaled to 16--32 GPUs to match ADELIA's wall-clock time, FD consumes $5$--$8\times$ more energy.

cs.DC↗

arXiv2026

Acceleration of Atomistic NEGF: Algorithms, Parallelization, and Machine Learning

The Non-equilibrium Green's function (NEGF) formalism is a particularly powerful method to simulate the quantum transport properties of nanoscale devices such as transistors, photo-diodes, or memory cells, in the ballistic limit of transport or in the presence of various scattering sources such as electronphonon, electron-photon, or even electron-electron interactions. The inclusion of all these mechanisms has been first demonstrated in small systems, composed of a few atoms, before being scaled up to larger structures made of thousands of atoms. Also, the accuracy of the models has kept improving, from empirical to fully ab-initio ones, e.g., density functional theory (DFT). This paper summarizes key (algorithmic) achievements that have allowed us to bring DFT+NEGF simulations closer to the dimensions and functionality of realistic systems. The possibility of leveraging graph neural networks and machine learning to speed up ab-initio device simulations is discussed as well.

cond-mat.mtrl-sci↗

arXiv2026

Parallel Quadratic Selected Inversion in Quantum Transport Simulation

Driven by Moore's Law, the dimensions of transistors have been pushed down to the nanometer scale. Advanced quantum transport (QT) solvers are required to accurately simulate such nano-devices. The non-equilibrium Green's function (NEGF) formalism lends itself optimally to these tasks, but it is computationally very intensive, involving the selected inversion (SI) of matrices and the selected solution of quadratic matrix (SQ) equations. Existing algorithms to tackle these numerical problems are ideally suited to GPU acceleration, e.g., the so-called recursive Green's function (RGF) technique, but they are typically sequential, require block-tridiagonal (BT) matrices as inputs, and their implementation has been so far restricted to shared memory parallelism, thus limiting the achievable device sizes. To address these shortcomings, we introduce distributed methods that build on RGF and enable parallel selected inversion and selected solution of the quadratic matrix equation. We further extend them to handle BT matrices with arrowhead, which allows for the investigation of multi-terminal transistor structures. We evaluate the performance of our approach on a real dataset from the QT simulation of a nano-ribbon transistor and compare it with the sparse direct package PARDISO. When scaling to 16 GPUs, our fused SI and SQ solver is 5.2x faster than the SI module of PARDISO applied to a device 16x shorter. These results highlight the potential of our method to accelerate NEGF-based nano-device simulations.

cs.DC↗

arXiv2025

Accelerated Spatio-Temporal Bayesian Modeling for Multivariate Gaussian Processes

Multivariate Gaussian processes (GPs) offer a powerful probabilistic framework to represent complex interdependent phenomena. They pose, however, significant computational challenges in high-dimensional settings, which frequently arise in spatial-temporal applications. We present DALIA, a highly scalable framework for performing Bayesian inference tasks on spatio-temporal multivariate GPs, based on the methodology of integrated nested Laplace approximations. Our approach relies on a sparse inverse covariance matrix formulation of the GP, puts forward a GPU-accelerated block-dense approach, and introduces a hierarchical, triple-layer, distributed memory parallel scheme. We showcase weak scaling performance surpassing the state-of-the-art by two orders of magnitude on a model whose parameter space is 8$\times$ larger and measure strong scaling speedups of three orders of magnitude when running on 496 GH200 superchips on the Alps supercomputer. Applying DALIA to air pollution data from northern Italy over 48 days, we showcase refined spatial resolutions over the aggregated pollutant measurements.

stat.CO↗

arXiv2025

Ab-initio Quantum Transport with the GW Approximation, 42,240 Atoms, and Sustained Exascale Performance

Designing nanoscale electronic devices such as the currently manufactured nanoribbon field-effect transistors (NRFETs) requires advanced modeling tools capturing all relevant quantum mechanical effects. State-of-the-art approaches combine the non-equilibrium Green's function (NEGF) formalism and density functional theory (DFT). However, as device dimensions do not exceed a few nanometers anymore, electrons are confined in ultra-small volumes, giving rise to strong electron-electron interactions. To account for these critical effects, DFT+NEGF solvers should be extended with the GW approximation, which massively increases their computational intensity. Here, we present the first implementation of the NEGF+GW scheme capable of handling NRFET geometries with dimensions comparable to experiments. This package, called QuaTrEx, makes use of a novel spatial domain decomposition scheme, can treat devices made of up to 84,480 atoms, scales very well on the Alps and Frontier supercomputers (>80% weak scaling efficiency), and sustains an exascale FP64 performance on 42,240 atoms (1.15 Eflop/s).

cs.DC↗

arXiv2025

Distributed Equivariant Graph Neural Networks for Large-Scale Electronic Structure Prediction

Equivariant Graph Neural Networks (eGNNs) trained on density-functional theory (DFT) data can potentially perform electronic structure prediction at unprecedented scales, enabling investigation of the electronic properties of materials with extended defects, interfaces, or exhibiting disordered phases. However, as interactions between atomic orbitals typically extend over 10+ angstroms, the graph representations required for this task tend to be densely connected, and the memory requirements to perform training and inference on these large structures can exceed the limits of modern GPUs. Here we present a distributed eGNN implementation which leverages direct GPU communication and introduce a partitioning strategy of the input graph to reduce the number of embedding exchanges between GPUs. Our implementation shows strong scaling up to 128 GPUs, and weak scaling up to 512 GPUs with 87% parallel efficiency for structures with 3,000 to 190,000 atoms on the Alps supercomputer.

cs.LG↗

arXiv2025

Learning the Electronic Hamiltonian of Large Atomic Structures

Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of materials, subverting ab initio density functional theory (DFT) calculations when the underlying lattices can be represented as small and/or repeatable unit cells (i.e., molecules and periodic crystals). Realistic systems are, however, non-ideal and generally characterized by higher structural complexity. As such, they require large (10+ Angstroms) unit cells and thousands of atoms to be accurately described. At these scales, DFT becomes computationally prohibitive, making GNNs especially attractive. In this work, we present a strictly local equivariant GNN capable of learning the electronic Hamiltonian (H) of realistically extended materials. It incorporates an augmented partitioning approach that enables training on arbitrarily large structures while preserving local atomic environments beyond boundaries. We demonstrate its capabilities by predicting the electronic Hamiltonian of various systems with up to 3,000 nodes (atoms), 500,000+ edges, ~28 million orbital interactions (nonzero entries of H), and $\leq$0.53% error in the eigenvalue spectra. Our work expands the applicability of current electronic property prediction methods to some of the most challenging cases encountered in computational materials science, namely systems with disorder, interfaces, and defects.

cond-mat.mtrl-sci↗

arXiv2025

Comparing Parallel Functional Array Languages: Programming and Performance

Parallel functional array languages are an emerging class of programming languages that promise to combine low-effort parallel programming with good performance and performance portability. We systematically compare the designs and implementations of five different functional array languages: Accelerate, APL, DaCe, Futhark, and SaC. We demonstrate the expressiveness of functional array programming by means of four challenging benchmarks, namely N-body simulation, MultiGrid, Quickhull, and Flash Attention. These benchmarks represent a range of application domains and parallel computational models. We argue that the functional array code is much shorter and more comprehensible than the hand-optimized baseline implementations because it omits architecture-specific aspects. Instead, the language implementations generate both multicore and GPU executables from a single source code base. Hence, we further argue that functional array code could more easily be ported to, and optimized for, new parallel architectures than conventional implementations of numerical kernels. We demonstrate this potential by reporting the performance of the five parallel functional array languages on a total of 39 instances of the four benchmarks on both a 32-core AMD EPYC 7313 multicore system and on an NVIDIA A30 GPU. We explore in-depth why each language performs well or not so well on each benchmark and architecture. We argue that the results demonstrate that mature functional array languages have the potential to deliver performance competitive with the best available conventional techniques.

cs.PL↗

arXiv2025

Serinv: A Scalable Library for the Selected Inversion of Block-Tridiagonal with Arrowhead Matrices

The inversion of structured sparse matrices is a key but computationally and memory-intensive operation in many scientific applications. There are cases, however, where only particular entries of the full inverse are required. This has motivated the development of so-called selected-inversion algorithms, capable of computing only specific elements of the full inverse. Currently, most of them are either shared-memory codes or limited to CPU implementations. Here, we introduce Serinv, a scalable library providing distributed, GPU-based algorithms for the selected inversion and Cholesky decomposition of positive-definite, block-tridiagonal arrowhead matrices. This matrix class is highly relevant in statistical climate modeling and materials science applications. The performance of Serinv is demonstrated on synthetic and real datasets from statistical air temperature prediction models. In our numerical tests, Serinv achieves 32.3% strong and 47.2% weak scaling efficiency and up to two orders of magnitude speedup over the sparse direct solvers PARDISO and MUMPS on 16 GPUs.

cs.DC↗

arXiv2024

Electron-Electron Interactions in Device Simulation via Non-equilibrium Green's Functions and the GW Approximation

The continuous scaling of metal-oxide-semiconductor field-effect transistors (MOSFETs) has led to device geometries where charged carriers are increasingly confined to ever smaller channel cross sections. This development is associated with reduced screening of long-range Coulomb interactions. To accurately predict the behavior of such ultra-scaled devices, electron-electron (e-e) interactions must be explicitly incorporated in their quantum transport simulation. In this paper, we present an \textit{ab initio} atomistic simulation framework based on density functional theory, the non-equilibrium Green's function formalism, and the self-consistent GW approximation to perform this task. The implemented method is first validated with a carbon nanotube test structure before being applied to calculate the transfer characteristics of a silicon nanowire MOSFET in a gate-all-around configuration. As a consequence of e-e scattering, the energy and spatial distribution of the carrier and current densities both significantly change, while the on-current of the transistor decreases owing to the Coulomb repulsion between the electrons. Furthermore, we demonstrate how the resulting bandgap modulation of the nanowire channel as a function of the gate-to-source voltage could potentially improve the device performance. To the best of our knowledge, this study is the first one reporting large-scale atomistic quantum transport simulations of nano-devices under non-equilibrium conditions and in the presence of e-e interactions within the GW approximation.

cond-mat.mes-hall↗

arXiv2024

Arrow Matrix Decomposition: A Novel Approach for Communication-Efficient Sparse Matrix Multiplication

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single compute node, data transfer becomes a bottleneck. An approach based on dense matrix multiplication algorithms leads to suboptimal scalability and fails to exploit the sparsity in the problem. To address these challenges, we propose decomposing the sparse matrix into a small number of highly structured matrices called arrow matrices, which are connected by permutations. Our approach enables communication-avoiding multiplications, achieving a polynomial reduction in communication volume per iteration for matrices corresponding to planar graphs and other minor-excluded families of graphs. Our evaluation demonstrates that our approach outperforms a state-of-the-art method for sparse matrix multiplication on matrices with hundreds of millions of rows, offering near-linear strong and weak scaling.

cs.DC↗

arXiv2023

FuzzyFlow: Leveraging Dataflow To Find and Squash Program Optimization Bugs

The current hardware landscape and application scale is driving performance engineers towards writing bespoke optimizations. Verifying such optimizations, and generating minimal failing cases, is important for robustness in the face of changing program conditions, such as inputs and sizes. However, isolation of minimal test-cases from existing applications and generating new configurations are often difficult due to side effects on the system state, mostly related to dataflow. This paper introduces FuzzyFlow: a fault localization and test case extraction framework designed to test program optimizations. We leverage dataflow program representations to capture a fully reproducible system state and area-of-effect for optimizations to enable fast checking for semantic equivalence. To reduce testing time, we design an algorithm for minimizing test inputs, trading off memory for recomputation. We demonstrate FuzzyFlow on example use cases in real-world applications where the approach provides up to 528 times faster optimization testing and debugging compared to traditional approaches.

cs.SE↗

arXiv2023

On the Parallel I/O Optimality of Linear Algebra Kernels: Near-Optimal Matrix Factorizations

Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for Cholesky and LU factorizations that utilize an asymptotically communication-optimal 2.5D decomposition. We first establish a theoretical framework for deriving parallel I/O lower bounds for linear algebra kernels, and then utilize its insights to derive Cholesky and LU schedules, both communicating N^3/(P*sqrt(M)) elements per processor, where M is the local memory size. The empirical results match our theoretical analysis: our implementations communicate significantly less than Intel MKL, SLATE, and the asymptotically communication-optimal CANDMC and CAPITAL libraries. Our code outperforms these state-of-the-art libraries in almost all tested scenarios, with matrix sizes ranging from 2,048 to 262,144 on up to 512 CPU nodes of the Piz Daint supercomputer, decreasing the time-to-solution by up to three times. Our code is ScaLAPACK-compatible and available as an open-source library.

cs.DC↗

arXiv2022

Deinsum: Practically I/O Optimal Multilinear Algebra

Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously hard problem. State-of-the-art libraries rely on heuristics and often fall back to suboptimal tensor folding and BLAS calls. We present Deinsum, an automated framework for distributed multilinear algebra computations expressed in Einstein notation, based on rigorous mathematical tools to address this problem. Our framework automatically derives data movement-optimal tiling and generates corresponding distributed schedules, further optimizing the performance of local computations by increasing their arithmetic intensity. To show the benefits of our approach, we test it on two important tensor kernel classes: Matricized Tensor Times Khatri-Rao Products and Tensor Times Matrix chains. We show performance results and scaling on the Piz Daint supercomputer, with up to 19x speedup over state-of-the-art solutions on 512 nodes.

cs.DC↗