arXiv subjects

Fabian Böhm

Publications and source records attributed to Fabian Böhm.

17 recordsLinked to original sources

arXiv2026

TERRA-NG v1.0: Extreme-Scale, GPU-accelerated Mantle Convection

We present TERRA-NG, a portable, GPU-accelerated, matrix-free mantle-convection code. A single Kokkos C++ implementation runs at scale on NVIDIA, AMD, and Intel GPU supercomputers. TERRA-NG has a deliberately narrow design: built on a radially extruded mesh of spherical wedges, tailored to the spherical shell geometry, which enables domain-specific optimizations like single quadrature-point integral-evaluations, radial coordinate storage compression and radial shared-memory tiling. The corresponding low-order $W_1$-iso-$W_2/W_1$ wedge-based Stokes--energy discretisation is verified against the Zhong et al.(2008) spherical-shell convection benchmark suite. We showcase TERRA-NG through strong- and weak-scaling on the JUWELS Booster (NVIDIA A100), MareNostrum 5 (NVIDIA H100), LUMI-G (AMD MI250X), Hunter (AMD MI300A APU), and SuperMUC-NG Phase 2 (Intel PVC) supercomputers. Coupled mantle convection simulations at $\sim\!11$ km and $\sim\!5.6$ km radial spacing ($\sim 2.8$ B and $\sim 22$ B DoFs) can be run routinely on standard node partitions of all considered systems. Global $\sim\!1$ km-per-gridpoint mantle convection ($\sim 1.4$ T DoFs) is feasible on an extreme-scale allocation, and a sub-km hero-run at $\sim\!0.7$ km grid spacing scaling up to $\sim 11,000$ GPUs of LUMI-G ($\sim 11$ T DoFs) shows the potential of the code on future, larger machines.

cs.CE↗

arXiv2026

Performance Analysis of Low-Order, GPU-accelerated Finite Element Kernels using Kokkos

We study performance portability for low-order, matrix-free finite element kernels, using the example of a vectorial, variable-coefficient PDE operator originating in geophysical models. Written in Kokkos, the kernel is compared on NVIDIA H100, AMD MI250X, AMD MI300A and Intel PVC Max 1550 GPUs. Owing to its low order and to optimizations that reduce the arithmetic, the kernel has a low arithmetic intensity, so that its performance is determined by how the finite element assembly is mapped onto the memory hierarchy. This is a dimension in which the architectures differ even within one vendor family, causing different performance characteristics. We examine how Kokkos' hierarchical parallelism and shared scratch memory, which are used for the shared degrees of freedom of the conforming discretization, behave on each device. Finally, we show how portability gaps can be narrowed with tuning levers such as the size of the thread groups, the balance between occupancy and register use, and the atomic accumulation strategy at the end of the kernel.

cs.PF↗

arXiv2026

Continuous-time nonlinear closed-loop in-memory computing for high-accuracy massive MIMO detection

Analog in-memory computing (IMC) has emerged as a promising approach for accelerating matrix operations by exploiting the intrinsic physics of memory arrays. To date, however, most IMC architectures have focused on linear algebra workloads in which computation is encoded in the equilibrium state of a physical system. Extending these principles to nonlinear optimization remains challenging and typically relies on iterative algorithms composed of repeated linear operations. Here, we introduce a continuous-time nonlinear closed-loop IMC architecture for box-constrained zero-forcing (BCZF) decoding in massive multiple-input multiple-output (MIMO) systems. The proposed architecture embeds the decoding problem directly within the dynamics of a nonlinear feedback network of memory arrays and supply-limited operational amplifiers, allowing solutions to emerge through continuous-time physical optimization. We derive a compact analytical model of the circuit and show that its trajectories minimize an equivalent energy function. Experimental emulation using a fabricated IMC chip confirms the predicted dynamics under realistic hardware nonidealities for up to 16x16 MIMO systems. To overcome the finite precision of analog hardware, we extend mixed-precision iterative refinement from linear algebra to nonlinear continuous-time optimization, enabling reliable detection of high-order modulation formats including 256-QAM. Benchmark projections indicate operation from ultra-low-energy approximate decoding to high-accuracy massive MIMO detection. Together, these results extend closed-loop IMC from equilibrium-based linear algebra to continuous-time nonlinear optimization and establish a pathway toward efficient physical accelerators for high-accuracy wireless communications.

cs.ET↗

arXiv2026

Accelerating Hybrid XOR$-$CNF Boolean Satisfiability Problems Natively with In-Memory Computing

The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more efficiently by representing them with a combination of exclusive OR (XOR) and conjunctive normal form (CNF) clauses. We propose a hardware accelerator architecture that natively embeds and solves such hybrid XOR--CNF problems using in-memory computing hardware. To achieve this, we introduce an algorithm and demonstrate, both experimentally and through simulations, how it can be efficiently implemented with memristor crossbar arrays. Compared to the conventional approaches that translate XOR--CNF problems to pure CNF problems, our simulations show that the accelerator improves computation speed, energy efficiency, and chip area utilization of in-memory accelerators by $\sim$10$\times$ for a set of hard cryptographic benchmarking problems. Moreover, the accelerator achieves a $\sim$10$\times$ speedup and a $\sim$1000$\times$ gain in energy efficiency over state-of-the-art SAT solvers running on CPUs.

cs.ET↗

arXiv2025

Large-scale Multigrid with Adaptive Galerkin Coarsening

We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous coarse-grid operators: Galerkin coarse grid approximation is applied locally in regions with large coefficient gradients, while lightweight, direct coarse grid approximation is used elsewhere. This selective application ensures that local Galerkin operators are computed and stored only where necessary, minimizing memory requirements while maintaining robust convergence. We demonstrate the method on a suite of sinker benchmark problems for the generalized Stokes equation, including grid-aligned and unaligned viscosity jumps, smoothly varying viscosity functions with large gradients, and different viscosity evaluation techniques. We analytically quantify the solver's memory consumption and demonstrate its efficiency by solving Stokes problems with $10^{10}$ degrees of freedom, viscosity jumps of $10^{6}$ magnitude, and more than 100{,}000 parallel processes.

cs.PF↗

arXiv2025

Parallel Tempering-Inspired Distributed Binary Optimization with In-Memory Computing

In-memory computing (IMC) has been shown to be a promising approach for solving binary optimization problems while significantly reducing energy and latency. Building on the advantages of parallel computation, we propose an IMC-compatible parallelism framework based on the physics-inspired parallel tempering (PT) algorithm, enabling cross-replica communication to improve the performance of IMC solvers. This framework enables an IMC solver not only to improve performance beyond what can be achieved through parallelization, but also affords greater flexibility for the search process with low hardware overhead. We justify that the framework can be applied to almost any IMC solver. We demonstrate the effectiveness of the framework for the Boolean satisfiability (SAT) problem, using the WalkSAT heuristic as a proxy for existing IMC solvers. The resulting PT-inspired cooperative WalkSAT (PTIC-WalkSAT) algorithm outperforms the standard WalkSAT heuristic in terms of the iterations-to-solution in 84.0% of the tested problem instances and its naïve parallel variant (PA-WalkSAT) does so in 64.9% of the instances, and with a higher success rate in the majority of instances. An estimate of the energy overhead of the PTIC framework for two hardware accelerator architectures indicates that in both cases the overhead of running the PTIC framework would be less than 1% of the total energy required to run each accelerator.

cs.ET↗

arXiv2025

Roadmap on Neuromorphic Photonics

This roadmap consolidates recent advances while exploring emerging applications, reflecting the remarkable diversity of hardware platforms, neuromorphic concepts, and implementation philosophies reported in the field. It emphasizes the critical role of cross-disciplinary collaboration in this rapidly evolving field.

cs.ET↗

arXiv2025

Solving Boolean satisfiability problems with resistive content addressable memories

Solving optimization problems is a highly demanding workload requiring high-performance computing systems. Optimization solvers are usually difficult to parallelize in conventional digital architectures, particularly when stochastic decisions are involved. Recently, analog computing architectures for accelerating stochastic optimization solvers have been presented, but they were limited to academic problems in quadratic polynomial format. Here we present KLIMA, a k-Local In-Memory Accelerator with resistive Content Addressable Memories (CAMs) and Dot-Product Engines (DPEs) to accelerate the solution of high-order industry-relevant optimization problems, in particular Boolean Satisfiability. By co-designing the optimization heuristics and circuit architecture we improve the speed and energy to solution up to 182x compared to the digital state of the art.

cs.ET↗

arXiv2024

Code Generation and Performance Engineering for Matrix-Free Finite Element Methods on Hybrid Tetrahedral Grids

This paper introduces a code generator designed for node-level optimized, extreme-scalable, matrix-free finite element operators on hybrid tetrahedral grids. It optimizes the local evaluation of bilinear forms through various techniques including tabulation, relocation of loop invariants, and inter-element vectorization - implemented as transformations of an abstract syntax tree. A key contribution is the development, analysis, and generation of efficient loop patterns that leverage the local structure of the underlying tetrahedral grid. These significantly enhance cache locality and arithmetic intensity, mitigating bandwidth-pressure associated with compute-sparse, low-order operators. The paper demonstrates the generator's capabilities through a comprehensive educational cycle of performance analysis, bottleneck identification, and emission of dedicated optimizations. For three differential operators ($-Δ$, $-\nabla \cdot (k(\mathbf{x})\, \nabla\,)$, $α(\mathbf{x})\, \mathbf{curl}\ \mathbf{curl} + β(\mathbf{x}) $), we determine the set of most effective optimizations. Applied by the generator, they result in speed-ups of up to 58$\times$ compared to reference implementations. Detailed node-level performance analysis yields matrix-free operators with a throughput of 1.3 to 2.1 GDoF/s, achieving up to 62% peak performance on a 36-core Intel Ice Lake socket. Finally, the solution of the curl-curl problem with more than a trillion ($ 10^{12}$) degrees of freedom on 21504 processes in less than 50 seconds demonstrates the generated operators' performance and extreme-scalability as part of a full multigrid solver.

cs.CE↗

arXiv2024

Tuning and Testing an Online Feedback Optimization Controller to Provide Curative Distribution Grid Flexibility

Due to more volatile generation, flexibility will become more important in transmission grids. One potential source of this flexibility can be distribution grids. A flexibility request from the transmission grid to a distribution grid then needs to be split up onto the different flexibility providing units (FPU) in the distribution grid. One potential way to do this is Online Feedback Optimization (OFO). OFO is a new control method that steers power systems to the optimal solution of an optimization problem using minimal model information and computation power. This paper will show how to choose the optimization problem and how to tune the OFO controller. Afterward, we test the resulting controller on a real distribution grid laboratory and show its performance, its interaction with other controllers in the grid, and how it copes with disturbances. Overall, the paper makes a clear recommendation on how to phrase the optimization problem and tune the OFO controller. Furthermore, it experimentally verifies that an OFO controller is a powerful tool to disaggregate flexibility requests onto FPUs while satisfying operational constraints inside the flexibility providing distribution grid.

eess.SY↗

arXiv2023

Providing Curative Distribution Grid Flexibility Using Online Feedback Optimization

Distribution grid flexibility is discussed as a possible measure in curative system operation, yielding a need for an efficient and robust coordination mechanism for the joint flexibility provision by individual units to the transmission grid. This paper introduces a method to coordinate distribution grid level flexibility as a fast-responding curative measure based on Online Feedback Optimization. We utilize an optimization algorithm in a closed loop with the distribution grid to dispatch set points for active and reactive power to flexibility providing units. The approach is evaluated in an experimental setup, utilizing assets connected to an exemplary low voltage grid. Online Feedback Optimization is found to be both a viable as well as a highly effective approach to coordinate distributed energy resources in real-time curative system operation.

eess.SY↗

arXiv2023

Fundamental Data Structures for Matrix-Free Finite Elements on Hybrid Tetrahedral Grids

This paper presents efficient data structures for the implementation of matrix-free finite element methods on block-structured, hybrid tetrahedral grids. It provides a complete categorization of all geometric sub-objects that emerge from the regular refinement of the unstructured, tetrahedral coarse grid and describes efficient iteration patterns and analytical linearization functions for the mapping of coefficients to memory addresses. This foundation enables the implementation of fast, extreme-scalable, matrix-free, iterative solvers, and in particular geometric multigrid methods by design. Their application to the variable-coefficient Stokes system subject to an enriched Galerkin discretization and to the curl-curl problem discretized with Nédélec edge elements showcases the flexibility of the implementation. Eventually, the solution of a curl-curl problem with $1.6 \cdot 10^{11}$ (more than one hundred billion) unknowns on more than $32000$ processes with a matrix-free full multigrid solver demonstrates its extreme-scalability.

cs.CE↗

arXiv2022

Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning

Ising machines are a promising non-von-Neumann computational concept for neural network training and combinatorial optimization. However, while various neural networks can be implemented with Ising machines, their inability to perform fast statistical sampling makes them inefficient for training neural networks compared to digital computers. Here, we introduce a universal concept to achieve ultrafast statistical sampling with analog Ising machines by injecting noise. With an opto-electronic Ising machine, we experimentally demonstrate that this can be used for accurate sampling of Boltzmann distributions and for unsupervised training of neural networks, with equal accuracy as software-based training. Through simulations, we find that Ising machines can perform statistical sampling orders-of-magnitudes faster than software-based methods. This enables the use of Ising machines beyond combinatorial optimization and makes them into efficient tools for machine learning and other applications.

physics.app-ph↗

arXiv2021

Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity

Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find optimal solutions. Here, we investigate how the system's nonlinear transfer function can mitigate amplitude inhomogeneity and improve computational performance. By simulating Ising machines with polynomial, periodic, sigmoid and clipped transfer functions and benchmarking them with MaxCut optimization problems, we find the choice of transfer function to have a significant influence on the calculation time and solution quality. For periodic, sigmoid and clipped transfer functions, we report order-of-magnitude improvements in the time-to-solution compared to conventional polynomial models, which we link to the suppression of amplitude inhomogeneity induced by saturation of the transfer function. This provides insights into the suitability of systems for building Ising machines and presents an efficient way for overcoming performance limitations.

physics.app-ph↗

arXiv2021

HyperSec: Visual Analytics for blockchain security monitoring

Today, permissioned blockchains are being adopted by large organizations for business critical operations. Consequently, they are subject to attacks by malicious actors. Researchers have discovered and enumerated a number of attacks that could threaten availability, integrity and confidentiality of blockchain data. However, currently it remains difficult to detect these attacks. We argue that security experts need appropriate visualizations to assist them in detecting attacks on blockchain networks. To achieve this, we develop HyperSec, a visual analytics monitoring tool that provides relevant information at a glance to detect ongoing attacks on Hyperledger Fabric. For evaluation, we connect the HyperSec prototype to a Hyperledger Fabric test network. The results show that common attacks on Fabric can be detected by a security expert using HyperSec's visualizations.

cs.CR↗

arXiv2016

Small Chimera States without Multistability in a Globally Delay-Coupled Network of Four Lasers

We present results obtained for a network of four delay-coupled lasers modelled by Lang-Kobayashi-type equations. We find small chimera states consisting of a pair of synchronized lasers and two unsynchronized lasers. One class of these small chimera states can be understood as intermediate steps on the route from synchronization to desynchronization and we present the entire chain of bifurcations giving birth to them. This class of small chimeras can exhibit limit-cycle or quasiperiodic dynamics. A second type of small chimera states exists apparently disconnected from any region of synchronization, arising from pair synchronization inside the chaotic desynchronized regime. In contrast to previously reported chimera states in globally coupled networks, we find that the small chimera state is the only stable solution of the system for certain parameter regions, i.e. we do not need to specially prepare initial conditions.

nlin.AO↗

arXiv2014

Amplitude-phase coupling drives chimera states in globally coupled laser networks

For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the amplitude, phase, and inversion of the coupled lasers. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand nonlocal coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions. The existence is linked to a regime of multistability between the synchronous steady state and asynchronous periodic solutions. We show that amplitude-phase coupling, a concept common in different fields, is necessary for the formation of the chimera states.

nlin.CD↗