The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, the location/values of the applied Dirichlet/Neumann boundary conditions, body forces and material properties, among others. We have previously introduced hybridization of classical linear iterative solvers with neural operators for specific geometries, but they tend to not perform well on geometries not previously seen during training (Zhang et al., 2024). We partially addressed this challenge by introducing the deep operator network Geo-DeepONet and hybridizing it with Krylov-based iterative linear solvers (Lee et al., 2025a), which, despite learning effectively across arbitrary unstructured meshes without requiring retraining, led to only modest reductions in iterations compared to state-of-the-art preconditioners. In this study we introduce Neural Subspace Proper Orthogonal Decomposition (NSPOD), a multigrid-like deep operator network-based preconditioner, which can reduce the number of iterations needed for convergence in Krylov-based linear iterative solvers on complex curved domains, performing comparably to state-of-the-art algebraic multigrid preconditioners, and substantially improving on other widely used standard preconditioners, such as Jacobi or SOR, in both number of iterations and computational time. We expect that the findings in this study lead to more efficient hybrid preconditioners that complement the convergence properties of current gold-standard preconditioning methods for solid mechanics PDEs in three dimensions. We demonstrate its efficiency via numerical experiments on a linearized version of solid mechanics PDEs applied to unstructured domains obtained from complex CAD geometries. We expect that the findings in this study lead to more efficient hybrid preconditioners that can match, or possibly even surpass, the convergence properties of the current gold-standard preconditioning methods when applied to solid mechanics PDEs.
This study investigates domain decomposition strategies for high-performance smoothed particle Galerkin (SPG) modeling of single-grit diamond scribing of silicon carbide fiber-reinforced silicon carbide (SiCf/SiC) composites. Domain decomposition enables massively parallel processing (MPP) by partitioning the SPG model into subdomains, each assigned to a processor for parallel execution. The SPG model without domain decomposition is first validated against experimentally measured scribing forces and is used as the baseline. The computational time and force prediction error associated with three domain decomposition strategies are evaluated to identify the trade-off between scaling efficiency and numerical stability. Three principles for optimal domain decomposition are identified. First, subdomains should contain similar numbers of particles to ensure balanced workload across processors and maximize computational efficiency. Second, the number of subdomains should be selected to balance computational speedup and numerical stability. Too few subdomains underutilize available computational resources, while too many increase inter-subdomain communication and may amplify numerical discrepancies and force fluctuations. Third, subdomain boundaries should avoid high-deformation and high-contact regions. Aligning subdomains parallel to the cutting direction confines active deformation within fewer subdomains, reduces data exchange, and improves both accuracy and computational efficiency. Based on these findings, we envision that GPU-accelerated high-performance computing (HPC) architectures with thousands of processing cores can enable large-scale multi-grit grinding simulations using SPG modeling.
Dynamic power consumption has become a dominant concern in modern digital designs, with reports indicating that glitches can contribute up to 40% of total dynamic power consumption. Traditional approaches to evaluating glitch power, such as static analysis and dynamic simulation, face tradeoffs between accuracy and efficiency. This article presents a Graph Neural Network (GNN)-based model that leverages machine learning to estimate glitch rates. The model learns the structural and timing features of the circuit and utilizes a small set of input patterns to predict glitch rates after gate sizing-based Engineering Change Order (ECO). By integrating the predicted glitch rates with a commercial power analysis tool, the proposed method enables rapid identification of glitch hotspots, accelerating power optimization during the signoff stage. Experimental results highlight the effectiveness of the proposed model, achieving an average Root Mean Square Error (RMSE) of 0.0867 and a correlation coefficient of 0.9100 in glitch rate prediction. Moreover, the approach identifies glitch hotspots with high accuracy, correctly labeling 83.4% of the top 5% highest glitch power gates and 89.78% of the top 10%. Compared to relying solely on commercial tools for glitch power estimation within the optimization flow, the proposed method reduces runtime by an average of 35.78% when the iteration count matches the circuit's logic level.
The Quantum Lattice Boltzmann Method (QLBM) has emerged as one of the most promising quantum computing approaches for the numerical simulation of problems in computational fluid dynamics (CFD). The dynamics is formulated in terms of mesoscopic particle distribution functions governed by a discrete Boltzmann transport equation, comprising local streaming and collision operations. In this work, the resulting macroscopic behavior corresponds to the advection-diffusion equation, which we adopt as a canonical model problem for transport phenomena. Building upon recent progress in QLBM implementations, we advance towards more realistic problem settings that better reflect conventional CFD requirements. We address, for the first time, transport under the action of non uniform velocity fields on quantum hardware. We implement our demonstration using IonQ's trapped-ion systems including Forte generation systems and a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We identify the density readout and subsequent reloading of the fluid density as a potential bottleneck of the current algorithm and discuss several approaches to mitigate this bottleneck. We identify the use of MPS shadow tomography as a promising method to efficiently scale the readout to large system with complex density distributions. Lastly, we introduce and simulate a novel method to implement wall boundaries for advection-diffusion in QLBM, and discuss the prospects of scaling to higher-complexity problems.
Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating solvers. In this paper, we measure the end-to-end performance of a hybrid quantum-classical framework designed to accelerate Finite Element Analysis (FEA) by integrating a quantum solver for GPP into Synopsys/Ansys' LS-DYNA multiphysics simulation software. The quantum solver we use is based on Iterative-QAOA, a scalable, non-variational quantum approach for optimization. We focus on two specific classes of FEA problems, namely vibrational (eigenmode) analysis and transient simulation. We report numerical simulations on up to 150 qubits done on NVIDIA's CUDA-Q/cuTensorNet and implementation on IonQ's Forte quantum hardware. The potential impact on LS-DYNA workflows is quantified by measuring the wall-clock time-to-solution for complex problem instances, including vibrational analysis of large finite element models of a sedan car and a Rolls-Royce jet engine, as well as transient simulations of a drill and an impeller. We performed end-to-end performance measurements on meshes comprising up to 35 million elements. Measurements were conducted using LS-DYNA in distributed-memory mode via Message Passing Interface (MPI) on AWS and Synopsys compute clusters. Our findings indicate that with a quantum computer in the loop, amortized LS-DYNA wall-clock time can be improved by up to 15
