Kyung Min Kim | Searcharxiv

arXiv2026

Verification and Performance Assessment of NuDEAL, a GPU-Accelerated Deterministic Transport Framework on Unstructured Meshes

High-fidelity neutronic analyses of advanced reactors require deterministic transport solvers capable of handling complex unstructured geometries while maintaining computational efficiency. This work presents the development and verification of three GPU-accelerated deterministic solvers implemented within a unified framework, Neutronics using Deterministic Finite Element Algorithm (NuDEAL): the planar Method of Characteristics coupled with the Hybrid Finite Element Method (MOC/HFEM), the Discontinuous Galerkin Method of Characteristics (DGMOC), and the Discontinuous Finite Element discrete ordinate method (DFEM-SN). These solvers provide complementary capabilities for consistently solving the multigroup transport equation and can be selectively employed to balance accuracy, computational cost, and memory requirements for a given problem. All methods emphasize efficient GPU execution by leveraging memory alignment, compressed-flux storage, and sequential azimuthal sweeps. The solvers are validated on the C5G7 benchmark and applied to advanced reactor problems, including the ABTR, Empire microreactor, and MSRE. DFEM-SN achieved the highest accuracy, with eigenvalue errors below 50 pcm, while MOC/HFEM and DGMOC provided superior efficiency, with single-GPU runtimes comparable to those of large CPU clusters. The results demonstrate that deterministic GPU solvers on unstructured meshes can deliver both accuracy and scalability, enabling practical whole-core simulations for heterogeneous advanced reactors. The unified NuDEAL framework establishes a foundation for future extensions toward transient and multiphysics analyses on large-scale GPU architectures.

physics.comp-ph↗

arXiv2026

A Hardware-aware Hopfield Network with a Nonlinear Memristor Array for Robust Associative Memory with Superlinear Capacity

Associative memory retrieves complete patterns from partial or corrupted inputs and constitutes a primitive form of generative inference. Classical Hopfield networks (CHN) provide a canonical framework for associative memory but suffer from limited memory capacity. Recently, modern Hopfield networks (MHN) were introduced to achieve higher capacity by using explicit pattern-wise storage and neurons with the softmax activation function, which makes the MHN vulnerable to noise and the hardware implementation complicated due to its network size varying with the number of stored patterns. Here, we introduce a hardware-aware Hopfield network (HHN), in which the intrinsic nonlinear current-voltage characteristics of a charge-trap memristor are leveraged to engineer the energy landscape of the HN, increasing the memory capacity. Using a 25 x 25 nonlinear memristor array, we demonstrate reliable reconstruction of corrupted patterns with memory capacity far exceeding the classical limit (K ~ 0.14N, where N is the number of neurons). The HHN preserves Hopfield-type energy-minimization dynamics and remains robust to synaptic conductance noise. Large-scale simulations on high-dimensional image data reveal an empirical memory capacity scaling of K ~ 0.3 x N^1.2 under a fixed synaptic budget. These results establish HHN as a scalable hardware-native architecture for low-power associative memory and generative inference.

cond-mat.dis-nn↗