Kratos Framework: Multi-Domain Computational Platforms

• Kratos Framework is a collection of specialized computational platforms that support heterogeneous astrophysical simulations, FPGA DNN benchmarking, LPWAN development, and IoT access control.
• It employs layered architectures, rigorous numerical methods, mixed-precision techniques, and cross-platform optimizations to ensure high performance and accuracy.
• Applications include simulating stellar phenomena, benchmarking unrolled DNNs in FPGAs, evaluating LPWAN protocols, and enforcing smart home security policies.

Kratos Framework refers to several distinct computational and systems frameworks, each independently developed for different scientific and engineering domains. Salient examples include: (1) the Kratos Framework for heterogeneous astrophysical simulations encompassing high-performance multiphysics solvers; (2) Kratos, an FPGA benchmarking suite for unrolled DNN primitives with fine-grained sparsity and mixed precision; (3) KRATOS, an open-source platform for rapid research in low-power wide-area networks (LPWANs); and (4) KRATOS, a multi-user, multi-device-aware access control system for smart homes. This article provides a comprehensive and rigorous account of these frameworks, focusing on their architectures, computational methodologies, verification, and benchmarked capabilities.

1. Heterogeneous Astrophysical Simulation: Kratos Framework

The Kratos Framework for heterogeneous astrophysical simulations is a performance-portable, GPU-native C++ infrastructure designed for multiphysics modeling in astrophysics, such as magnetohydrodynamics, thermochemistry, and radiative transfer. The design targets both consumer-level and HPC-class GPUs, with portable backends for CUDA, HIP, and CPU environments (Wang, 4 Jan 2025, Wang, 7 Apr 2025, Wang et al., 1 Feb 2026).

1.1 Layered Architecture

Kratos adopts three horizontally layered infrastructures:

• Device Abstraction Layer (DAL): Encapsulates GPU/CPU memory management, kernel launches, and device selection. All GPU code targets the intersection of CUDA/HIP, ensuring cross-vendor compatibility.
• Runtime Layer: Implements block-based task lists, MPIv3-aware process management, and nonblocking communication with stream/MPI overlap. Mesh management operates through hierarchical $2^d$-trees for AMR, with load balancing via lexicographic or Hilbert space-filling curves.
• Physics Modules Layer: Modular design supports hydrodynamics, MHD, gravity, thermochemistry, and radiative transfer. Each module maintains independent task lists and exposes an advance(Δt) interface. Coupling is via structure-of-arrays field data and shallow “data proxies” with pointer passing to minimize deep device-host transfers.

1.2 Hydrodynamics and Thermochemistry

• Hydrodynamics: Second-order Godunov finite-volume methods with PLM (minmod TVD slope limiter), HLLC Riemann solver, and Heun (RK2) or van Leer integrators. Conservative variables are double precision; most arithmetic is performed in single precision to maximize device throughput while maintaining conservation to machine accuracy.
• Thermochemistry: Operator-split, cell-local integration using a parallelized Crout LU decomposition with partial pivoting for the stiff ODE system (network sizes $N_\text{species}\sim30{-}50$; Jacobian matrices up to $2500$ entries). Rates and species vector accumulations use mixed/fp64 types for accuracy.

1.3 Ray-Tracing Radiation

• Long-characteristics, multi-band, cell-by-cell ray-tracing. Each thread block handles a ray; intersections with curvilinear mesh faces are solved for each cell via root-solving.
• Deposited photo-heating and photo-ionization rates are calculated by attenuating incident fluxes through optical depths.

1.4 Performance and Portability

• Throughput on RTX 4090: up to $21.6\times10^6$ cells/s in single-precision, $17.1\times10^6$ cells/s mixed, $2.4\times10^6$ cells/s double.
• Scaling: strong scaling efficiency reaches $84\%$ across $8\times$RTX4090s (Wang, 7 Apr 2025).
• Mixed-precision arithmetic yields $5\text{--}7\times$ speedup on consumer GPUs relative to double precision (Wang, 4 Jan 2025).

2. Numerical Algorithms and Conservation Properties

The Kratos astrophysics framework incorporates algorithmic innovations for robust coupling of physics modules while maintaining critical conservation laws.

2.1 Stoichiometry-Compatible Reconstruction

Advection of chemical species is performed with an element-conserving, higher-order reconstruction. Projecting PLM slopes onto the stoichiometric null space via SVD ensures that the element flux $\sum_s \mathcal N_{\nu, s} \mathcal F^s_{i-1/2}$ exactly matches the advected elemental abundance, enforcing conservation at every flux interface. This avoids per-interface matrix inversion and maintains formal second-order accuracy (Wang, 7 Apr 2025).

2.2 Mixed-Precision ODE Integration

The stiff thermochemical ODE system is integrated using a warp-synchronous, parallel Crout LU decomposition. Each thread processes a matrix row, with synchronization after each step to limit warp divergence. This design is optimized for both GPUs and CPUs (OpenMP/HIP-CPU), with mixed-precision variants balancing accuracy and throughput (Wang, 7 Apr 2025).

2.3 Verification and Benchmarks

Kratos matches semi-analytic and industry-standard code results:

Test Problem	Error Metrics/Comparison	Reference
0D combustion (Cantera)	Species to $10^{-3}$, temperature to $10^{-4}$	(Wang, 7 Apr 2025)
Strömgren spheres	Density, $x_e$, $T$ within $\lesssim5\%$	(Wang, 7 Apr 2025)
Detonation (SDT toolbox)	Species and detonation velocity within $0.3\%$	(Wang, 7 Apr 2025)
1D/2D hydro shock tubes	Agreement to plotting resolution	(Wang, 4 Jan 2025)

3. Applications and Use Cases

Kratos is demonstrated for a range of sophisticated multiphysics scenarios:

• Ultra-hot Jupiter WASP-121b: Simulations involving compressible hydro, non-LTE thermochemistry with 32 species, and 8-band radiative transfer reveal spiral arm outflow morphologies, processes of stellar wind confinement, and spectral signatures in Na, Fe, He bands. Simulations on two RTX 4090s achieved $50$–$100\times$ CPU speedups for 300 h evolutions (Wang et al., 1 Feb 2026).
• ISM turbulence and photoevaporation: Non-ideal MHD, microphysics, and direct photoionization/matter coupling enabled by module composition (Wang, 4 Jan 2025, Wang, 7 Apr 2025).
• Stellar jet and supernova detonation modeling: Coupled hydro and chemistry provide quantitative predictions for nucleosynthetic yield and shock structure.

4. FPGA Unrolled DNNs: Kratos Benchmark Suite

Kratos also denotes a focused FPGA benchmark for unrolled DNN primitives employing fine-grained sparsity and mixed precision (Dai et al., 2024).

4.1 Architectural Features

• Unrolled Design: Each MAC is physically instantiated in logic, allowing pruning of zero-weight/bits at synthesis for proportional area and power reduction.
• Supported Kernels: GEMM (tree or systolic), 1D/2D convolution, each in pixel-wise, row-parallel, or fully unrolled styles.
• Sparsity and Precision: Supports unstructured sparsity values up to $90\%$ and precisions $1$–$8$ bits.
• Implementation: SystemVerilog generator, Quartus/VTR tool flows, ALM utilization measured across Arria 10 and area-delay trade-offs in VTR-modeled fabrics.

4.2 Benchmarking Results

• Area Scaling: Multiply–add trees prune logic almost linearly with sparsity ($s$): observed ALM usage $\approx (1-s) \cdot \text{ALMs}(s=0)$; e.g., $90\%$ sparsity yields $>90\%$ area reduction (Fig. 3).
• Precision Scaling: Reducing from 8→4 bits shrinks area by $2.9\times$; 8→2 bits by $~6\times$; 8→1 bit by $~10\times$ (Fig. 4).
• Frequency: Fully unrolled circuits reach $600$–$800$ MHz; unconstrained designs up to $1$ GHz.
• Power: Dynamic power correlates with area and switching activity; $90\%$ sparsity and $4$-bit width yields $10\times$ lower dynamic power than dense 8-bit baselines.
• LUT Sizing Case Study: Reducing LUT size from $K=6$ (conventional) to $K=3$ (specialized) in FPGA fabric halves area with modest ($10$–$20\%$) delay penalty, suggesting architectural path for sparse, low-bit DNNs (Dai et al., 2024).

5. Other Instantiations: LPWAN and Access Control

Additional frameworks under the Kratos name exist in distinct domains.

5.1 Open-Source LPWAN Platform

• KRATOS LPWAN: Open-source platform for LoRa/LPWAN experimentation, integrates COTS MSP430 microcontroller and SX1276 transceiver, runs ContikiOS, achieves $>95\%$ packet delivery at $600$ m; power consumption metrics: sleep $1.8$ μW, LoRa TX (+14 dBm) $240$ mW (Piyare et al., 2018).
• Features: Energy harvesting (BQ25570 PMU), WuRX standby at $1.8$ μW, versatile API compatible with ContikiOS, multi-hop mesh support, event-driven low-power operation.

5.2 Multi-User Smart Home Access Control

• KRATOS Access Control: Multi-user, multi-device, priority- and context-aware ABAC policy engine for smart homes. Formal quintuple policy model $(P,U,D,\mathcal{C},A)$; centralized conflict negotiation supports hard/soft/priority/competition conflicts, enforces policies with $<2$ s latency per action, $100\%$ detection of test privileges violations (Sikder et al., 2019).

6. Limitations and Development Directions

6.1 Astrophysical Kratos

• Lacks AMR in leading implementations, limiting small-scale turbulence fidelity.
• MHD, cosmic-ray, self-gravity, and polarized radiative transfer still under development (Wang, 7 Apr 2025, Wang et al., 1 Feb 2026).
• Usability improvements (Python bindings, plugin ecosystem, checkpointing) and extension to large-domain exoplanet tail modeling planned.

6.2 FPGA Kratos

• Fully unrolled DNNs remain device-area limited for large topologies; solutions such as weight-sharing/folding are open (Dai et al., 2024).
• Community-oriented benchmarking suite is open-source to foster new CAD flows and fabric designs.

6.3 Other Frameworks

• LPWAN Kratos: Expansion to wider range, additional energy-harvesting types, and MAC protocol extensibility in progress (Piyare et al., 2018).
• Access Control Kratos: Usability studies, platform expansions, and malicious app sandboxing planned (Sikder et al., 2019).

7. Summary

Kratos Framework encompasses high-performance, extensible simulation infrastructure for heterogeneous astrophysical computing, systematic unrolled DNN benchmarking on FPGAs, LPWAN development hardware/software, and robust IoT access control middleware. Across these domains, Kratos frameworks are characterized by modular architectures, rigorous numerical algorithm design, and systematic benchmarking to validate performance and accuracy. In astrophysical computing, Kratos demonstrates at-scale coupled multiphysics with GPU-accelerated throughput, element- and energy-conserving schemes, and extensibility to microphysics and advanced radiative models. In hardware-centric contexts, Kratos defines practical limits and architectural pathways for sparse, low-bit DNNs on FPGAs and delivers reproducible, open-source evaluation ecosystems for networked or access-controlled devices. Continued development across all Kratos instantiations signals an ongoing shift toward domain-specific, performance-portable, and community-extensible computational platforms.