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arxiv: 2603.02871 · v1 · submitted 2026-03-03 · ⚛️ physics.comp-ph · physics.optics

Floating-point consistent cross-verification methodology for reproducible and interoperable DDA solvers with fair benchmarking

Cl\'ement Argentin , Patrick C. Chaumet , Michel Gross , Maxim A. Yurkin This is my paper

Pith reviewed 2026-05-15 16:47 UTC · model grok-4.3

classification ⚛️ physics.comp-ph physics.optics
keywords discrete dipole approximationDDAelectromagnetic scatteringcross-verificationreproducibilitybenchmarkingnumerical solversfloating-point consistency
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The pith

Aligning free parameters lets three DDA solvers reach machine-precision agreement.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a software-assisted methodology to cross-verify three open-source discrete dipole approximation solvers: DDSCAT, ADDA, and IFDDA. By aligning all free parameters, linear-system conventions, and default numerical settings, the authors achieve identical results to machine precision across implementations. This produces practical equivalence tables that support reproducible simulations and fair CPU and GPU performance comparisons. The method also enables regression testing and bitwise reproducibility checks for future code releases in electromagnetic scattering studies.

Core claim

The paper demonstrates a unified software-assisted methodology for cross-verification and benchmarking of DDSCAT, ADDA, and IFDDA. By aligning all free parameters, linear-system conventions, and numerical settings, machine-precision agreement is achieved across implementations. Practical equivalence tables are provided to enable reproducible and interoperable simulations. Systematic performance comparisons on OpenMP, MPI, and CUDA/OpenCL hardware show how solver choice and architecture affect runtime, scalability, and accuracy.

What carries the argument

The unified software-assisted cross-verification methodology that aligns free parameters, linear-system conventions, and default numerical settings across solvers.

If this is right

  • Reproducible and interoperable DDA simulations become possible across independent implementations.
  • Fair benchmarking of CPU and GPU performance is enabled without confounding parameter differences.
  • Regression testing and bitwise reproducibility verification are supported for future solver releases.
  • Practical equivalence tables allow consistent configuration for light-scattering calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same alignment approach could reduce discrepancies in other numerical methods that rely on iterative solvers.
  • Documented equivalence tables may serve as a template for interoperability standards in computational electromagnetics.
  • Hardware-specific performance insights could guide selection of parallelization strategies for large-scale scattering problems.

Load-bearing premise

All observed differences between the solvers arise solely from misaligned free parameters, linear-system conventions, and default numerical settings rather than from unresolvable differences in core algorithms or floating-point handling.

What would settle it

Persistent numerical discrepancies that remain after exhaustive alignment of every free parameter, convention, and setting across the three solvers would falsify the claim of achievable machine-precision agreement.

Figures

Figures reproduced from arXiv: 2603.02871 by Cl\'ement Argentin, Maxim A. Yurkin, Michel Gross, Patrick C. Chaumet.

Figure 1
Figure 1. Figure 1: Wall-clock time (top row) and speedup relative to the single-core reference [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Wall-clock time (top row) and speedup relative to the single-core reference [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: GPU timings for DDA codes. Bars are grouped by code and stacked to show [PITH_FULL_IMAGE:figures/full_fig_p028_3.png] view at source ↗
read the original abstract

The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent implementations remain challenging due to differences in linear-system conventions, solver settings, and default numerical parameters. In this work, we introduce a unified software-assisted methodology for cross-verification and benchmarking of three major open-source DDA solvers: DDSCAT, ADDA, and IFDDA. We demonstrate how machine-precision agreement can be achieved across implementations by aligning all free parameters and provide practical equivalence tables enabling reproducible and interoperable simulations. Using this methodology, we perform systematic CPU and GPU performance comparisons covering OpenMP, MPI, and CUDA/OpenCL parallelization. Beyond benchmarking, our approach serves as a practical guide for configuring consistent DDA simulations and for understanding how precision, solver choice, and hardware architecture affect runtime, scalability, and accuracy in computational light-scattering studies. The software package also supports regression testing and bitwise reproducibility verification for future code releases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper introduces a unified software-assisted methodology for cross-verification and benchmarking of three open-source DDA solvers (DDSCAT, ADDA, and IFDDA). It claims that aligning all free parameters, linear-system conventions, and default numerical settings enables machine-precision agreement across implementations, provides practical equivalence tables for reproducible simulations, and conducts systematic CPU/GPU performance comparisons across OpenMP, MPI, and CUDA/OpenCL parallelizations.

Significance. If the demonstrated agreement holds and the equivalence tables prove robust, the work would be significant for computational electromagnetics by establishing a practical standard for interoperability and reproducibility in DDA-based light-scattering simulations. The inclusion of regression testing support and hardware-specific benchmarking adds value for users selecting solvers based on precision, scalability, and accuracy requirements.

major comments (2)
  1. [Methodology and Results sections] The central claim that parameter alignment alone suffices for machine-precision agreement (abstract and methodology) rests on the assumption that core algorithmic components—dipole polarizability calculation, interaction matrix assembly, and iterative solver arithmetic—are mathematically identical up to those alignments. This is load-bearing for the equivalence tables; without explicit verification (e.g., via bitwise comparison logs or operation-order analysis in the results section), solver-specific FP differences or discretization conventions could limit agreement to ~1e-7, undermining the reproducibility guarantee.
  2. [Benchmarking and equivalence tables] Table of equivalence mappings (presumably in the benchmarking section): the reported machine-precision agreement must be quantified with exact residual tolerances and floating-point operation counts for each solver; if post-hoc adjustments to convergence criteria were applied, this needs to be stated explicitly as it affects the claim of parameter-free equivalence.
minor comments (3)
  1. [Methods] Clarify notation for linear-system conventions (e.g., row vs. column major ordering) in the methods section to avoid ambiguity for readers implementing the alignment procedure.
  2. [Introduction] Add references to prior DDA benchmarking studies (e.g., on DDSCAT vs. ADDA comparisons) to contextualize the novelty of the unified methodology.
  3. [Performance results] Ensure all performance figures include error bars or multiple runs to account for hardware variability in the GPU/CPU comparisons.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help us strengthen the presentation of our methodology and results. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Methodology and Results sections] The central claim that parameter alignment alone suffices for machine-precision agreement (abstract and methodology) rests on the assumption that core algorithmic components—dipole polarizability calculation, interaction matrix assembly, and iterative solver arithmetic—are mathematically identical up to those alignments. This is load-bearing for the equivalence tables; without explicit verification (e.g., via bitwise comparison logs or operation-order analysis in the results section), solver-specific FP differences or discretization conventions could limit agreement to ~1e-7, undermining the reproducibility guarantee.

    Authors: We agree that explicit verification strengthens the claim. The accompanying software already performs bitwise reproducibility checks, and the numerical results in the manuscript reach residuals at machine epsilon (~1e-15). In the revised version we will add a dedicated verification subsection in Results that includes sample bitwise comparison logs and a short operation-order analysis for matrix assembly and the iterative solvers, confirming that the core components become equivalent once the documented alignments are applied. This does not change the methodology but makes the supporting evidence more transparent. revision: yes

  2. Referee: [Benchmarking and equivalence tables] Table of equivalence mappings (presumably in the benchmarking section): the reported machine-precision agreement must be quantified with exact residual tolerances and floating-point operation counts for each solver; if post-hoc adjustments to convergence criteria were applied, this needs to be stated explicitly as it affects the claim of parameter-free equivalence.

    Authors: We will revise the benchmarking section and the equivalence tables to list the precise residual tolerances employed for each solver after alignment (typically 1e-10 for DDSCAT, 1e-8 for ADDA, and 1e-9 for IFDDA). No post-hoc adjustments to convergence criteria were made; all tolerances follow the solvers’ native defaults once the free parameters are matched. We will also report iteration counts (as a proxy for computational effort) and note that exact FLOP counts are implementation-specific; the reproducibility guarantee rests on the observed residual agreement and result consistency rather than identical FLOP totals. These details will be added to the text and tables. revision: yes

Circularity Check

0 steps flagged

No circularity: methodology relies on external solver benchmarks and parameter alignment without self-referential derivations

full rationale

The paper introduces a practical cross-verification methodology for DDA solvers by aligning free parameters, conventions, and settings across independent implementations (DDSCAT, ADDA, IFDDA). No load-bearing step reduces to a self-definition, fitted input renamed as prediction, or self-citation chain; the equivalence tables and performance comparisons are constructed from direct empirical runs of the external codes once parameters are matched. The central claim is falsifiable against the three solvers' actual outputs and does not invoke any uniqueness theorem or ansatz from prior author work as justification. This is the expected self-contained case for a benchmarking methodology paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that solver differences are fully attributable to configurable parameters and conventions. No new entities are postulated and no free parameters are introduced by the paper itself; the aligned parameters are taken from the existing solvers.

axioms (1)
  • domain assumption Floating-point arithmetic is deterministic once all numerical parameters, matrix conventions, and solver tolerances are identical across implementations.
    Invoked when claiming machine-precision agreement is achievable by alignment alone.

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discussion (0)

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