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arxiv: 2512.08614 · v3 · submitted 2025-12-09 · ⚛️ physics.optics · physics.comp-ph

PyMieDiff: A differentiable Mie scattering library

Oscar K. C. Jackson , Simone De Liberato , Otto L. Muskens , Peter R. Wiecha This is my paper

Pith reviewed 2026-05-16 23:31 UTC · model grok-4.3

classification ⚛️ physics.optics physics.comp-ph
keywords Mie scatteringdifferentiable programmingPyTorchspherical particlesnanophotonicslight scatteringGPU accelerationautograd
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0 comments X

The pith

PyMieDiff implements Mie scattering calculations inside PyTorch so gradients flow through scattering simulations for layered spherical particles.

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

The paper presents PyMieDiff as a fully differentiable, GPU-compatible library that brings Mie scattering theory into the PyTorch ecosystem for layered spherical particles. All inputs such as geometry, material dispersion, wavelengths, and observation angles are handled as tensors, allowing automatic differentiation through the entire computation. The library supplies custom autograd-compatible spherical Bessel and Hankel functions plus vectorized routines that return scattering efficiencies, angular patterns, and near-fields. This construction lets users embed classical electromagnetic scattering directly into gradient-based optimization or physics-informed neural networks without leaving the machine-learning framework.

Core claim

PyMieDiff is a fully differentiable, GPU-compatible implementation of Mie scattering for layered, spherical particles in PyTorch that provides native autograd-compatible spherical Bessel and Hankel functions, vectorized evaluation of Mie coefficients, and APIs for computing efficiencies, angular scattering, and near-fields, with all inputs represented as tensors to enable seamless integration with gradient-based optimization or physics-informed neural networks.

What carries the argument

Autograd-compatible spherical Bessel and Hankel functions that support vectorized, differentiable evaluation of Mie scattering coefficients for multi-layered spheres.

Load-bearing premise

The provided implementations of the spherical Bessel and Hankel functions and Mie coefficient formulas are numerically accurate and produce gradients that match the analytic derivatives of Mie theory.

What would settle it

Direct numerical comparison of scattering efficiencies and near-fields computed by PyMieDiff against finite-difference approximations and against independent non-differentiable Mie codes for a range of particle radii, layer thicknesses, and refractive indices.

Figures

Figures reproduced from arXiv: 2512.08614 by Oscar K. C. Jackson, Otto L. Muskens, Peter R. Wiecha, Simone De Liberato.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Light scattering by spherical-shaped particles of sizes comparable to the wavelength is foundational in many areas of science, from chemistry to atmospheric science, photonics and nanotechnology. With the new capabilities offered by machine learning, there is a great interest in end-to-end differentiable frameworks for scattering calculations. Here we introduce PyMieDiff, a fully differentiable, GPU-compatible implementation of Mie scattering for layered, spherical particles in PyTorch. The library provides native, autograd-compatible spherical Bessel and Hankel functions, vectorized evaluation of Mie coefficients, and APIs for computing efficiencies, angular scattering, and near-fields. All inputs - geometry, material dispersion, wavelengths, and observation angles and positions - are represented as tensors, enabling seamless integration with gradient-based optimisation or physics-informed neural networks. The toolkit can also be combined with "TorchGDM" for end-to-end differentiable multi-particle scattering simulations. PyMieDiff is available under an open source licence at https://github.com/UoS-Integrated-Nanophotonics-group/MieDiff.

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 / 2 minor

Summary. The manuscript introduces PyMieDiff, a PyTorch library implementing fully differentiable Mie scattering for layered spherical particles. It provides native autograd-compatible spherical Bessel and Hankel functions, vectorized Mie coefficient evaluation, and tensor-based APIs for scattering efficiencies, angular distributions, and near-fields, with seamless integration to gradient-based optimization and the TorchGDM multi-particle framework.

Significance. If the numerical correctness and gradient accuracy are established, the library would enable end-to-end differentiable scattering simulations in nanophotonics, supporting inverse design, physics-informed neural networks, and hybrid ML-physics workflows. The open-source release and GPU compatibility are positive features for reproducibility in the field.

major comments (2)
  1. [Implementation description (abstract and methods)] The central claim that the custom spherical Bessel/Hankel implementations and recursive Mie coefficient formulas produce both forward values and gradients matching analytic Mie theory lacks any supporting numerical evidence. No finite-difference comparisons, reference-code cross-checks, or stability tests for complex arguments and large orders are described, which directly undermines the advertised differentiability for optimization tasks.
  2. [Spherical Bessel/Hankel and Mie coefficient sections] The handling of branch cuts, recurrence relations, and numerical stability for the autograd-compatible special functions is not specified. Any discrepancy here would propagate to all downstream quantities (efficiencies, angular scattering, near-fields) and break end-to-end differentiability, yet no validation protocol is provided.
minor comments (2)
  1. [Abstract] The GitHub link should include explicit installation instructions, example notebooks demonstrating gradient computation, and a clear statement of the supported particle layering and size-parameter range.
  2. [API description] Notation for the layered-sphere coefficients (e.g., how the recursive formulas are vectorized over tensors) should be clarified with a short pseudocode or equation block to aid readers implementing similar functionality.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and for recognizing the potential of PyMieDiff for end-to-end differentiable nanophotonics workflows. We agree that the current manuscript lacks explicit numerical validation of both forward values and gradients, as well as details on numerical stability. We will revise the manuscript to address these points directly.

read point-by-point responses

  1. Referee: The central claim that the custom spherical Bessel/Hankel implementations and recursive Mie coefficient formulas produce both forward values and gradients matching analytic Mie theory lacks any supporting numerical evidence. No finite-difference comparisons, reference-code cross-checks, or stability tests for complex arguments and large orders are described, which directly undermines the advertised differentiability for optimization tasks.

    Authors: We agree that the manuscript does not currently include numerical evidence supporting the accuracy of forward computations and gradients. In the revised version we will add a dedicated validation section containing: (i) direct comparisons of scattering efficiencies and angular patterns against analytic Mie theory and established non-differentiable codes (e.g., PyMieScatt) for both real and complex refractive indices; (ii) finite-difference gradient checks across a range of particle sizes, layer thicknesses, and wavelengths; and (iii) stability tests for high orders and complex arguments. These additions will substantiate the differentiability claims. revision: yes

  2. Referee: The handling of branch cuts, recurrence relations, and numerical stability for the autograd-compatible special functions is not specified. Any discrepancy here would propagate to all downstream quantities (efficiencies, angular scattering, near-fields) and break end-to-end differentiability, yet no validation protocol is provided.

    Authors: We acknowledge that the manuscript does not describe the numerical treatment of branch cuts, the specific recurrence relations implemented for spherical Bessel and Hankel functions, or the validation protocol used to ensure stability. In the revision we will expand the methods section to document these choices explicitly, including how branch cuts are handled for complex arguments and the safeguards applied during recurrence. We will also include a validation protocol subsection that reports agreement metrics with reference implementations over the relevant parameter space. revision: yes

Circularity Check

0 steps flagged

No circularity: software library announcement with no derivation chain

full rationale

The paper introduces PyMieDiff as a PyTorch implementation of standard Mie scattering for layered spheres, providing autograd-compatible spherical Bessel/Hankel functions and related APIs. No new physical derivations, parameter fits, or predictions are claimed; the central assertion is simply the existence and feature set of the released code. No self-citations, ansatzes, or uniqueness theorems are invoked to justify any result. The implementation details rest on established Mie theory without reducing any output to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No new physical axioms, free parameters, or invented entities are introduced; the work is a computational re-implementation of standard Mie theory in differentiable form.

pith-pipeline@v0.9.0 · 5487 in / 1099 out tokens · 41368 ms · 2026-05-16T23:31:33.083021+00:00 · methodology

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Reference graph

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