Overall assessment

This study introduces a hybrid Bayesian neural network (BNN) model trained on discrete dipole approximation (DDA) simulations for black carbon (BC)-containing particles. The description of the proposed model is generally clear. A total of eight input features are considered: five particle-related inputs (number of BC particles, coating amount, fractal dimension, volume-equivalent size parameter, and imaginary refractive index of the coating) and three additional inputs derived from homogeneous-sphere Mie calculations (extinction coefficient, single-scattering albedo, and asymmetry parameter). The three model outputs consist of optical properties (extinction coefficient, single-scattering albedo, and asymmetry parameter) from DDA simulations. In addition, the treatment and decomposition of aleatoric and epistemic uncertainty are generally well explained.

Overall, the manuscript is well written, well organized, and easy to follow, except for some details in the machine-learning-related sections where I am not an expert. The scope is well addressed, and the general methodology and evaluation approaches appear reasonable. However, several aspects would benefit from additional clarification. Therefore, I recommend publication after the authors address the comments listed below.

Specific comments

Different assumptions between Ensemble I and II (Table 1 and related discussion): Why do differences exist with respect to wavelength, coating refractive index, AAE of the coating, and other parameters?

Figure 1: What is the distinction between the blue and brown particles? I assume the partially transparent regions indicate coatings, but it was not entirely clear whether the figure simply represents uncoated versus coated particles.

How is the core fractal dimension (Df,c) calculated? It would be helpful to provide at least a brief definition or formulation in the Appendix. In addition, the definition or relationship of (Df,c) with other parameters appears to differ between Ensembles I and II, which was somewhat difficult to follow.

L79: Is it reasonable to assume a single fixed value for the BC refractive index? Does the BC refractive index have a known uncertainty range or variability that should be considered?

L130: Naming of input properties. For clarity, it may be helpful to explicitly distinguish the two groups of input features. For example, the first five inputs could be described as “microphysical/morphological descriptors,” while Qext, SSA, and g could be referred to as “optical-property descriptors” or “physics-based optical descriptors.” The authors do not necessarily need to follow these specific suggestions, but clearer categorization of the input features would improve readability. In particular, I found it somewhat difficult to follow the transition from optical-property-based inputs to the more general term “particle properties.”

Sections 5 & 6: These results appear to demonstrate the superiority of the proposed hybrid BNN over the homogeneous-sphere and core-shell assumptions. However, this outcome seems somewhat expected because the DDA simulations are treated as the reference truth, and the hybrid BNN is directly trained on those DDA-generated optical properties. Therefore, Figures 3–5 may reflect the superiority of morphology-resolving DDA physics itself rather than the unique advantage of the hybrid BNN architecture. I wonder if the authors could clarify more explicitly what aspects of the improvement should be attributed to the Bayesian/surrogate framework versus the underlying DDA-based physical representation.

Figure 5: The SHAP analysis suggests that the homogeneous-sphere optical-property inputs contribute substantially to the hybrid BNN predictions. Since the framework conceptually combines homogeneous-sphere optical information with morphology-aware particle descriptors, it would be very helpful to more directly quantify the relative influence of these two groups of inputs on the final predictions. For example, an analysis comparing the hybrid BNN predictions with the corresponding homogeneous-sphere optical properties could help clarify the extent to which morphology-dependent particle information contributes beyond the baseline optical physics.

Figure 6: In panels B, E, and H, the hybrid BNN appears to exhibit relatively larger errors within portions of the parameter range represented in the training dataset. I may be misunderstanding the interpretation of this figure, but I initially expected the prediction errors to be minimized near the training-domain conditions. Additional clarification on how these perturbed-parameter experiments relate to the original training manifold versus the shaded “training range” would help improve interpretation of the figure.

Uncertainty decomposition and Monte Carlo sampling: The uncertainty decomposition is an important component of the proposed hybrid BNN framework, but the manuscript provides relatively limited examples and interpretation of its behavior across different particle conditions. Are there general patterns or tendencies in the aleatoric versus epistemic uncertainty components with respect to particle size, morphology, coating amount, or wavelength? In addition, how sensitive are the uncertainty estimates to the Monte Carlo sampling sizes used during inference? Some discussion regarding convergence behavior and the choice of sampling size would help clarify the robustness of the uncertainty characterization.

Section 8: Since epistemic uncertainty is interpreted as uncertainty associated with limited training coverage, it would be interesting to examine how the epistemic and aleatoric uncertainty components change when the size of the training dataset is artificially reduced (e.g., using half of the current training samples). Such an experiment may help demonstrate whether the epistemic uncertainty behaves consistently with the proposed interpretation, and it may be possible without requiring additional DDA simulations.

From the perspective of future radiative transfer and remote sensing applications, it would be interesting to know whether the framework could eventually be extended to predict more detailed angular scattering information beyond the asymmetry parameter, such as single-particle phase functions or phase-matrix-related quantities. Although the current study focuses on single-particle optical properties, such extensions could further increase the applicability of the framework to aerosol optics studies.

The paper describes a new hybrid Bayesian neural network model trained on discrete dipole approximation (DDA) simulations to better simulate the optical properties of particles containing black carbon. The authors compare the performance of the model with homogeneous and coated-sphere Mie theory and find that the Bayesian NN model performs better when simulating several optical parameters. One of the particularly interesting aspects of the study is the ability of the model to also determine uncertainties and therefore understand which input parameter space in DDA should be explored further.

The paper is well written and mostly clear, and the study is detailed and impactful.  After the authors address the reviewers’ comments, I think the paper should be published.

General comments

• The paper uses DDA as the truth, which is very reasonable; however, it would be interesting if the authors would also venture into providing some recommendations on what experimental laboratory or field studies should focus on in terms of “tuning” parameters, observational variables, scenarios or conditions, to fill similar gaps to those the authors identify in DDA simulation space.
• It would have been interesting to also add comparisons with the RDG approximation, at least for uncoated BC particles.
• Perhaps a stronger emphasis should have been given to the absorption because, in the atmosphere, the other optical parameters (for example, scattering, SSA and g) are dominated by particles other than those containing BC, owing to their lower concentrations; while it is the absorption properties of BC that are more radiatively important (e.g., to determine heating rates) despite their lower concentration due to their stronger absorption cross sections with respect to most of the other atmospheric particles. For example, in Figure 3, I would also add a plot with Qabs (instead of relegating it to Figure E1), even if that might be somewhat less sensitive to Df.
• Some additional references on previous work on these issues, especially in the realm of experiments and field studies, would be helpful.

Specific comments

• Line 30. Restructuring can also happen during cloud processing.
• Beginning of section 2. While Ensemble II “represents scenarios where liquid coatings induce restructuring via surface tension and capillary forces”, what does Ensemble I represent? Is this more consistent with processes such as cloud-induced compaction, or cases where the coating (other than water), initially present on the particle, eventually evaporates?
• Title of section 2.3: Although I do understand the reason for this wording choice, “numerically exact” might seem a contradiction with the term “approximation” in reference to the numerical model used (DDA). Perhaps a different section title would be better.
• Line 120: “other similar models” such as?
• The meaning of aleatoric vs. epistemic uncertainty is relatively clear; however, it would be even clearer if a simple example for each were provided.
• Line 159: Does theta include W and b (weights and biases)? If so, I find it confusing that later (in several following points in the paper) theta is referred to as " weights” only.
• Lines 188-189: What is the reason for the miscalibration?
• Line 192 and following: So, is tau just a tuning knob to match the validation targets?
• Line 208: How is the Gaussian noise chosen?
• Line 248: The distinction between Df and Df,c is important. Can the authors explain how the two are calculated? Related to this point, on line 250, it is mentioned that Df<=2 represents uncoated or coated particles not significantly compacted. Is the compaction here referring to the core alone or to the full particle? If it refers to the core only, as it would seem more physically appropriate, then the coating could still result in a particle with an overall Df much higher than 2 even when the core is little or not at all compacted; for example, in the case where the coating is so thick that the information on the underlying core morphology is lost and the coating looks close to spherical on the outside surface. Some clarification on these points would be useful.
• Line 255: This asymptotic behavior is reasonable and has been shown in the literature before.
• Lines 282 – 283: As written, this sentence seems to imply more of a numerical or mathematical reason for the low sensitivity of Qabs to Df, just resulting from error cancellations in the calculations of Qext and SSA. However, I believe the low sensitivity of Qabs to Df has a much more physical foundation, at least for uncoated particles; a reason that is also at the root of why the simple RDG approximation (based on compounded monomer number or total mass) for Qabs works relatively well as compared to Qsca and therefore also for Qext and SSA. It is true that in the model here, Qabs is given by Qext and 1-SSA to account for conservation of energy, but the physical lower sensitivity of Qabs is reflected, not caused by this mathematical relation.
• Line 298: This has indeed been shown to be the case in previous literature.
• Line 299: Define meff.