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Embedding physics in neural networks yields models that generalize across photonic devices

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2026-07-09 15:22 UTC pith:ALOTT5VT

load-bearing objection Grey-box modeling review with useful cross-case comparison; DML case incomplete, modularity claim rests on unverified linearity assumption. the 3 major comments →

arxiv 2607.07274 v1 pith:ALOTT5VT submitted 2026-07-08 physics.optics eess.SP

Beyond white- and black-box modeling tools in optical communications and optical computing: physics-informed data-driven modeling

Isidora Teofilovic , Sergio Hernandez Fernandez , Metodi P. Yankov , Christophe Peucheret , Darko Zibar , Francesco Da Ros This is my paper
classification physics.optics eess.SP
keywords physics-informed neural networksgrey-box modelingphotonic integrated circuitsoptical amplifiersdirectly-modulated lasersinterferometer meshesdigital twinscrosstalk compensation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that physics-informed data-driven models — which train neural networks using both measurement data and a physics-based loss term — strike the best balance across four metrics that matter for designing and controlling photonic systems: accuracy, training-data efficiency, generalizability, and modularity. The authors compare three modeling paradigms (pure physics equations, pure data-driven neural networks, and their hybrid) on three benchmark photonic components: Raman optical amplifiers, directly-modulated lasers, and interferometer meshes used for optical computing. The central mechanism is a composite loss function that combines a standard data-fitting term with a physics-constraint term, weighted by a single parameter k. When the physics term encodes even a partial physical relationship — such as the exponential decay of thermal crosstalk with distance in an interferometer mesh — the resulting model learns the device-specific behavior from data while inheriting the cross-device functional dependencies from the physics. The most concrete evidence comes from the interferometer mesh: a grey-box model trained on one hexagonal cell of a 72-element mesh achieves a global test error of 0.61 pm across all six cells, outperforming both a pure data-driven model (0.93 pm, which overfits to the training cell) and a pure physics model (0.72 pm, which lacks device-specific corrections). The grey-box model also converges with fewer training samples than the black-box alternative. If this holds broadly, it means that accurate digital twins of complex photonic circuits could be built from a single representative unit cell and a partial physical model, rather than requiring exhaustive measurement campaigns on every device.

Core claim

The paper's central claim is that a weighted combination of data-driven and physics-driven loss terms, even when the physics is only partially known, produces models that generalize across physical devices better than either pure physics or pure data-driven approaches, while requiring less training data than the latter and remaining differentiable for gradient-based optimization. The evidence is strongest for the interferometer mesh case, where the grey-box model's advantage in cross-device generalization is demonstrated quantitatively, and where the modular structure of the mesh allows a single-cell model to be translated and linearly combined to predict crosstalk across the full chip.

What carries the argument

The composite loss function L_total = (1-k)·L_data + k·L_physics, where L_data is a standard mean-squared-error term on input-output data and L_physics penalizes predictions that violate a known physical relationship (e.g., exponential thermal decay). The parameter k balances the two terms; the authors find k=0.5 optimal for cross-device generalization in the interferometer mesh case. A secondary mechanism is transfer learning: a simple physics model is trained on few samples, used to generate large synthetic datasets, which pre-train a more complex neural network that is then fine-tuned on the original few real samples.

Load-bearing premise

The claim that grey-box models generalize better rests on the assumption that the physics embedded in the loss term captures functional dependencies that are genuinely common across devices. For the interferometer mesh, this means the exponential thermal decay model accurately represents the dominant crosstalk mechanism in every cell. If unmodeled effects — such as optical crosstalk from waveguide crossings or fabrication-induced variations — dominate in certain cells, the物理学

What would settle it

If a grey-box model trained on one cell of an interferometer mesh, using a thermal-decay physics loss, were tested on a cell where the dominant crosstalk mechanism is optical (not thermal) and showed no generalization advantage over a pure data-driven model, the core claim would be weakened.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Digital twins of programmable photonic chips could be constructed by characterizing a single unit cell and translating its model across the chip by symmetry, rather than measuring every component individually.
  • The physics-informed loss approach could extend to other photonic components where partial physical models exist but full multiphysics models are intractable, such as silicon photonics with combined thermal-optical-electrical crosstalk.
  • Gradient-based end-to-end optimization of full optical communication links becomes feasible when differentiable grey-box models of amplifiers, lasers, and fibers are cascaded modularly.
  • The transfer-learning workflow (train simple physics model, generate synthetic data, pre-train neural network, fine-tune on real data) offers a practical recipe for data-constrained photonic manufacturing environments.

Where Pith is reading between the lines

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

  • The choice of which physical relationship to embed in the loss function becomes a design decision that trades generality for specificity: a more general physics term (e.g., energy conservation) would constrain less but apply more broadly, while a device-specific term (e.g., a particular thermal decay model) constrains more but may fail if the dominant physics differs across devices.
  • If fabrication variability introduces effects not captured by the embedded physics (e.g., waveguide roughness causing optical crosstalk that does not follow the thermal decay model), the grey-box advantage would diminish, and the optimal k would shift toward the data-driven regime — suggesting that k itself could serve as a diagnostic for how well the chosen physics describes the system.
  • The modular linear-combination framework for multi-cell crosstalk compensation (Eqs. 6-12) implicitly assumes crosstalk contributions are linearly superposable; if nonlinear crosstalk interactions become significant at higher device densities, this framework would need extension.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper presents a comparative analysis of three modeling paradigms—white-box (WB, physics-based), black-box (BB, data-driven), and grey-box (GB, physics-informed data-driven)—applied to three photonic use cases: Raman amplifiers, directly modulated lasers (DMLs), and interferometer meshes. The central claim is that GB models offer significant advantages in generalizability and modularity while preserving data efficiency and limiting model complexity. The paper reviews and contextualizes the authors' prior work, extending a conference submission with new quantitative results for interferometer meshes, particularly on inter-cell generalization and modular crosstalk compensation.

Significance. The topic is timely and relevant to the optical communications and optical computing communities. The systematic cross-case comparison of modeling paradigms, with quantitative metrics (RMSE, inference time, parameter count), is a useful contribution. The modular crosstalk compensation framework for interferometer meshes (Section III-D) and the transfer-learning workflow for data-constrained settings (Section III-B) are concrete, falsifiable contributions. The paper provides actionable guidance for practitioners building digital twins of photonic systems.

major comments (3)
  1. The paper's central claim of GB advantages 'across three benchmark use cases' is structurally incomplete for the DML case. Section II-B.2 and Fig. 3 present only WB and BB models for DMLs; no GB model is discussed or evaluated. Section III-D acknowledges that 'No modular DML model has yet been reported.' The abstract and conclusion should be revised to accurately reflect that the three-way WB/BB/GB comparison is carried out for two use cases (amplifiers, meshes), while the DML case is a two-way WB/BB comparison. As written, the framing overstates the breadth of the GB evidence.
  2. Section III-D, Eqs. (7)-(12): The modular crosstalk compensation framework rests on the assumption that thermal crosstalk contributions sum linearly (Eq. 7: Δλ_i = Σ_{j≠i} Δλ_{i,j}). This linearity is asserted ('thermal XT effects are expected to sum up linearly') but not experimentally verified. The model's RMSE is approximately 0.6 pm (Table I); if nonlinear effects (thermal saturation, optical crosstalk, fabrication-dependent coupling) cause deviations exceeding this threshold, the framework's compensation accuracy degrades. Since modularity is a central claimed advantage of GB models, the authors should either provide experimental validation of the linearity assumption for multi-MRR configurations or explicitly state this as a limitation and qualify the modularity claim accordingly.
  3. Section III-C, Fig. 11a: The hyperparameter k (Eq. 5) is selected as k=0.5 based on the best global test RMSE across all six cells. Selecting a hyperparameter on the test set risks optimistic bias in the reported generalization performance. The authors should either use a validation set for k selection or report sensitivity of the global RMSE to k across a range of values, and discuss whether the k=0.5 optimum is robust or an artifact of the specific test data. This is load-bearing because the generalization advantage of GB over WB (0.61 vs. 0.72 pm, Table I) is modest and could be within the uncertainty introduced by hyperparameter selection.
minor comments (6)
  1. The paper is heavily self-referential, with the majority of cited results for each use case authored by the present authors ([23], [32], [48], [80], [89], [90]). While this is understandable for a review of the authors' own work, broader context from independent groups would strengthen the comparative claims. Consider adding a brief discussion of how the authors' GB approach relates to other physics-informed ML efforts in photonics beyond the cited works.
  2. Section II-C, Eq. (5): The loss function L_total = (1-k)·L_data + k·L_physics is introduced, but the specific form of L_physics for each use case is not consistently defined. For the interferometer mesh, L_physics is based on the thermal decay model (Eq. 4), but for Raman amplifiers and DMLs, the physics loss is not explicitly stated. Adding a brief description of L_physics for each case would improve self-containedness.
  3. Fig. 2(b): The caption references 'fitted WB model and learned BB model' but does not specify the training dataset size or model architecture for the BB model shown. Adding these details would make the comparison more interpretable.
  4. Section III-A, Fig. 7(b): The x-axis is labeled 'number of parameters' but the WB model (ThDM) and GB model (PILR) have very different parameter counts (81 vs. 13500+ for BB). The log scale or explicit parameter counts for each model would improve the clarity of the complexity comparison.
  5. The manuscript header reads 'JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015' and the manuscript received date is 'April 19, 2005; revised August 26, 2015.' These appear to be template artifacts and should be corrected before publication.
  6. Section II-A.3, Eq. (3): The MZI transfer function is written with j (imaginary unit) but the phase shifters use e^{jθ_1} and e^{jθ_2}. The notation is standard but the switch between j and e^{jθ} could be made consistent. Also, the transition from Eq. (3) to the discussion of crosstalk models could more explicitly state how the GB construction modifies Eq. (3).

Circularity Check

0 steps flagged

No genuine circularity found; heavy self-citation provides experimental data and implementations, not tautological theoretical claims.

full rationale

The paper is a comparative review of three modeling paradigms across three use cases. I examined each load-bearing derivation chain for circularity: (1) The GB model's physics loss (Eq. 5) uses the thermal decay model (Eq. 4) whose parameters are fitted during training. This is standard grey-box modeling — the physics constraint imposes a functional *form* (exponential decay with distance), while the predictions (wavelength shifts for unseen cells) are not the quantities being fitted. The generalization claim (Table I, Fig. 11) is that this form transfers across cells, which is an empirically testable hypothesis, not a tautology. (2) The modular crosstalk framework (Eqs. 6–12) is a mathematical derivation conditional on the linearity assumption (Eq. 7). The paper explicitly flags this as an assumption ('thermal XT effects are expected to sum up linearly'), not a derived result. An unverified assumption is a correctness risk, not circularity. (3) The transfer learning workflow (Fig. 8b) uses a WB model to generate synthetic data for pre-training a BB model — this is a methodology, not a circular derivation. (4) The heavy self-citation ([23], [32], [48], [80], [89], [90]) references the authors' own experimental measurements and model implementations. These provide independently reproducible data and code, not theoretical claims that would make the present argument tautological. The cited works are externally falsifiable (measurements on physical devices, published code/architectures). No step in the derivation chain reduces to its own inputs by construction. Score 2 reflects the heavy self-citation pattern, which is not load-bearing for circularity but is worth noting for independence of evidence.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The paper introduces no new physical entities or particles. Free parameters are standard physical/modeling quantities fitted to data. The key axioms are domain assumptions about thermal crosstalk linearity and exponential decay, plus the ad-hoc assumption that physics loss improves generalization.

free parameters (4)
  • k (loss weight) = 0.5
    Weight parameter in Eq. 5 controlling balance between data-driven and physics loss; optimized to k=0.5 for best device-generalization (Section III-C, Fig. 11a)
  • p1, p2, p3 (thermal decay)
    Fitting parameters in thermal decay model (Eq. 4) for temperature evolution with distance
  • Raman efficiency CR
    Fitted to measurement data in WB Raman model (Section II-A.1)
  • Laser rate equation parameters (g0, alpha, tau_n, etc.)
    Physical parameters extracted from measurements for DML WB model (Section II-A.2)
axioms (3)
  • domain assumption Thermal crosstalk effects sum linearly across multiple MRRs on the same mesh
    Section III-D, Eq. 7: assumes Delta_lambda_i is the sum of individual contributions Delta_lambda_i,j. This is stated but not independently verified for the general case.
  • domain assumption Thermal diffusion follows exponential decay with distance from heating element
    Section II-A.3, Eq. 4: the ThDM model assumes exponential decay, confirmed by numerical simulation [24] but is an approximation of the full thermal diffusion equation.
  • ad hoc to paper Physics-informed loss terms improve generalization by encoding functional dependencies common across devices
    Section II-C: the central assumption that L_physics captures cross-device physics. The paper provides empirical evidence (Fig. 11) but no theoretical guarantee.

pith-pipeline@v1.1.0-glm · 25409 in / 2485 out tokens · 281356 ms · 2026-07-09T15:22:00.057699+00:00 · methodology

0 comments
read the original abstract

Efficient optimization and control of photonic computing and communication systems increasingly rely on accurate surrogate models/digital twins. While data-driven models may achieve faster inference than traditional physics-based methods, they typically suffer from poor training data efficiency and limited generalizability. To address this trade-off, physics-informed data-driven modeling has emerged as a powerful hybrid paradigm. This paper presents a comparative analysis of these three modeling paradigms across three benchmark use cases: optical amplifiers, directly modulated lasers, and interferometer meshes. By evaluating model complexity, data efficiency, generalizability, and modularity, this work provides a detailed analysis of the respective trade-offs and highlights the advantages of combining physical insight with data-driven learning.

Figures

Figures reproduced from arXiv: 2607.07274 by Christophe Peucheret, Darko Zibar, Francesco Da Ros, Isidora Teofilovic, Metodi P. Yankov, Sergio Hernandez Fernandez.

Figure 1
Figure 1. Figure 1: Main category of modeling approaches: (a) physical models (WB) where a system of physical equations is fitted to data; (b) physics-informed [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: DML - (a) Setup of short-reach link based on DMLs, highlighting the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Raman amplifier - (a) Raman amplifier setup relying on multi-pump [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Hexagonal MZI mesh - Transfer function of the emulated micro-ring [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Direct neural network models mapping inputs and/or parameters into the predicted output: (a) Raman amplifier; (b) DML-based link; (c) XT in an [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Grey-box modeling - neural-network-aided physical model. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Model complexity - (a) trade-off between inference time and model accuracy for the DML BB (Volterra, TDNN, LSTM and CAT) and WB (ODE solver) models (adapted from [32]) (b) trade-off between model parameters and model accuracy for the hexagonal MZI mesh BB (linear fit and LR), WB (ThDM) and GB (PILR) models. shift directly scales with the number of fitted parameters in the models. The comparison between WB … view at source ↗
Figure 8
Figure 8. Figure 8: Data efficiency - (a) comparison between training and testing RMSE as a function of training dataset size for WB and BB models of the 3 × 3 MZI architecture (inset), adapted from [90]); (b) proposed workflow for enhancing model accuracy under strong training data constraints through transfer learning; (c) performance of WB and BB models compared with TL-GB model, adapted from [90] directly related to the n… view at source ↗
Figure 9
Figure 9. Figure 9: Data efficiency - Self-Testing RMSE as a function of the training dataset size: comparison between ThDM (WB), LR (BB) and PILR (GB) models. Shaded areas refer to the standard deviation over 10 training datasets. dataset size does not scale favorably with the number of devices. Therefore, alternative paradigms have been sought. As discussed in Section II-C, physical knowledge embedded in the models improves… view at source ↗
Figure 10
Figure 10. Figure 10: Generalizability - Raman amplifier optimization for a target output power spectral profile for (a) forward pumping across two spans (second span with remote pumping) and (b) bidirectional pumping across a single span. The optimization target is compared with the predicted power from the GB model and the power obtained from a computationally heavier fully WB model (Adapted from [80]. As shown in [80], ML-a… view at source ↗
Figure 11
Figure 11. Figure 11: Generalizability - (a) Testing RMSE across all unit cells as a function of the loss-weight parameter for the GB model. (inset) schematic of the programmable PIC highlighting the hexagonal unit cells considered. (b) Comparison of WB, BB and GB based on the RMSE over the test unit cells for the model trained on cell 5. (c) Data-efficiency evaluated through the global RMSE as a function of the training datas… view at source ↗
Figure 12
Figure 12. Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Modularity - Conceptual modularity of crosstalk in multi-cell MZI meshes: translation of a single-cell generalizable model and linear combination of the translated models provides the model of the full PIC. {ai,j} contains the contributions of the MZI forming MRR j to the wavelength shift of the resonances of MRR i. For the ThDM model, the elements of (ai,j ) are given by applying (4), whereas for LR-type… view at source ↗

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