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Physics-Informed Explainable Machine Learning for Predicting Wavelength- Dependent Optical Modulation of Neuronal Activity

This study presents a physics-informed, explainable machine learning framework that integrates optical and biological features to predict wavelength-dependent neuronal modulation, achieving modest predictive accuracy for firing rates and higher accuracy for membrane potential while providing calibrated uncertainty estimates for future experimental validation.

Original authors: Md. Rasel Islam, Shazid Mahmud Labim, Nazmul Hasan, Md. Sadiqur Rahman Zihad, Md. Rabiul Islam, Md. Shariful Islam

Published 2026-10-26

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CC BY 4.0

Original authors: Md. Rasel Islam, Shazid Mahmud Labim, Nazmul Hasan, Md. Sadiqur Rahman Zihad, Md. Rabiul Islam, Md. Shariful Islam

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Light has long been known to influence the living world, from the way plants turn toward the sun to how our own eyes adjust to the dark. In the realm of neuroscience, researchers have recently discovered that shining light of specific colors onto the brain can subtly alter the activity of nerve cells without the need for surgery or implanted electrodes. This technique, known as photobiomodulation, uses low-intensity beams to nudge the electrical signals that neurons use to communicate. However, the relationship between the color of the light and the brain's reaction is far from simple. The effect depends on a complex web of factors: how deep the light must travel through tissue, how much energy the cells absorb, and the specific biological sensitivity of the neurons themselves. Because these variables interact in unpredictable ways, scientists have struggled to predict exactly how a particular beam of light will change brain activity, leaving the field with many promising results but few reliable rules for how to apply them.

To tackle this uncertainty, a team of researchers from the Islamic University in Bangladesh developed a new computational approach that blends the laws of physics with modern artificial intelligence. Instead of relying solely on patterns found in data, they built a system that understands the physical journey of light as it moves from a source, through tissue, and finally into a neuron. They created a massive digital library containing one hundred thousand simulated scenarios, covering a wide spectrum of light colors from 400 to 700 nanometers, which spans the range from violet to red. In this virtual environment, they tested how different combinations of light intensity, exposure time, and tissue depth affected two main types of neurons: those that excite the brain and those that calm it down. The goal was to see if a machine could learn to predict the change in a neuron's firing rate based on the physical properties of the light and the biological characteristics of the cell.

The researchers found that simply feeding the computer the raw numbers of the experiment, such as the color of the light or the power of the beam, was not enough to make accurate predictions. The model struggled to find a clear pattern, often guessing with very little confidence. However, when they added "physics-informed" features—calculations that described exactly how much light energy actually reached the neurons after passing through tissue and how sensitive those neurons were to specific colors—the model's performance improved. The system learned that the most important factors were not just the color of the light, but the effective dose of energy that the cells actually received and the specific gain of the biological response. By teaching the machine to respect the physical laws of how light travels and interacts with matter, the researchers were able to uncover a clearer, more interpretable relationship between the stimulus and the response.

Despite these improvements, the study revealed that predicting the exact change in a neuron's firing rate remains a difficult challenge. Even with the advanced physics-based model, the predictions were only modestly accurate when tested on light colors the computer had never seen before. The model could identify general trends, such as a stronger response in the blue-green part of the spectrum, but it could not precisely forecast the outcome for every single case. This suggests that while the physical dose of light is a major driver, there are other hidden biological factors at play that the current model cannot yet capture. Interestingly, the model performed much better when predicting changes in the electrical voltage across the neuron's membrane compared to changes in its firing rate, indicating that different aspects of neuronal activity respond to light in different ways.

The researchers also used special tools to make the machine's reasoning transparent, allowing them to see exactly which factors were driving the predictions. They discovered that the model relied heavily on variables related to the biological optical dose and the photo-modulation gain, rather than just the wavelength of the light itself. This confirmed that the color of the light matters primarily because it changes how much energy is absorbed and how the tissue scatters it. The study also tested how robust the model was by adding random noise to the input data, simulating the kind of measurement errors that happen in real-world experiments. The model's performance dropped as the noise increased, highlighting that precise measurements of light and tissue properties are essential for reliable predictions.

Ultimately, this work serves as a powerful proof of concept rather than a final solution. The data used in the study was generated by computer simulations, not from actual experiments on living brains, so the results represent a theoretical framework that needs to be tested in the real world. The researchers demonstrated that combining physical laws with machine learning can create a more understandable and physically plausible way to study how light affects the brain. By showing that the most successful predictions come from understanding the underlying mechanics of light delivery, the study provides a new roadmap for designing better non-invasive therapies. It suggests that future treatments for neurological conditions may need to be highly personalized, taking into account the specific optical properties of a patient's tissue and the precise biological sensitivity of their neurons, rather than relying on a one-size-fits-all approach to light therapy.

Technical Summary: Physics-Informed Explainable Machine Learning for Predicting Wavelength-Dependent Optical Modulation of Neuronal Activity

Problem Statement
Photobiomodulation (PBM) offers a non-invasive method to modulate neural function, yet the quantitative link between optical stimulus parameters (wavelength, intensity, dose) and neuronal response remains poorly understood. Experimental protocols vary significantly in wavelength, power, and delivery geometry, leading to heterogeneous and sometimes conflicting biological results. Purely data-driven machine learning (ML) approaches struggle in this domain because they often rely on statistical correlations without accounting for the underlying physical mechanisms of photon-tissue interaction (e.g., absorption, scattering, penetration depth). Consequently, these "black-box" models may lack physical plausibility and fail to generalize to unseen wavelengths or tissue conditions. Furthermore, existing predictive models often lack interpretability, making it difficult to discern which physical or biological factors drive specific neuronal outcomes. This study addresses the gap in developing a predictive framework that integrates optical physics, biological sensitivity, and explainable AI to model wavelength-dependent neuronal modulation.

Methodology
The authors developed a Physics-Informed Explainable Machine Learning (PIEML) framework using a computationally generated dataset of 100,000 samples. The dataset spans a wavelength range of 400–700 nm and includes two neuronal phenotypes (excitatory and inhibitory).

Feature Engineering: The study utilized three distinct feature representations to isolate the contribution of physical knowledge:
1. Data-only: Raw experimental parameters (wavelength, intensity, exposure time) and baseline neuronal properties.
2. Physics-informed: Augmented with optical-physics descriptors derived from analytical relationships (e.g., photon energy, effective attenuation, transmission, absorbed energy).
3. Full Mechanistic: Included biological response descriptors (e.g., wavelength sensitivity, opsin sensitivity, photo-modulation gain, biological optical dose).
Validation Strategy: To rigorously test generalization, the authors employed a wavelength-grouped validation strategy. A "locked" test set containing unseen wavelengths was held out, ensuring the model could not simply memorize specific wavelength labels. This was complemented by 5-fold grouped cross-validation and a "leave-neuron-type-out" domain-shift analysis.
Modeling Approach: Multiple regression algorithms (Ridge, Extra Trees, HistGradientBoosting, XGBoost) were benchmarked. A physics-informed residual learning approach was also tested, where a transparent mechanistic prior (based on biological optical dose and photo-modulation gain) was fitted first, and an ML model was trained to predict the residuals.
Explainability and Uncertainty: The study employed SHAP (SHapley Additive exPlanations), permutation importance, and partial dependence plots to interpret feature contributions. Predictive uncertainty was quantified using split-conformal prediction, and robustness was assessed via input-noise perturbation (1–20%).

Key Results

Predictive Performance: The inclusion of physics-informed and mechanistic features yielded modest but consistent improvements over data-only models. For the primary endpoint (percentage change in firing rate), the full mechanistic feature set increased the locked-test $R^2$ from 0.012 (data-only) to 0.035. The Root Mean Squared Error (RMSE) decreased from 8.10 to 8.00 percentage points.
Endpoint Dependency: Predictability varied significantly by endpoint. While firing rate modulation was difficult to predict ( $R^2 \approx 0.035$ ), the modulation of membrane potential was significantly more learnable, achieving an $R^2$ of 0.388.
Feature Importance: Explainability analyses (SHAP and permutation importance) identified photo-modulation gain, biological optical dose, wavelength sensitivity, tissue scattering, and peak wavelength as the most critical predictors. Notably, raw wavelength ranked lower than derived mechanistic variables, suggesting wavelength acts primarily through its influence on photon energy, tissue attenuation, and biological sensitivity.
Generalization and Robustness: The model demonstrated the ability to capture the dominant spectral structure (e.g., a response peak in the 460–495 nm range) even on unseen wavelengths. However, performance degraded monotonically with input noise; at 20% noise, the model's $R^2$ dropped to negative values, indicating sensitivity to measurement uncertainty.
Uncertainty Quantification: Split-conformal calibration achieved an empirical coverage of 90.2% for nominal 90% prediction intervals, providing calibrated uncertainty estimates despite the modest point-prediction accuracy.

Significance and Claims
The paper positions this work as a computational framework and hypothesis-generating tool rather than a validated experimental predictor. The authors explicitly state that the dataset was computationally generated and lacks the biological heterogeneity and noise of real neuronal systems.

The primary significance of the study lies in demonstrating that:

Physics-informed features provide incremental predictive value and improve model interpretability over purely data-driven approaches in optical neuromodulation.
Explainable AI can successfully identify non-linear, context-dependent interactions between optical dose, tissue properties, and biological sensitivity, revealing that neuronal modulation is a coupled optical-biophysical process.
Endpoint specificity is crucial; the learnability of neuronal responses varies drastically depending on the measured variable (e.g., membrane potential vs. firing rate).
Rigorous validation (wavelength-grouped splitting) is necessary to avoid overestimating model performance in optical domains where parameters are highly correlated.

The authors conclude that while the framework offers a systematic, interpretable method to investigate wavelength-dependent responses, its generalizability to real neuronal systems requires validation through independent experimental datasets involving electrophysiology and calcium imaging.

Technical Summary: Physics-Informed Explainable Machine Learning for Predicting Wavelength-Dependent Optical Modulation of Neuronal Activity

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