Coating Color Matching Using Physics-Informed Spectral Inversion
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Solution Overview
Problem
Existing color matching techniques for coatings are inefficient, time-consuming, and inaccurate, making it difficult to achieve precise color matching in industrial applications.
Innovation Solution
A physics-informed machine learning algorithm, utilizing a radiative transfer function as a regularization agent, processes color measurements from a spectrophotometer to generate a set of color components that accurately match the target color curve, incorporating Kubelka-Munk theory to constrain admissible solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional color matching techniques are used, then the process is simple to implement, but the accuracy and efficiency of color matching deteriorates
Solution Approach 1:
The patent transforms the color matching problem from traditional RGB or CIELAB color spaces into a physics-based radiative transfer model parameter space. By changing the parameter representation from simple color values to physical optical properties (absorption coefficients, scattering coefficients, layer thicknesses), the system achieves higher measurement precision while maintaining manageable complexity through automated inversion algorithms.
Solution Approach 2:
The patent replaces traditional empirical color matching methods with a physics-informed machine learning system that uses radiative transfer equations. This substitution of mechanical/empirical approaches with physics-based computational models enables accurate color matching by modeling light interaction with coating layers, resolving the contradiction between accuracy and complexity.
2Measurement precision
If iterative color matching methods are used, then the accuracy improves, but the time consumption increases
Solution Approach 1:
The patent performs preliminary action by pre-computing the radiative transfer model responses for various coating configurations and storing them in a lookup table or training dataset. During actual color matching, the system quickly retrieves or interpolates from these pre-computed results using the physics-informed machine learning algorithm, avoiding time-consuming iterative simulations while maintaining high accuracy.
Solution Approach 2:
The patent creates a computational copy of the physical radiative transfer process through machine learning models trained on simulated or experimental data. This digital twin or surrogate model replicates the complex light-coating interactions without requiring repeated physical measurements or full radiative transfer simulations, significantly reducing time while preserving accuracy.
3Manufacturing precision
If physical constraints are added to limit solution space, then the accuracy of color components improves, but the complexity of processing increases
Solution Approach 1:
The patent changes the parameter space from unconstrained color component values to physically meaningful parameters (absorption coefficients, scattering coefficients, layer thicknesses) that inherently satisfy physical constraints. This parameter transformation embeds physical laws directly into the solution space, improving manufacturing precision while the physics-informed machine learning algorithm handles the processing complexity efficiently.
Solution Approach 2:
The patent implements self-service through physics-informed regularisation where the radiative transfer equations automatically constrain the solution space. The machine learning algorithm uses embedded physical knowledge to guide the inversion process, allowing the system to self-regulate and produce physically valid color component solutions without requiring complex external constraint enforcement mechanisms.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method enables more efficient, accurate, and less time-consuming color matching processes by constraining the solution space with physical laws, resulting in precise color recipes for coatings.
Implementation Method 1
receive, from a spectrophotometer, a color measurement of a first coating, wherein the color measurement corresponds with a first color curve
Implementation Method 2
a radiative transfer function acts as a regularization agent that limits a space of admissible solutions within the physics-informed machine learning algorithm
Data Source
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AI summary
A system may receive, from a spectrophotometer, a color measurement of a first coating, wherein the color measurement corresponds with a first color curve. Additionally, the system may process, with a physics-informed machine learning algorithm, information derived from the first color curve, wherein a radiative transfer function acts as a regularization agent that limits a space of admissible solutions within the physics-informed machine learning algorithm. The system may also generate, from an output of the physics-informed machine learning algorithm, a set of one or more color components that, if mixed, correspond to the first color curve.