PI-DSN: Physics-Informed Dual-Branch Neural Network Solves Few-Shot Inverse Problem in Diffraction Measurement

PI-DSN (Physics-Informed Dual-Branch Neural Network) is an open-source project for filament diameter measurement in the precision manufacturing field. Its core innovation lies in solving the inverse problem of diffraction measurement with only 8-10 real measurement samples. This method integrates physical prior knowledge with data-driven learning, has cross-sample generalization ability, is suitable for industrial scenarios with scarce samples, and provides a practical paradigm for solving physical inverse problems.

Diffraction measurement technology infers filament diameter by analyzing Fraunhofer diffraction patterns, which is a typical physical inverse problem. However, it faces three major challenges: parameter coupling (mutual influence of multiple physical parameters), simulation-measurement discrepancy (structural deviation), and sample scarcity (high cost of high-quality real samples). Traditional deep learning requires a large number of labeled samples, which is difficult to meet industrial needs.

PI-DSN adopts a dual-branch architecture:

1. Data-driven branch: Learns statistical features from diffraction patterns
2. Physics-constrained branch: Embeds the Fraunhofer diffraction equation to ensure results conform to optical principles

To address the sample scarcity problem, the Measurement-Guided Data Augmentation (MDGA) strategy is proposed: generates simulated patterns based on a small number of real samples, covers the diameter range through Latin hypercube sampling, adjusts simulated data using statistical characteristics of real samples, and narrows the domain gap.

1. Coarse-grained fitting: Uses MATLAB's differential evolution algorithm to extract initial diameter estimates from FFT spectra
2. Simulated sample library construction: Performs Latin hypercube sampling based on initial estimates to generate labeled simulated diffraction patterns
3. Network training: Loads simulated samples and introduces physical constraints using an adaptive loss weight strategy
4. Unlabeled checkpoint selection: Monitors prediction stability via Exponential Moving Average (EMA) and automatically selects the optimal model

PI-DSN demonstrates strong generalization ability: the model trained on FIL001 filaments can be directly applied to FIL002 without retraining; it maintains stable accuracy at 75mm and 120mm focal lengths, verifying its robustness to changes in optical system parameters.

The project has high engineering maturity:

• Environment configuration: Supports conda/pip and is compatible with multiple platforms
• Path management: Flexible configuration via environment variables to avoid hardcoding
• Automation tools: Includes path verification and repair scripts
• Pre-trained weights: Provides EMA checkpoints for direct inference
• Paper reproduction: Offers complete scripts for reproducing charts (FFT baseline, parameter coupling visualization, etc.)

The idea of PI-DSN can be extended to physical inverse problem fields such as material characterization, optical detection, and non-destructive testing. Its core insight: high-quality physical prior knowledge can significantly reduce data requirements, and physics-guided learning is more practical in scenarios with high labeling costs.

PI-DSN represents the cutting-edge direction of integrating machine learning and physical modeling, proving the key role of physical priors in few-shot learning. The project provides complete code and experimental processes, making it a high-quality open-source resource for researchers in precision measurement, optical engineering, and physics-informed neural networks.