Data-efficient hybrid physics—Machine learning model for ultrafast laser ablation

Machine learning has been used to predict laser ablation depth but typically requires large data sets that are costly and slow to collect. This limits its usefulness in industrial applications where only a small number of measurements are available. We evaluate a hybrid model that combines the two-temperature model (TTM) with a residual neural network to improve prediction accuracy when training data are limited. The model retains the physics of the TTM and adds a targeted correction where its predictions diverge from measured values. We test this approach on four materials (silicon, steel, copper, and aluminum) and two scan types (line and raster) and compare it with both the TTM alone and a gradient boosting model. Tests focus on small training sets (10–100 samples) and evaluate prediction accuracy, sensitivity to sampling, and generalization across experimental setups. The hybrid model consistently gives higher R2 scores and lower normalized errors, outperforming both the TTM and machine learning models in low-data settings. These results show that machine learning can effectively improve the accuracy of physics-based models for industrial laser processing.