The quasi-isentropic loading method based on multidimensional gradient structures plays a critical role in acquiring dynamic physical parameters and significantly enhances the service safety of materials. This study proposes a physics-guided machine learning (PGML) framework for high-fidelity prediction of quasi-isentropic loading waveforms under data-scarce conditions. The framework systematically integrates physical principles into the learning process through mathematically regulated inductive biases and deep feature engineering. By integrating shock propagation physics and an attention mechanism, this approach transforms sparse data into interpretable visual representations, achieving an R2 > 0.96 and 18.5 m/s MAE with only 528 samples while reducing shape alignment error by over 35% compared to baselines. The 4 × 4 augmentation strategy delivers a breakthrough performance in small-data prediction, achieving radically enhanced accuracy and training efficiency across impact velocities. A PGML framework, constrained by shock wave propagation behavior, coupled with SHAP analysis, reveals that the Hill coefficient (h) and curvature modulation parameter (K) dominate the loading path, providing interpretable insights into waveform modulation. The presented framework establishes a transformative, data-efficient paradigm for graded structure material design, substantially diminishing the dependency on resource-intensive simulations and experiments.
Liu et al. (2026) studied this question.