Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves

2026-01-10

arXiv.org

AI Summary

This work proposes a physics-informed Gaussian process regression framework for high-fidelity prediction of material Hugoniot curves under shock loading, circumventing the need for costly large-scale molecular dynamics (MD) simulations. By embedding the Rankine–Hugoniot jump conditions and a probabilistic Taylor expansion directly into the covariance function, the model enforces thermodynamic consistency while requiring only a limited set of MD data points. The approach accurately reconstructs shock compression paths and quantifies predictive uncertainty through the posterior distribution. Demonstrated on silicon carbide, the method not only efficiently reproduces the Hugoniot curve but also elucidates the transition mechanisms from elastic to plastic and phase-transition waves. Furthermore, it enables interpretable hyperparameter optimization, offering both physical insight and computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

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• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process employs a probabilistic Taylor series expansion in conjunction with the Rankine-Hugoniot jump conditions between the various shocked material states to construct a thermodynamically consistent covariance function. This leads to the formulation of an optimization problem over a small number of interpretable hyperparameters and enables the identification of regime transitions, from a leading elastic wave to trailing plastic and phase transformation waves. This work is motivated by the need to investigate shock-driven material response for materials discovery and for offering mechanistic insights in regimes where experimental characterizations and simulations are costly. The proposed methodology relies on large-scale molecular dynamics which are an accurate but expensive computational alternative to experiments. Under these constraints, the proposed methodology establishes Hugoniot curves from a limited number of molecular dynamics simulations. We consider silicon carbide as a representative material and atomic-level simulations are performed using a reverse ballistic approach together with appropriate interatomic potentials. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior.

Problem

• Hugoniot curve
• shockwave simulation
• material response
• phase transformation
• molecular dynamics

Innovation

• Physics-constrained Gaussian Process
• Hugoniot curve
• Rankine-Hugoniot conditions
• Probabilistic Taylor expansion
• Molecular dynamics