dorsal/arxiv
View SchemaPhysics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves
| Authors | George D. Pasparakis, Himanshu Sharma, Rushik Desai, Chunyu Li, Alejandro Strachan, Lori Graham-Brady, Michael D. Shields |
|---|---|
| Categories | |
| ArXiv ID | 2601.06655vv1 |
| URL | https://arxiv.org/abs/2601.06655 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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"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.",
"arxiv_id": "2601.06655",
"authors": [
"George D. Pasparakis",
"Himanshu Sharma",
"Rushik Desai",
"Chunyu Li",
"Alejandro Strachan",
"Lori Graham-Brady",
"Michael D. Shields"
],
"categories": [
"cs.CE",
"physics.comp-ph",
"stat.ML"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves",
"url": "https://arxiv.org/abs/2601.06655",
"version": "v1"
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