Adaptive Uncertainty-Guided Surrogates for Efficient phase field Modeling of Dendritic Solidification

TL;DR

This paper introduces an adaptive surrogate modeling approach using uncertainty quantification with machine learning techniques to efficiently simulate dendritic solidification, significantly reducing computational costs and environmental impact.

Contribution

It develops an uncertainty-guided adaptive sampling framework combining CNNs and XGBoost for efficient phase field modeling of dendritic solidification, with a focus on reducing simulations and environmental footprint.

Findings

Achieves accurate predictions with fewer phase field simulations.

Effectively identifies high-uncertainty regions for adaptive sampling.

Reduces $CO_2$ emissions compared to traditional sampling methods.

Abstract

The high computational cost of phase field simulations remains a major limitation for predicting dendritic solidification in metals, particularly in additive manufacturing, where microstructural control is critical. This work presents a surrogate model for dendritic solidification that employs uncertainty-driven adaptive sampling with XGBoost and CNNs, including a self-supervised strategy, to efficiently approximate the spatio-temporal evolution while reducing costly phase field simulations. The proposed adaptive strategy leverages model uncertainty, approximated via Monte Carlo dropout for CNNs and bagging for XGBoost, to identify high-uncertainty regions where new samples are generated locally within hyperspheres, progressively refining the spatio-temporal design space and achieving accurate predictions with significantly fewer phase field simulations than an Optimal Latin Hypercube Sampling optimized via discrete Particle Swarm Optimization (OLHS-PSO). The framework systematically investigates how temporal instance selection, adaptive sampling, and the choice between domain-informed and data-driven surrogates affect spatio-temporal model performance. Evaluation considers not only computational cost but also the number of expensive phase field simulations, surrogate accuracy, and associated $CO_2$ emissions, providing a comprehensive assessment of model performance as well as their related environmental impact.