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

TL;DR

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.

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.

Figures (14)

• Figure 1: Extracted spatial features for the XGBoost model and for $(i,j)$ pixel.
• Figure 2: Architecture of the convolutional neuronal network. $t_0$, $t_1$, ..., $t_n$ are the training temporal instances.
• Figure 3: Architecture of the Variational Auto Encoder used in the self-supervised CNN
• Figure 4: $7$ points LHS sampling for the $[0,1]\times[0,1]$ space.
• Figure 5: Transformation toward the local and global optimum. The example shows the local optimum case; the global case is symmetric.