Predicting Grain Growth Evolution Under Complex Thermal Profiles with Deep Learning through Thermal Descriptor Modulation

Abstract

Predicting microstructure evolution during thermomechanical treatment is essential for determining the final mechanical properties of a material, yet conventional simulations based on Partial Differential Equations (PDEs) remain computationally expensive. Our prior Deep Learning (DL) framework using Convolutional Long Short-Term Memory (ConvLSTM) has proven effective in accelerating grain growth prediction, though its applicability was limited to constant-temperature or single-rate thermal profiles. As the model was trained exclusively under constant thermal conditions, it cannot account for the thermal history dependence of grain boundary kinetics, fundamentally limiting its applicability to the time-varying thermal profiles characteristic of industrial heat treatment processes. This study extends the previous framework by incorporating Feature-wise Linear Modulation (FiLM) for thermal conditioning to predict grain growth under complex, time-varying thermal profiles. The model was trained on a large dataset of grain growth evolution under thermal profiles with heating and cooling rates ranging from 0.01 kelvin per second to 10 kelvin per second. The results demonstrate that the proposed thermal conditioning mechanism enables the model to capture the influence of variable thermal profiles on grain boundary migration kinetics. Across the three test scenarios of increasing complexity, the model achieved a Structural Similarity Index Measure (SSIM) of up to 0.93 and mean grain size error below 3.2%. Despite the architectural extensions, inference time remains on the order of seconds per prediction sequence, preserving the computational advantage over PDE-based simulations.

Figures (11)

• Figure 1: Neural network architectures for grain growth prediction: (a) encoder-decoder + ConvLSTM framework from the previous study; (b) extended framework with thermal conditioning through FiLM, where a thermal conditioning module generates scale ($\gamma$) and shift ($\beta$) parameters to modulate the latent features based on instantaneous $T$ and $\mathrm{d}T/\mathrm{d}t$.
• Figure 2: Thermal profiles for the three test scenarios: temperature evolution (left column) and corresponding thermal rate $\mathrm{d}T/\mathrm{d}t$ (right column) for Scenario 1 (a, b), Scenario 2 (c, d), and Scenario 3 (e, f).
• Figure 3: Error heatmap for Scenario 1: (a) end of heating phase ($t = 18min$); (b) end of cooling phase ($t = 59min$). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
• Figure 4: Error heatmap for Scenario 2: (a) start of cooling phase ($t = 26min$); (b) end of cooling phase ($t = 59min$). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
• Figure 5: Error heatmap for Scenario 3: (a) end of first heating ($t = 17min$); (b) end of partial cooling ($t = 25min$); (c) end of reheating ($t = 32min$); (d) end of final cooling ($t = 59min$). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)