Physics integrated neural model improves sintering predictions
Retrainable physics-integrated neural differentiable modeling of sintering across material systems
Machine Learning
Summary
Sintering, a key process for making ceramics, is hard to predict because many factors interact in complex ways and data is limited. The authors created a new modeling approach called Sinter-PiNDiff that combines physics knowledge with neural networks to better predict how density and grain size change in different materials during sintering. Their model adapts to different ceramics and outperforms standard neural networks on unseen data. It also shows that density changes directly influence how sintering proceeds. This framework helps design sintering processes even when data is sparse and estimates uncertainty in predictions.
What this means in practice
- •For materials engineers: Predict sintering outcomes like density and grain size across various ceramics with limited experimental data to optimize manufacturing processes.
- •For process developers: Select and fine-tune sintering conditions with uncertainty estimates to improve reliability of ceramic production at scale.
Authors
Zeping Chen, Ani Aprahamian, Khachatur V. Manukyan, Tengfei Luo
Abstract
Sintering is widely used to manufacture ceramics, but coupled densification and grain growth, material-dependent kinetics, and sparse measurements complicate predictive modeling and process design. We present Sinter-PiNDiff, a retrainable physics-integrated neural differentiable framework for predicting density and grain-size evolution. Two neural networks learn densification and grain-growth coefficients within coupled rate equations, while a smooth saturation factor attenuates densification near theoretical density. The same governing structure, network architecture, and training procedure were fitted independently to published data for MgO, Al-doped ZnO, and CaO-doped ThO2. Tests at held-out temperatures and compositions yielded the lowest mean error in all twelve material-metric comparisons against multilayer perceptron and residual network baselines. For MgO, Al-doped ZnO, and CaO-doped ThO2, respectively, density normalized root-mean-square errors were 14.6%, 10.8%, and 14.4%, and grain-size errors using the same metric were 8.6%, 12.1%, and 19.3%. Removing evolving density from both neural-network inputs increased density and grain-size trajectory errors in all three systems and ten of twelve aggregate errors, supporting density-dependent kinetic feedback. Deep ensembles estimated model disagreement, but empirical coverage showed that the uncertainty bands were not calibrated and did not capture all model-data discrepancies. These results establish Sinter-PiNDiff as a retrainable framework for sparse-data prediction and uncertainty-informed selection of sintering conditions.