Physics-informed data-driven modelling of aluminium processing

Abstract

In this thesis, the integration of physics-based insights and experimental data in the modelling of precipitation hardening (PH) is investigated. To set up the context, a fitting parameter is calibrated in a partial differential equation (PDE) using Physics-Informed Neural Network (PINN), a machine learning (ML) framework that integrates physical laws in a data-driven neural network (NN). A one-dimensional Burgers equation is employed as a representative test case. PINN merges data-driven and physics-based pathways, where the loss function penalises deviations from experimental data and physics-based PDE residual. Through systematic studies, the effects of NN hyperparameters (depth, width), training dataset size, and parameter initialisation are examined. Results demonstrate PINN’s strengths in robust convergence to the true parameter values even under data-scarce conditions. Gradient-based optimisation ensures physical plausibility, especially in cases of poor or even physically incorrect initial guesses, where gradient-free methods often fail. These findings highlight the advantages of a well-established integration framework, a reliable model structure, and experimental data as important tools for parameter estimation, setting the foundation for the subsequent part of the thesis. PH is the primary mechanism for strengthening 6xxx series aluminium alloys. The characteristics of the precipitates play a crucial role in determining the mechanical properties. Particularly, predicting yield strength (YS) based on microstructure is experimentally complex and costly because its key variables such as precipitate radius, spacing, and volume fraction are difficult to measure. Physics-based modelling (PBM), such as Kampmann–Wagner Numerical (KWN), has emerged to tackle these complications utilising advancements in simulation environments. Nevertheless, these approaches require numerous free parameters and ongoing debates over governing equations. Conversely, purely data-driven models struggle with insufficient datasets and physical interpretability. Moreover, the complex dynamics between internal model variables have led both approaches to adopt heuristic optimisation methods, such as Powell or Nelder-Mead, which fail to exploit valuable gradient information. To overcome these issues, a gradient-based optimisation for KWN is proposed, incorporating CALPHAD (CALculation of PHAse Diagrams) and a strength model. The novelties include facilitating differentiability via smoothed approximations of conditional logic, adding regularisation terms to the loss function to maintain the physical relationship between parameter instances, and using per-parameter learning rates for each instance of the fitting parameters. To reduce the computational complexity, a single size-class and a single precipitate type are assumed. Model calibration is guided by a mean squared error (MSE) loss function that aligns the YS predictions with interpolated experimental data using L2 regularisation for penalising deviations from a purely PBM structure. A comparison shows that gradient-based ADAptive Moment Estimation (Adam) outperforms gradient-free Powell and Nelder-Mead by converging faster, requiring fewer PBM evaluations, and yielding more physically plausible parameters. Finally, the model output is validated with a second set of composition and process parameters, with microstructure data, and a unit test, highlighting the power of gradient-based calibration techniques in the modelling of 6xxx series PH.