Neural Network Modeling of Microstructure Complexity Using Digital Libraries

Microstructure evolution in matter is often modeled numerically using field or level-set solvers, mirroring the dual representation of spatiotemporal complexity in terms of pixel or voxel data, and geometrical forms in vector graphics. Motivated by this analog, as well as the structural and event-driven nature of artificial and spiking neural networks, respectively, we evaluate their performance in learning and predicting fatigue crack growth and Turing pattern development. Predictions are made based on digital libraries constructed from computer simulations, which can be replaced by experimental data to lift the mathematical overconstraints of physics. Our assessment suggests that the leaky integrate-and-fire neuron model offers superior predictive accuracy with fewer parameters and less memory usage, alleviating the accuracy-cost tradeoff in contrast to the common practices in computer vision tasks. Examination of network architectures shows that these benefits arise from its reduced weight range and sparser connections. The study highlights the capability of event-driven models in tackling problems with evolutionary bulk-phase and interface behaviors using the digital library approach.

Physics-Transfer Learning for Material Strength Screening

The strength of materials, like many problems in the natural sciences, spans multiple length and time scales, and the solution has to balance accuracy and performance. Peierls stress is one of the central concepts in crystal plasticity that measures the strength through the resistance of a dislocation to plastic flow. The determination of Peierls stress involves a multiscale nature depending on both elastic lattice responses and the energy landscape of crystal slips. Material screening by strength via the Peierls stress from first-principles calculations is computationally intractable for the nonlocal characteristics of dislocations, and not included in the state-of-the-art computational material databases. In this work, we propose a physics-transfer framework to learn the physics of crystal plasticity from empirical atomistic simulations and then predict the Peierls stress from chemically accurate density functional theory-based calculations of material parameters. Notably, the strengths of single-crystalline metals can be predicted from a few single-point calculations for the deformed lattice and on the {\gamma} surface, allowing efficient, high-throughput screening for material discovery. Uncertainty quantification is carried out to assess the accuracy of models and sources of errors, showing reduced physical and system uncertainties in the predictions by elevating the fidelity of training models. This physics-transfer framework can be generalized to other problems facing the accuracy-performance dilemma, by harnessing the hierarchy of physics in the multiscale models of materials science.

Predicting Fatigue Crack Growth via Path Slicing and Re-Weighting

Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design. However, fatigue often involves entangled complexities of material microstructures and service conditions, making diagnosis and prognosis of fatigue damage challenging. We report a statistical learning framework to predict the growth of fatigue cracks and the life-to-failure of the components under loading conditions with uncertainties. Digital libraries of fatigue crack patterns and the remaining life are constructed by high-fidelity physical simulations. Dimensionality reduction and neural network architectures are then used to learn the history dependence and nonlinearity of fatigue crack growth. Path-slicing and re-weighting techniques are introduced to handle the statistical noises and rare events. The predicted fatigue crack patterns are self-updated and self-corrected by the evolving crack patterns. The end-to-end approach is validated by representative examples with fatigue cracks in plates, which showcase the digital-twin scenario in real-time structural health monitoring and fatigue life prediction for maintenance management decision-making.

A Data-Driven Approach to Morphogenesis under Structural Instability

Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict their spatiotemporal complexities. A machine-learning framework is proposed based on the physical modeling of morphogenesis triggered by internal or external forcing. Digital libraries of structural patterns are constructed from the simulation data, which are then used to recognize the abnormalities, predict their development, and assist in risk assessment and prognosis. The capabilities to identify the key bifurcation characteristics and predict the history-dependent development from the global and local features are demonstrated by examples of brain growth and aerospace structural design, which offer guidelines for disease diagnosis/prognosis and instability-tolerant design.