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Determining process-structure-property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process-structure and structure-property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model (CPFEM) matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. To solve this stochastic inverse problem, we employ a recently developed uncertainty quantification (UQ) framework based on push-forward probability measures, which combines techniques from measure theory and Bayes rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning (ML) Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure-property linkages.
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve its solutio
Determining a process-structure-property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials design are o
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are base
Forecasting the movements of stock prices is one the most challenging problems in financial markets analysis. In this paper, we use Machine Learning (ML) algorithms for the prediction of future price movements using limit order book data. Two differe
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the algorithmic