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A twin law is not a symmetry operation of the full set of basis points. [2] Twin laws include reflection operations, rotation operations, and the inversion operation. Reflection twinning is described by the Miller indices of the twin plane (i.e. {hkl}) while rotational twinning is described by the direction of the twin axis (i.e. <hkl ...
Physics-informed neural networks for solving Navier–Stokes equations. Physics-informed neural networks (PINNs), [1] also referred to as Theory-Trained Neural Networks (TTNs), [2] are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs).
A twin boundary is a defect that introduces a plane of mirror symmetry in the ordering of a crystal. For example, in cubic close-packed crystals, the stacking sequence of a twin boundary would be ABCABCBACBA. On planes of single crystals, steps between atomically flat terraces can also be regarded as planar defects.
Feature learning is intended to result in faster training or better performance in task-specific settings than if the data was input directly (compare transfer learning). [1] In machine learning (ML), feature learning or representation learning [2] is a set of techniques that allow a system to automatically discover the representations needed ...
The striped borders correspond to perfectly matched layers, which are used to simulate open boundaries by absorbing the outgoing waves. A perfectly matched layer ( PML ) is an artificial absorbing layer for wave equations , commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially ...
In machine learning (ML), a learning curve (or training curve) is a graphical representation that shows how a model's performance on a training set (and usually a validation set) changes with the number of training iterations (epochs) or the amount of training data. [1]
In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number of tunable parameters in a model, it becomes more ...
In machine learning, the margin of a single data point is defined to be the distance from the data point to a decision boundary. Note that there are many distances and decision boundaries that may be appropriate for certain datasets and goals.