Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation

Imbalanced Deep Learning by Minority Class Incremental Rectification

Model learning from class imbalanced training data is a long-standing and significant challenge for machine learning. In particular, existing deep learning methods consider mostly either class balanced data or moderately imbalanced data in model training, and ignore the challenge of learning from significantly imbalanced training data. To address this problem, we formulate a class imbalanced deep learning model based on batch-wise incremental minority (sparsely sampled) class rectification by hard sample mining in majority (frequently sampled) classes during model training. This model is designed to minimise the dominant effect of majority classes by discovering sparsely sampled boundaries of minority classes in an iterative batch-wise learning process. To that end, we introduce a Class Rectification Loss (CRL) function that can be deployed readily in deep network architectures. Extensive experimental evaluations are conducted on three imbalanced person attribute benchmark datasets (CelebA, X-Domain, DeepFashion) and one balanced object category benchmark dataset (CIFAR-100). These experimental results demonstrate the performance advantages and model scalability of the proposed batch-wise incremental minority class rectification model over the existing state-of-the-art models for addressing the problem of imbalanced data learning.Comment: Accepted for IEEE Trans. Pattern Analysis and Machine Intelligenc

Surface phase separation in nanosized charge-ordered manganites

Recent experiments showed that the robust charge-ordering in manganites can be weakened by reducing the grain size down to nanoscale. Weak ferromagnetism was evidenced in both nanoparticles and nanowires of charge-ordered manganites. To explain these observations, a phenomenological model based on surface phase separation is proposed. The relaxation of superexchange interaction on the surface layer allows formation of a ferromagnetic shell, whose thickness increases with decreasing grain size. Possible exchange bias and softening of the ferromagnetic transition in nanosized charge-ordered manganites are predicted.Comment: 4 pages, 3 figure

Incompressible SPH simulation of wave interaction with porous structure

In this paper an incompressible Smoothed Particle Hydrodynamics (ISPH) method is applied to investigate the flow motion in and around the porous structure. In order to describe in a simple and effective way the flow through the interface between the porous region and pure fluid region within the SPH framework, a heuristic boundary treatment method has been proposed. The ISPH model is first verified against a theoretical model of wave propagation over a porous bed and then further validated by comparing the predicted wave surface profiles and flow velocity fields with the experiment data for a typical case of flow motion around and inside a submerged porous structure. The good agreement has demonstrated that the improved ISPH model developed in this work is capable of modelling wave interaction with porous structures

Unsupervised Deep Learning by Neighbourhood Discovery

Deep convolutional neural networks (CNNs) have demonstrated remarkable success in computer vision by supervisedly learning strong visual feature representations. However, training CNNs relies heavily on the availability of exhaustive training data annotations, limiting significantly their deployment and scalability in many application scenarios. In this work, we introduce a generic unsupervised deep learning approach to training deep models without the need for any manual label supervision. Specifically, we progressively discover sample anchored/centred neighbourhoods to reason and learn the underlying class decision boundaries iteratively and accumulatively. Every single neighbourhood is specially formulated so that all the member samples can share the same unseen class labels at high probability for facilitating the extraction of class discriminative feature representations during training. Experiments on image classification show the performance advantages of the proposed method over the state-of-the-art unsupervised learning models on six benchmarks including both coarse-grained and fine-grained object image categorisation.Comment: 36th International Conference on Machine Learning (ICML'19). Code is available at https://github.com/Raymond-sci/AN