A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems.

Developing methods of domain decomposition (DDM) has been widely studied in the field of numerical computation to estimate solutions of partial differential equations (PDEs). Several case studies have also reported that it is feasible to use the domain decomposition approach for the application of artificial neural networks (ANNs) to solve PDEs. In this study, we devised a pretraining scheme called smoothing with a basis reconstruction process on the structure of ANNs and then implemented the classic concept of DDM. The pretraining process that is engaged at the beginning of the training epochs can make the approximation basis become well-posed on the domain so that the quality of the estimated solution is enhanced. We report that such a well-organized pretraining scheme may affect any NN-based PDE solvers as we can speed up the approximation, improve the solution's smoothness, and so on. Numerical experiments were performed to verify the effectiveness of the proposed DDM method on ANN for estimating solutions of PDEs. Results revealed that this method could be used as a tool for tasks in general machine learning.

A Cognitive Sample Consensus Method for the Stitching of Drone-Based Aerial Images Supported by a Generative Adversarial Network for False Positive Reduction.

When using drone-based aerial images for panoramic image generation, the unstableness of the shooting angle often deteriorates the quality of the resulting image. To prevent these polluting effects from affecting the stitching process, this study proposes deep learning-based outlier rejection schemes that apply the architecture of the generative adversarial network (GAN) to reduce the falsely estimated hypothesis relating to a transform produced by a given baseline method, such as the random sample consensus method (RANSAC). To organize the training dataset, we obtain rigid transforms to resample the images via the operation of RANSAC for the correspondences produced by the scale-invariant feature transform descriptors. In the proposed method, the discriminator of GAN makes a pre-judgment of whether the estimated target hypothesis sample produced by RANSAC is true or false, and it recalls the generator to confirm the authenticity of the discriminator's inference by comparing the differences between the generated samples and the target sample. We have tested the proposed method for drone-based aerial images and some miscellaneous images. The proposed method has been shown to have relatively stable and good performances even in receiver-operated tough conditions.

Termite population size estimation based on termite tunnel patterns using a convolutional neural network.

Subterranean termites live in large colonies under the ground where they build an elaborate network of tunnels for foraging. In this study, we explored how the termite population size can be estimated using partial information on tunnel patterns. To achieve this, we used an agent-based model to create tunnel patterns that were characterized by three variables: the number of simulated termites (N), passing probability of two termites encountering one another (P), and distance that termites move soil particles (D). To explore whether the N value could be estimated using a partial termite tunnel pattern, we generated four tunnel pattern groups by partially obscuring different areas in an image of a complete tunnel pattern, where: (1) the outer area of the tunnel pattern was obscured (I-pattern); (2) half of the tunnel pattern was obscured (H-pattern); (3) the inner region of the tunnel pattern was obscured (O-pattern); and (4) I- and O-patterns (IO-pattern) were combined. For each group, 80% of the tunnel patterns were used to train a convolutional neural network while the remaining 20% were used for estimating the N value. Estimation results showed that the N estimates for IO-patterns were the most accurate, followed by I-, H-, and O-patterns. This indicates that termite population size can be estimated based on tunnel information near the center of a colony. We briefly discuss the advantages and disadvantages of this method for estimating termite population size.

Differentiation of the Follicular Neoplasm on the Gray-Scale US by Image Selection Subsampling along with the Marginal Outline Using Convolutional Neural Network.

We conducted differentiations between thyroid follicular adenoma and carcinoma for 8-bit bitmap ultrasonography (US) images utilizing a deep-learning approach. For the data sets, we gathered small-boxed selected images adjacent to the marginal outline of nodules and applied a convolutional neural network (CNN) to have differentiation, based on a statistical aggregation, that is, a decision by majority. From the implementation of the method, introducing a newly devised, scalable, parameterized normalization treatment, we observed meaningful aspects in various experiments, collecting evidence regarding the existence of features retained on the margin of thyroid nodules, such as 89.51% of the overall differentiation accuracy for the test data, with 93.19% of accuracy for benign adenoma and 71.05% for carcinoma, from 230 benign adenoma and 77 carcinoma US images, where we used only 39 benign adenomas and 39 carcinomas to train the CNN model, and, with these extremely small training data sets and their model, we tested 191 benign adenomas and 38 carcinomas. We present numerical results including area under receiver operating characteristic (AUROC).