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Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some problems, this simulation is infeasible, leading to the discretization of state variable space and the need to train one neural network for each data point. This approach becomes computationally inefficient when dealing with large state variable spaces. In this paper, we consider a class of this type of stochastic optimal control problems and introduce an effective solution employing multitask neural networks. To train our multitask neural network, we introduce a novel scheme that dynamically balances the learning across tasks. Through numerical experiments on real-world derivatives pricing problems, we prove that our method outperforms state-of-the-art approaches.

Tracking ripening tomatoes is time consuming and labor intensive. Artificial intelligence technologies combined with those of computer vision can help users optimize the process of monitoring the ripening status of plants. To this end, we have proposed a tomato ripening monitoring approach based on deep learning in complex scenes. The objective is to detect mature tomatoes and harvest them in a timely manner. The proposed approach is declined in two parts. Firstly, the images of the scene are transmitted to the pre-processing layer. This process allows the detection of areas of interest (area of the image containing tomatoes). Then, these images are used as input to the maturity detection layer. This layer, based on a deep neural network learning algorithm, classifies the tomato thumbnails provided to it in one of the following five categories: green, brittle, pink, pale red, mature red. The experiments are based on images collected from the internet gathered through searches using tomato state across diverse languages including English, German, French, and Spanish. The experimental results of the maturity detection layer on a dataset composed of images of tomatoes taken under the extreme conditions, gave a good classification rate.

Typical pipelines for model geometry generation in computational biomedicine stem from images, which are usually considered to be at rest, despite the object being in mechanical equilibrium under several forces. We refer to the stress-free geometry computation as the reference configuration problem, and in this work we extend such a formulation to the theory of fully nonlinear poroelastic media. The main steps are (i) writing the equations in terms of the reference porosity and (ii) defining a time dependent problem whose steady state solution is the reference porosity. This problem can be computationally challenging as it can require several hundreds of iterations to converge, so we propose the use of Anderson acceleration to speed up this procedure. Our evidence shows that this strategy can reduce the number of iterations up to 80\%. In addition, we note that a primal formulation of the nonlinear mass conservation equations is not consistent due to the presence of second order derivatives of the displacement, which we alleviate through adequate mixed formulations. All claims are validated through numerical simulations in both idealized and realistic scenarios.

Random fields are ubiquitous mathematical structures in physics, with applications ranging from thermodynamics and statistical physics to quantum field theory and cosmology. Recent works on information geometry of Gaussian random fields proposed mathematical expressions for the components of the metric tensor of the underlying parametric space, allowing the computation of the Gaussian curvature in each point of the manifold that represents the space of all possible parameter values that define such mathematical model. A key result in the dynamics of these random fields concerns the curvature effect, a series of variations in the curvature that happens in the parametric space when there are significant increase/decrease in the inverse temperature parameter. In this paper, we propose a numerical algorithm for the computation of geodesic curves in the Gaussian random fields manifold by deriving the 27 Christoffel symbols of the metric required for the definition of the Euler-Lagrange equations. The fourth-order Runge-Kutta method is applied to solve the Euler-Lagrange equations using an iterative approach based in Markov Chain Monte Carlo simulation. Our results reveal that, when the system undergoes phase trasitions, the geodesic dispersion phenomenon emerges: the geodesic curve obtained by reversing the system of differential equations in time, diverges from the original geodesic curve, as we move from zero curvature configurations (Euclidean geometry) to negative curvature configurations (hyperbolic-like geometry), and vice-versa. This phenomenon suggest that, time irreversibility in random field dynamics can be a direct consequence of the geometry of the underlying parametric space.

Since the start of the operational use of ensemble prediction systems, ensemble-based probabilistic forecasting has become the most advanced approach in weather prediction. However, despite the persistent development of the last three decades, ensemble forecasts still often suffer from the lack of calibration and might exhibit systematic bias, which calls for some form of statistical post-processing. Nowadays, one can choose from a large variety of post-processing approaches, where parametric methods provide full predictive distributions of the investigated weather quantity. Parameter estimation in these models is based on training data consisting of past forecast-observation pairs, thus post-processed forecasts are usually available only at those locations where training data are accessible. We propose a general clustering-based interpolation technique of extending calibrated predictive distributions from observation stations to any location in the ensemble domain where there are ensemble forecasts at hand. Focusing on the ensemble model output statistics (EMOS) post-processing technique, in a case study based on wind speed ensemble forecasts of the European Centre for Medium-Range Weather Forecasts, we demonstrate the predictive performance of various versions of the suggested method and show its superiority over the regionally estimated and interpolated EMOS models and the raw ensemble forecasts as well.

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural networks, PINNs are trained as surrogate models to approximate solutions without the need for label data. Nevertheless, even though PINNs have shown remarkable performance, they can face difficulties, especially when dealing with equations featuring rapidly changing solutions. These difficulties encompass slow convergence, susceptibility to becoming trapped in local minima, and reduced solution accuracy. To address these issues, we propose a binary structured physics-informed neural network (BsPINN) framework, which employs binary structured neural network (BsNN) as the neural network component. By leveraging a binary structure that reduces inter-neuron connections compared to fully connected neural networks, BsPINNs excel in capturing the local features of solutions more effectively and efficiently. These features are particularly crucial for learning the rapidly changing in the nature of solutions. In a series of numerical experiments solving Burgers equation, Euler equation, Helmholtz equation, and high-dimension Poisson equation, BsPINNs exhibit superior convergence speed and heightened accuracy compared to PINNs. From these experiments, we discover that BsPINNs resolve the issues caused by increased hidden layers in PINNs resulting in over-smoothing, and prevent the decline in accuracy due to non-smoothness of PDEs solutions.

The classification of carotid artery ultrasound images is a crucial means for diagnosing carotid plaques, holding significant clinical relevance for predicting the risk of stroke. Recent research suggests that utilizing plaque segmentation as an auxiliary task for classification can enhance performance by leveraging the correlation between segmentation and classification tasks. However, this approach relies on obtaining a substantial amount of challenging-to-acquire segmentation annotations. This paper proposes a novel weakly supervised auxiliary task learning network model (WAL-Net) to explore the interdependence between carotid plaque classification and segmentation tasks. The plaque classification task is primary task, while the plaque segmentation task serves as an auxiliary task, providing valuable information to enhance the performance of the primary task. Weakly supervised learning is adopted in the auxiliary task to completely break away from the dependence on segmentation annotations. Experiments and evaluations are conducted on a dataset comprising 1270 carotid plaque ultrasound images from Wuhan University Zhongnan Hospital. Results indicate that the proposed method achieved an approximately 1.3% improvement in carotid plaque classification accuracy compared to the baseline network. Specifically, the accuracy of mixed-echoic plaques classification increased by approximately 3.3%, demonstrating the effectiveness of our approach.

In this study, we proposed a design methodology for a piezoelectric energy-harvesting device optimized for maximal power generation at a designated frequency using topology optimization. The proposed methodology emphasizes the design of a unimorph-type piezoelectric energy harvester, wherein a piezoelectric film is affixed to a singular side of a silicon cantilever beam. Both the substrate and the piezoelectric film components underwent concurrent optimization. Constraints were imposed to ensure that the resultant design is amenable to microfabrication, with specific emphasis on the etchability of piezoelectric energy harvesters. Several numerical examples were provided to validate the efficacy of the proposed method. The results showed that the proposed method derives both the substrate and piezoelectric designs that maximize the electromechanical coupling coefficient and allows the eigenfrequency of the device and minimum output voltage to be set to the desired values. Furthermore, the proposed method can provide solutions that satisfy the cross-sectional shape, substrate-depend, and minimum output voltage constraints. The solutions obtained by the proposed method are manufacturable in the field of microfabrication.

Object recognition and object pose estimation in robotic grasping continue to be significant challenges, since building a labelled dataset can be time consuming and financially costly in terms of data collection and annotation. In this work, we propose a synthetic data generation method that minimizes human intervention and makes downstream image segmentation algorithms more robust by combining a generated synthetic dataset with a smaller real-world dataset (hybrid dataset). Annotation experiments show that the proposed synthetic scene generation can diminish labelling time dramatically. RGB image segmentation is trained with hybrid dataset and combined with depth information to produce pixel-to-point correspondence of individual segmented objects. The object to grasp is then determined by the confidence score of the segmentation algorithm. Pick-and-place experiments demonstrate that segmentation trained on our hybrid dataset (98.9%, 70%) outperforms the real dataset and a publicly available dataset by (6.7%, 18.8%) and (2.8%, 10%) in terms of labelling and grasping success rate, respectively. Supplementary material is available at //sites.google.com/view/synthetic-dataset-generation.

This work is thought as an operative guide to discrete exterior calculus (DEC), but at the same time with a rigorous exposition. We present a version of (DEC) on cubic cell, defining it for discrete manifolds. An example of how it works, it is done on the discrete torus, where usual Gauss and Stokes theorems are recovered.