Abstract-- Estimation of signed distance functions (SDFs) from point cloud data has been shown to benefit many robot autonomy capabilities, including localization, mapping, motion planning, and control. Methods that support online and large-scale SDF reconstruction tend to rely on discrete volumetric data structures, which affect the continuity and differentiability of the SDF estimates. Recently, using implicit features, neural network methods have demonstrated high-fidelity and differentiable SDF reconstruction but they tend to be less efficient, can experience catastrophic forgetting and memory limitations in large environments, and are often restricted to truncated SDFs. This work proposes -SDF, a hybrid method that combines an explicit prior obtained from gradient-augmented octree interpolation with an implicit neural residual. Our method achieves non-truncated (Euclidean) SDF reconstruction with computational and memory efficiency comparable to volumetric methods and differentiability and accuracy comparable to neural network methods. Extensive experiments demonstrate that -SDF outperforms the state of the art in terms of accuracy and efficiency, providing a scalable solution for downstream tasks in robotics and computer vision. Accurate and differentiable geometric environment representations are critical for many functions in robot autonomy and computer vision, including simultaneous localization and mapping [1]-[3], rendering and AR/VR [4]-[6], autonomous navigation [7], [8] and manipulation [9]-[11].

In this study, we firstly propose an auxiliary equation neural networks method (AENNM), an innovative analytical method that integrates neural networks (NNs) models with the auxiliary equation method to obtain exact solutions of nonlinear partial differential equations (NLPDEs). A key novelty of this method is the introduction of a novel activation function derived from the solutions of the Riccati equation, establishing a new mathematical link between differential equations theory and deep learning. By combining the strong approximation capability of NNs with the high precision of symbolic computation, AENNM significantly enhances computational efficiency and accuracy. To demonstrate the effectiveness of the AENNM in solving NLPDEs, three numerical examples are investigated, including the nonlinear evolution equation, the Korteweg-de Vries-Burgers equation, and the (2+1)-dimensional Boussinesq equation. Furthermore, some new trial functions are constructed by setting specific activation functions within the "2-2-2-1" and "3-2-2-1" NNs models. By embedding the auxiliary equation method into the NNs framework, we derive previously unreported solutions. The exact analytical solutions are expressed in terms of hyperbolic functions, trigonometric functions, and rational functions. Finally, three-dimensional plots, contour plots, and density plots are presented to illustrate the dynamic characteristics of the obtained solutions. This research provides a novel methodological framework for addressing NLPDEs, with broad applicability across scientific and engineering fields.

In this work, the ability of rare VHE gamma ray selection with neural network methods is investigated in the case when cosmic radiation flux strongly prevails (ratio up to {10^4} over the gamma radiation flux from a point source). This ratio is valid for the Crab Nebula in the TeV energy range, since the Crab is a well-studied source for calibration and test of various methods and installations in gamma astronomy. The part of TAIGA experiment which includes three Imaging Atmospheric Cherenkov Telescopes observes this gamma-source too. Cherenkov telescopes obtain images of Extensive Air Showers. Hillas parameters can be used to analyse images in standard processing method, or images can be processed with convolutional neural networks. In this work we would like to describe the main steps and results obtained in the gamma/hadron separation task from the Crab Nebula with neural network methods. The results obtained are compared with standard processing method applied in the TAIGA collaboration and using Hillas parameter cuts. It is demonstrated that a signal was received at the level of higher than 5.5{\sigma} in 21 hours of Crab Nebula observations after processing the experimental data with the neural network method.

Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply-demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained and the parameters are identified, optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge-Kutta numerical method of order 4/5 (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system's components. However, this approach requires significant time and computational power due to the need for model training.

Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents significant challenges due to the complexity of the underlying equations and the computational resources required for accurate solutions. To address this, we have developed a novel method using neural network (NN) to efficiently solve solitons. A similar NN approach is Physics-Informed Neural Networks (PINN). In a comparative analysis between our method and PINN, we find that our method achieves shorter computation times while maintaining the same level of accuracy. This advancement in computational efficiency not only overcomes current limitations but also opens new avenues for studying topological solitons and their dynamical behavior.

Cooperating autonomous underwater vehicles (AUVs) often rely on acoustic communication to coordinate their actions effectively. However, the reliability of underwater acoustic communication decreases as the communication range between vehicles increases. Consequently, teams of cooperating AUVs typically make conservative assumptions about the maximum range at which they can communicate reliably. To address this limitation, we propose a novel approach that involves learning a map representing the probability of successful communication based on the locations of the transmitting and receiving vehicles. This probabilistic communication map accounts for factors such as the range between vehicles, environmental noise, and multi-path effects at a given location. In pursuit of this goal, we investigate the application of Gaussian process binary classification to generate the desired communication map. We specialize existing results to this specific binary classification problem and explore methods to incorporate uncertainty in vehicle location into the mapping process. Furthermore, we compare the prediction performance of the probability communication map generated using binary classification with that of a signal-to-noise ratio (SNR) communication map generated using Gaussian process regression. Our approach is experimentally validated using communication and navigation data collected during trials with a pair of Virginia Tech 690 AUVs.

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of neural networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.

Recent advances in image data processing through machine learning and especially deep neural networks (DNNs) allow for new optimization and performance-enhancement schemes for radiation detectors and imaging hardware through data-endowed artificial intelligence. We give an overview of data generation at photon sources, deep learning-based methods for image processing tasks, and hardware solutions for deep learning acceleration. Most existing deep learning approaches are trained offline, typically using large amounts of computational resources. However, once trained, DNNs can achieve fast inference speeds and can be deployed to edge devices. A new trend is edge computing with less energy consumption (hundreds of watts or less) and real-time analysis potential. While popularly used for edge computing, electronic-based hardware accelerators ranging from general purpose processors such as central processing units (CPUs) to application-specific integrated circuits (ASICs) are constantly reaching performance limits in latency, energy consumption, and other physical constraints. These limits give rise to next-generation analog neuromorhpic hardware platforms, such as optical neural networks (ONNs), for high parallel, low latency, and low energy computing to boost deep learning acceleration.

Rural and remote communities in Canada often rely on satellites to access the internet, but those connections are fraught with many glitches and service interruptions because the technology can be unreliable. The inequity in internet access between these communities and those who live in cities is an ongoing problem with myriad consequences for Canada's economic productivity. A team of researchers from the University of Waterloo and the National Research Council (NRC) are tackling this long-standing issue using machine learning. The team's method, the Multivariate Variance-based Genetic Ensemble Learning Method, merges several existing AI-driven models to detect anomalies in satellites and satellite networks before they can cause major problems. "For remote areas in Canada and around the world, satellites are often their best option for maintaining internet access," said Peng Hu, an adjunct professor of computer science and statistics and actuarial science at Waterloo and the corresponding author of the study.

One of the most crucial and challenging steps in the development of robots intended to restore the mobility of the human body after a loss of functional movement due to neurological injuries is the IK of physiological limbs, which consists of computing joint angles configuration based on the predefined input workspace coordinates. Generally speaking, the complexity of the IK problem depends on the geometry of the manipulator and the nonlinearity of its model, which gives the corresponding relation between the task and the joint spaces. Furthermore, IK solution is essential for the real-time control. Thus, it must be precise in order to enable the robot to perform the task successfully. IK techniques can be classified into three categories, namely, analytical method, numerical method, and intelligent method. The analytical method solves IK by solving a set of closed-form equations that can give the generalized coordinate value that drives the end effector of the manipulator to the predefined target position [1].