Physics and equality constrained artificial neural networks (PECANN) are grounded in methods of constrained optimization to properly constrain the solution of partial differential equations (PDEs) with their boundary and initial conditions and any high-fidelity data that may be available. To this end, adoption of the augmented Lagrangian method within the PECANN framework is paramount for learning the solution of PDEs without manually balancing the individual loss terms in the objective function used for determining the parameters of the neural network. Generally speaking, ALM combines the merits of the penalty and Lagrange multiplier methods while avoiding the ill conditioning and convergence issues associated singly with these methods . In the present work, we apply our PECANN framework to solve forward and inverse problems that have an expanded and diverse set of constraints. We show that ALM with its conventional formulation to update its penalty parameter and Lagrange multipliers stalls for such challenging problems. To address this issue, we propose an adaptive ALM in which each constraint is assigned a unique penalty parameter that evolve adaptively according to a rule inspired by the adaptive subgradient method. Additionally, we revise our PECANN formulation for improved computational efficiency and savings which allows for mini-batch training. We demonstrate the efficacy of our proposed approach by solving several forward and PDE-constrained inverse problems with noisy data, including simulation of incompressible fluid flows with a primitive-variables formulation of the Navier-Stokes equations up to a Reynolds number of 1000.

Modern quadrupedal robots are highly praised for their high degree of mobility, maneuverability, and ability to traverse through diverse terrains, making them well-suited for applications such as inspection and delivery [1, 2]. However, these robots' performance comes at the price of complex mechanical structures with many degrees of freedom to control. As a result, developing control systems that enable these robots to efficiently move and operate in dynamically changing environments is one of the most important tasks in the field of quadruped robotics research. Model predictive control (MPC) includes a range of widely adopted control methods [3] not only capable of efficiently handling industrial problems that entail complex processes [4, 5, 6], but that has also been successfully applied to other problems such as indoor microclimate control given its ability to operate over finite prediction horizons [?, 7, 8, 9]. In one of the early works on MPC's application to the motion of a real quadrupedal robot [10], the nonlinear optimization problem was converted into a quadratic program (QP) by linearizing the system dynamics along a desired walking trajectory. Importantly, the accuracy of the immediate robot dynamics approximation turned out to be more significant than that of the robot dynamics approximation over the prediction horizon. Notwithstanding the advantages of linearization of the system dynamics, nonlinear MPC finds application for quadrupedal robots [11]. As traditional MPC solvers can suffer from short planning horizon, convergence to local optima, errors in the dynamics model, and failure to account for future replanning [12]. Several new MPC-based control schemes have been introduced, each aiming to improve specific characteristics of interest.

In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential operator is realized by automatic differentiation. The eigenfunction of the eigenvalue problem is learned by the neural network and the iterative algorithms are implemented by optimizing the specially defined loss function. The largest positive eigenvalue, smallest eigenvalue and interior eigenvalues with the given prior knowledge can be solved efficiently. We examine the applicability and accuracy of our methods in the numerical experiments in one dimension, two dimensions and higher dimensions. Numerical results show that accurate eigenvalue and eigenfunction approximations can be obtained by our methods.

The task of Argument Mining, that is extracting argumentative sentences for a specific topic from large document sources, is an inherently difficult task for machine learning models and humans alike, as large Argument Mining datasets are rare and recognition of argumentative sentences requires expert knowledge. The task becomes even more difficult if it also involves stance detection of retrieved arguments. Given the cost and complexity of creating suitably large Argument Mining datasets, we ask whether it is necessary for acceptable performance to have datasets growing in size. Our findings show that, when using carefully composed training samples and a model pretrained on related tasks, we can reach 95% of the maximum performance while reducing the training sample size by at least 85%. This gain is consistent across three Argument Mining tasks on three different datasets. We also publish a new dataset for future benchmarking.

In question answering requiring common sense, language models (e.g., GPT-3) have been used to generate text expressing background knowledge that helps improve performance. Yet the cost of working with such models is very high; in this work, we finetune smaller language models to generate useful intermediate context, referred to here as elaborations. Our framework alternates between updating two language models -- an elaboration generator and an answer predictor -- allowing each to influence the other. Using less than 0.5% of the parameters of GPT-3, our model outperforms alternatives with similar sizes and closes the gap on GPT-3 on four commonsense question answering benchmarks. Human evaluations show that the quality of the generated elaborations is high.

Soil assessment is important for mobile robot planning and navigation on natural and planetary environments. Terramechanic characteristics can be inferred from the thermal behaviour of soils under the influence of sunlight using remote sensors such as Long-Wave Infrared cameras. However, this behaviour is greatly affected by the low atmospheric pressures of planets such as Mars, so practical models are needed to relate robot remote sensing data on Earth to target planetary exploration conditions. This article proposes a general framework based on multipurpose environmental chambers to generate representative diurnal cycle dataset pairs that can be useful to relate the thermal behaviour of a soil on Earth to the corresponding behaviour under planetary pressure conditions using remote sensing. Furthermore, we present an application of the proposed framework to generate datasets using the UMA-Laserlab chamber, which can replicate the atmospheric \ch{CO2} composition of Mars. In particular, we analyze the thermal behaviour of four soil samples of different granularity by comparing replicated Martian surface conditions and their Earth's diurnal cycle equivalent. Results indicate a correlation between granularity and thermal inertia that is consistent with available Mars surface measurements recorded by rovers. The resulting dataset pairs, consisting of representative diurnal cycle thermal images with heater, air, and subsurface temperatures, have been made available for the scientific community.

Active Simultaneous Localisation and Mapping (SLAM) is a critical problem in autonomous robotics, enabling robots to navigate to new regions while building an accurate model of their surroundings. Visual SLAM is a popular technique that uses virtual elements to enhance the experience. However, existing frontier-based exploration strategies can lead to a non-optimal path in scenarios where there are multiple frontiers with similar distance. This issue can impact the efficiency and accuracy of Visual SLAM, which is crucial for a wide range of robotic applications, such as search and rescue, exploration, and mapping. To address this issue, this research combines both an existing Visual-Graph SLAM known as ExploreORB with reinforcement learning. The proposed algorithm allows the robot to learn and optimize exploration routes through a reward-based system to create an accurate map of the environment with proper frontier selection. Frontier-based exploration is used to detect unexplored areas, while reinforcement learning optimizes the robot's movement by assigning rewards for optimal frontier points. Graph SLAM is then used to integrate the robot's sensory data and build an accurate map of the environment. The proposed algorithm aims to improve the efficiency and accuracy of ExploreORB by optimizing the exploration process of frontiers to build a more accurate map. To evaluate the effectiveness of the proposed approach, experiments will be conducted in various virtual environments using Gazebo, a robot simulation software. Results of these experiments will be compared with existing methods to demonstrate the potential of the proposed approach as an optimal solution for SLAM in autonomous robotics.

Phase association groups seismic wave arrivals according to their originating earthquakes. It is a fundamental task in a seismic data processing pipeline, but challenging to perform for smaller, high-rate seismic events which carry fundamental information about earthquake dynamics, especially with a commonly assumed inaccurate wave speed model. As a consequence, most association methods focus on larger events that occur at a lower rate and are thus easier to associate, even though microseismicity provides a valuable description of the elastic medium properties in the subsurface. In this paper, we show that association is possible at rates much higher than previously reported even when the wave speed is unknown. We propose Harpa, a high-rate seismic phase association method which leverages deep neural fields to build generative models of wave speeds and associated travel times, and first solves a joint spatio--temporal source localization and wave speed recovery problem, followed by association. We obviate the need for associated phases by interpreting arrival time data as probability measures and using an optimal transport loss to enforce data fidelity. The joint recovery problem is known to admit a unique solution under certain conditions but due to the non-convexity of the corresponding loss a simple gradient scheme converges to poor local minima. We show that this is effectively mitigated by stochastic gradient Langevin dynamics (SGLD). Numerical experiments show that \harpa~efficiently associates high-rate seismicity clouds over complex, unknown wave speeds and graciously handles noisy and missing picks.

This paper presents a novel and efficient collision checking approach called Updating and Collision Check Skipping Quad-tree (USQ) for multi-robot motion planning. USQ extends the standard quad-tree data structure through a time-efficient update mechanism, which significantly reduces the total number of collision checks and the collision checking time. In addition, it handles transitions at the quad-tree quadrant boundaries based on worst-case trajectories of agents. These extensions make quad-trees suitable for efficient collision checking in multi-robot motion planning of large robot teams. We evaluate the efficiency of USQ in comparison with Regenerating Quad-tree (RQ) from scratch at each timestep and naive pairwise collision checking across a variety of randomized environments. The results indicate that USQ significantly reduces the number of collision checks and the collision checking time compared to other baselines for different numbers of robots and map sizes. In a 50-robot experiment, USQ accurately detected all collisions, outperforming RQ which has longer run-times and/or misses up to 25% of collisions.

This research develops a novel sensor for aquatic robots inspired by the whiskers of harbor seals. This sensor can detect the movement of water, offering valuable data on speed, currents, barriers, and water disturbance. It employs a mechano-magnetic system, separating the whisker-like drag part from the electronic section, enhancing water resistance and durability. The flexible design allows customizing the drag component's shape for different uses. The study uses an analytical model to examine the sensor's capabilities, including aspects such as shape, cross-sectional area, ratio, and immersion depth of the whisker part. It also explores the effects of design on Vortex-Induced Vibrations (VIVs), a key focus in the study of biological and robotic aquatic whiskers. The sensor's practical use was tested on a remote-controlled boat, showing its proficiency in estimating water flow speed. This development has enormous potential to enhance navigation and perception for aquatic robots in various applications.