Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigen-vectors of the graph Laplacian. Graph laplacians are used to find low dimensional structures in high dimensional data. Here too, ER based analysis has advantages over eign-vector based methods. Unfortunately Von Luxburg et al. (2010) show that, when vertices correspond to a sample from a distribution over a metric space, the limit of the ER between distant points converges to a trivial quantity that holds no information about the structure of the graph. We show that by using scaling resistances in a graph with $n$ vertices by $n^2$, one gets a meaningful limit of the voltages and of effective resistances. We also show that by adding a "ground" node to a metric graph one gets a simple and natural way to compute all of the distances from a chosen point to all other points.

For a prolific art collector, Nicolai Tangen is remarkably relaxed about the prospect of masterpieces created by robots. The threat of AI-made paintings, impossible to distinguish from human brushstrokes, has sparked soul-searching and paranoia in the art world, but not with Tangen. "Hey, if it creates better art that's fantastic," says the Norwegian philanthropist, art historian and boss of the world's biggest sovereign wealth fund. "If you create something which is even more aesthetically pleasing, what's wrong about that?" Tangen's own gallery, a converted grain silo in the Norwegian seaside resort of Kristiansand, will open later this year to display one of the world's biggest collections of Nordic modernist art. Tangen has amassed more than 5,000 works by 300 artists.

For decades, people have been seeking for fishlike flapping motions that can realize underwater propulsion with low energy cost. Complexity of the nonstationary flow field around the flapping body makes this problem very difficult. In earlier studies, motion patterns are usually prescribed as certain periodic functions which constrains the following optimization process in a small subdomain of the whole motion space. In this work, to avoid this motion constraint, a variational autoencoder (VAE) is designed to compress various flapping motions into a simple action vector. Then we let a flapping airfoil continuously interact with water tunnel environment and adjust its action accordingly through a reinforcement learning (RL) framework. By this automatic close-looped experiment, we obtain several motion patterns that can result in high hydrodynamic efficiency comparing to pure harmonic motions with the same thrust level. And we find that, after numerous trials and errors, RL trainings in current experiment always converge to motion patterns that are close to harmonic motions. In other words, current work proves that harmonic motion with appropriate amplitude and frequency is always an optimal choice for efficient underwater propulsion. Furthermore, the RL framework proposed here can be also extended to the study of other complex swimming problems, which might pave the way for the creation of a robotic fish that can swim like a real fish.

Fault diagnosis is essential in industrial processes for monitoring the conditions of important machines. With the ever-increasing complexity of working conditions and demand for safety during production and operation, different diagnosis methods are required, and more importantly, an integrated fault diagnosis system that can cope with multiple tasks is highly desired. However, the diagnosis subtasks are often studied separately, and the currently available methods still need improvement for such a generalized system. To address this issue, we propose the Generalized Out-of-distribution Fault Diagnosis (GOOFD) framework to integrate diagnosis subtasks, such as fault detection, fault classification, and novel fault diagnosis. Additionally, a unified fault diagnosis method based on internal contrastive learning is put forward to underpin the proposed generalized framework. The method extracts features utilizing the internal contrastive learning technique and then recognizes the outliers based on the Mahalanobis distance. Experiments are conducted on a simulated benchmark dataset as well as two practical process datasets to evaluate the proposed framework. As demonstrated in the experiments, the proposed method achieves better performance compared with several existing techniques and thus verifies the effectiveness of the proposed framework.

We examine how transformers cope with two challenges: learning basic integer arithmetic, and generalizing to longer sequences than seen during training. We find that relative position embeddings enable length generalization for simple tasks, such as addition: models trained on $5$-digit numbers can perform $15$-digit sums. However, this method fails for multiplication, and we propose train set priming: adding a few ($10$ to $50$) long sequences to the training set. We show that priming allows models trained on $5$-digit $\times$ $3$-digit multiplications to generalize to $35\times 3$ examples. We also show that models can be primed for different generalization lengths, and that the priming sample size scales as the logarithm of the training set size. Finally, we discuss potential applications of priming beyond arithmetic.

In this article, a tutorial introduction to visual-inertial navigation(VIN) is presented. Visual and inertial perception are two complementary sensing modalities. Cameras and inertial measurement units (IMU) are the corresponding sensors for these two modalities. The low cost and light weight of camera-IMU sensor combinations make them ubiquitous in robotic navigation. Visual-inertial Navigation is a state estimation problem, that estimates the ego-motion and local environment of the sensor platform. This paper presents visual-inertial navigation in the classical state estimation framework, first illustrating the estimation problem in terms of state variables and system models, including related quantities representations (Parameterizations), IMU dynamic and camera measurement models, and corresponding general probabilistic graphical models (Factor Graph). Secondly, we investigate the existing model-based estimation methodologies, these involve filter-based and optimization-based frameworks and related on-manifold operations. We also discuss the calibration of some relevant parameters, also initialization of state of interest in optimization-based frameworks. Then the evaluation and improvement of VIN in terms of accuracy, efficiency, and robustness are discussed. Finally, we briefly mention the recent development of learning-based methods that may become alternatives to traditional model-based methods.

Accurate generation of realistic future scenarios of renewable energy generation is crucial for long-term planning and operation of electrical systems, especially considering the increasing focus on sustainable energy and the growing penetration of renewable generation in energy matrices. These predictions enable power system operators and energy planners to effectively manage the variability and intermittency associated with renewable generation, allowing for better grid stability, improved energy management, and enhanced decision-making processes. In this paper, we propose an innovative method for generating long-term hourly scenarios for wind and solar power generation, taking into consideration the correlation between these two energy sources. To achieve this, we combine the capabilities of a Variational Autoencoder (VAE) with the additional benefits of incorporating the Radial Basis Function (RBF) kernel in our artificial neural network architecture. By incorporating them, we aim to obtain a latent space with improved regularization properties. To evaluate the effectiveness of our proposed method, we conduct experiments in a representative study scenario, utilizing real-world wind and solar power generation data from the Brazil system. We compare the scenarios generated by our model with the observed data and with other sets of scenarios produced by a conventional VAE architecture. Our experimental results demonstrate that the proposed method can generate long-term hourly scenarios for wind and solar power generation that are highly correlated, accurately capturing the temporal and spatial characteristics of these energy sources. Taking advantage of the benefits of RBF in obtaining a well-regularized latent space, our approach offers improved accuracy and robustness in generating long-term hourly scenarios for renewable energy generation.

We introduce a novel method for gravitational wave detection that combines: 1) hybrid dilated convolution neural networks to accurately model both short-and long-range temporal sequential information of gravitational wave signals; and 2) graph neural networks to capture spatial correlations among gravitational wave observatories to consistently describe and identify the presence of a signal in a detector network. These spatiotemporal-graph AI models are tested for signal detection of gravitational waves emitted by quasi-circular, non-spinning and quasi-circular, spinning, non-precessing binary black hole mergers. For the latter case, we needed a dataset of 1.2 million modeled waveforms to densely sample this signal manifold. Thus, we reduced time-to-solution by training several AI models in the Polaris supercomputer at the Argonne Leadership Supercomputing Facility within 1.7 hours by distributing the training over 256 NVIDIA A100 GPUs, achieving optimal classification performance. This approach also exhibits strong scaling up to 512 NVIDIA A100 GPUs. We then created ensembles of AI models to process data from a three detector network, namely, the advanced LIGO Hanford and Livingston detectors, and the advanced Virgo detector. An ensemble of 2 AI models achieves state-of-the-art performance for signal detection, and reports seven misclassifications per decade of searched data, whereas an ensemble of 4 AI models achieves optimal performance for signal detection with two misclassifications for every decade of searched data. Finally, when we distributed AI inference over 128 GPUs in the Polaris supercomputer and 128 nodes in the Theta supercomputer, our AI ensemble is capable of processing a decade of gravitational wave data from a three detector network within 3.5 hours, i.e., 2.5 10

Recent advances in high-fidelity simulators have enabled closed-loop training of autonomous driving agents, potentially solving the distribution shift in training v.s. deployment and allowing training to be scaled both safely and cheaply. However, there is a lack of understanding of how to build effective training benchmarks for closed-loop training. In this work, we present the first empirical study which analyzes the effects of different training benchmark designs on the success of learning agents, such as how to design traffic scenarios and scale training environments. Furthermore, we show that many popular RL algorithms cannot achieve satisfactory performance in the context of autonomous driving, as they lack long-term planning and take an extremely long time to train. To address these issues, we propose trajectory value learning (TRAVL), an RL-based driving agent that performs planning with multistep look-ahead and exploits cheaply generated imagined data for efficient learning. Our experiments show that TRAVL can learn much faster and produce safer maneuvers compared to all the baselines. For more information, visit the project website: https://waabi.ai/research/travl

Environmental damage has been of much concern, particularly in coastal areas and the oceans, given climate change and the drastic effects of pollution and extreme climate events. Our present-day analytical capabilities, along with advancements in information acquisition techniques such as remote sensing, can be utilised for the management and study of coral reef ecosystems. In this paper, we present Reef-Insight, an unsupervised machine learning framework that features advanced clustering methods and remote sensing for reef habitat mapping. Our framework compares different clustering methods for reef habitat mapping using remote sensing data. We evaluate four major clustering approaches based on qualitative and visual assessments which include k-means, hierarchical clustering, Gaussian mixture model, and density-based clustering. We utilise remote sensing data featuring the One Tree Island reef in Australia's Southern Great Barrier Reef. Our results indicate that clustering methods using remote sensing data can well identify benthic and geomorphic clusters in reefs when compared with other studies. Our results indicate that Reef-Insight can generate detailed reef habitat maps outlining distinct reef habitats and has the potential to enable further insights for reef restoration projects.