Rough path theory is an abstract mathematical tool-set that allows the modelling This article provides a concise overview of and analysis of evolving systems across a some of the recent advances in the application broad spectrum of use cases. It extends of rough path theory to machine Newton's and Itô's calculus to model the learning. Controlled differential equations interactions of complex and messy data (CDEs) are discussed as the key mathematical streams. It has been influential within model to describe the interaction mathematics, in particular in stochastic of a stream with a physical control system.

This paper presents a family of autonomous Unmanned Aerial Vehicles (UAVs) platforms designed for a diverse range of indoor and outdoor applications. The proposed UAV design is highly modular in terms of used actuators, sensor configurations, and even UAV frames. This allows to achieve, with minimal effort, a proper experimental setup for single, as well as, multi robot scenarios. Presented platforms are intended to facilitate the transition from simulations, and simplified laboratory experiments, into the deployment of aerial robots into uncertain and hard-to-model real-world conditions. We present mechanical designs, electric configurations, and dynamic models of the UAVs, followed by numerous recommendations and technical details required for building such a fully autonomous UAV system for experimental verification of scientific achievements. To show strength and high variability of the proposed system, we present results of tens of completely different real-robot experiments in various environments using distinct actuator and sensory configurations.

A team of scientists at Los Alamos National Laboratory is applying machine-learning algorithms to subsurface imaging that will impact a variety of applications, including energy exploration, carbon capture and sequestration and estimating pathways of subsurface contaminant transport, according to new research published in IEEE Signal Processing Magazine. "The subsurface is extremely complex and full of uncertainty, and knowledge of its physical properties is vital for a variety of applications," said Youzuo Lin of Los Alamos' Energy and Earth System Science group and lead author of the paper. "This paper is the first systematic survey on physics-guided machine-learning techniques for computational wave imaging." The authors reviewed more than a 100 research articles, organizing them within a structured framework that highlights the most significant recent innovations in this area. These insights will be of value not only for subsurface imaging, but also for other computational wave imaging problems such as medical ultrasound imaging and acoustic sensing for materials science. The process of obtaining subsurface data from surface measurements is called seismic inversion.

We train deep learning models on thousands of galaxy catalogues from the state-of-the-art hydrodynamic simulations of the CAMELS project to perform regression and inference. We employ Graph Neural Networks (GNNs), architectures designed to work with irregular and sparse data, like the distribution of galaxies in the Universe. We first show that GNNs can learn to compute the power spectrum of galaxy catalogues with a few percent accuracy. We then train GNNs to perform likelihood-free inference at the galaxy-field level. Our models are able to infer the value of $\Omega_{\rm m}$ with a $\sim12\%-13\%$ accuracy just from the positions of $\sim1000$ galaxies in a volume of $(25~h^{-1}{\rm Mpc})^3$ at $z=0$ while accounting for astrophysical uncertainties as modelled in CAMELS. Incorporating information from galaxy properties, such as stellar mass, stellar metallicity, and stellar radius, increases the accuracy to $4\%-8\%$. Our models are built to be translational and rotational invariant, and they can extract information from any scale larger than the minimum distance between two galaxies. However, our models are not completely robust: testing on simulations run with a different subgrid physics than the ones used for training does not yield as accurate results.

Although extensive research in emergency collision avoidance has been carried out for straight or curved roads in a highway scenario, a general method that could be implemented for all road environments has not been thoroughly explored. Moreover, most current algorithms don't consider collision mitigation in an emergency. This functionality is essential since the problem may have no feasible solution. We propose a safe controller using model predictive control and artificial potential function to address these problems. A new artificial potential function inspired by line charge is proposed as the cost function for our model predictive controller. The vehicle dynamics and actuator limitations are set as constraints. The new artificial potential function considers the shape of all objects. In particular, the artificial potential function we proposed has the flexibility to fit the shape of the road structures, such as the intersection. We could also realize collision mitigation for a specific part of the vehicle by increasing the charge quantity at the corresponding place. We have tested our methods in 192 cases from 8 different scenarios in simulation with two different models. The simulation results show that the success rate of the proposed safe controller is 20% higher than using HJ-reachability with system decomposition by using a unicycle model. It could also decrease 43% of collision that happens at the pre-assigned part. The method is further validated in a dynamic bicycle model.

The release of toxic gases by industries, emissions from vehicles, and an increase in the concentration of harmful gases and particulate matter in the atmosphere are all contributing factors to the deterioration of the quality of the air. Factors such as industries, urbanization, population growth, and the increased use of vehicles contribute to the rapid increase in pollution levels, which can adversely impact human health. This paper presents a model for forecasting the air quality index in Nigeria using the Bi-directional LSTM model. The air pollution data was downloaded from an online database (UCL). The dataset was pre-processed using both pandas tools in python. The pre-processed result was used as input features in training a Bi-LSTM model in making future forecasts of the values of the particulate matter Pm2.5, and Pm10. The Bi-LSTM model was evaluated using some evaluation parameters such as mean square error, mean absolute error, absolute mean square, and R^2 square. The result of the Bi-LSTM shows a mean square error of 52.99%, relative mean square error of 7.28%, mean absolute error of 3.4%, and R^2 square of 97%. The model. This shows that the model follows a seamless trend in forecasting the air quality in Port Harcourt, Nigeria.

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr's three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the Moral Tractability Thesis (MTT).

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from noise are Wasserstein gradient flow in the space of probability measures. We are the first to prove this connection. Our understanding of Score-based (and Diffusion) generative models have matured and become more complete by drawing ideas from different fields like Bayesian inference, control theory, stochastic differential equation and Schrodinger bridge. However, many open questions and challenges remain. One problem, for example, is how to decrease the sampling time? We demonstrate that looking from geometric perspective enables us to answer many of these questions and provide new interpretations to some known results. Furthermore, geometric perspective enables us to devise an intuitive geometric solution to the problem of faster sampling. By augmenting traditional score-based generative models with a projection step, we show that we can generate high quality images with significantly fewer sampling-steps.

Seismic acquisition footprints appear as stably faint and dim structures and emerge fully spatially coherent, causing inevitable damage to useful signals during the suppression process. Various footprint removal methods, including filtering and sparse representation (SR), have been reported to attain promising results for surmounting this challenge. However, these methods, e.g., SR, rely solely on the handcrafted image priors of useful signals, which is sometimes an unreasonable demand if complex geological structures are contained in the given seismic data. As an alternative, this article proposes a footprint removal network (dubbed FR-Net) for the unsupervised suppression of acquired footprints without any assumptions regarding valuable signals. The key to the FR-Net is to design a unidirectional total variation (UTV) model for footprint acquisition according to the intrinsically directional property of noise. By strongly regularizing a deep convolutional autoencoder (DCAE) using the UTV model, our FR-Net transforms the DCAE from an entirely data-driven model to a \textcolor{black}{prior-augmented} approach, inheriting the superiority of the DCAE and our footprint model. Subsequently, the complete separation of the footprint noise and useful signals is projected in an unsupervised manner, specifically by optimizing the FR-Net via the backpropagation (BP) algorithm. We provide qualitative and quantitative evaluations conducted on three synthetic and field datasets, demonstrating that our FR-Net surpasses the previous state-of-the-art (SOTA) methods.

Inverse problems involve making inference about unknown parameters of a physical process using observational data, and are widely found in scientific and engineering applications. For example, in urban air quality and environmental monitoring, inverse problems aim at quickly pinpointing the sources of instantaneous emissions of gaseous pollutants that cause public health concerns (Eckhardt et al., 2008; Martinez-Camara et al., 2014; Hwang et al., 2019), or detecting fugitive emissions due to accidental releases from industrial operations (Hosseini and Stockie, 2016; Klein et al., 2016). In healthcare applications, inverse models have been employed to obtain heart-surface potentials from body-surface measurements, known as the inverse ECG problem (Yao and Yang, 2021). In Seismology, inverse problems aim at getting information about the structure of the forces acting in the earthquake's focus from seismic waves at Earth's surface (Apostol, 2019). Inverse modeling has also found its applications in detecting the impact location of the missing Malaysian Airlines MH370, using the drift of marine debris (Miron et al., 2019) or acoustic-gravity waves (Kadri, 2019). This paper investigates an important class of statistical inverse problems--the estimation of the initial condition of a spatio-temporal advection-diffusion process using spatially sparse data streams. Consider the detection of accidental releases of fugitive emissions from industrial operations (Hosseini and Stockie, 2016).