Francisco Caldas

Francisco M. Caldas, Cláudia Soares

Emergency Departments (EDs) are a fundamental element of the Portuguese National Health Service, serving as an entry point for users with diverse and very serious medical problems. Due to the inherent characteristics of the ED; forecasting the number of patients using the services is particularly challenging. And a mismatch between the affluence and the number of medical professionals can lead to a decrease in the quality of the services provided and create problems that have repercussions for the entire hospital, with the requisition of health care workers from other departments and the postponement of surgeries. ED overcrowding is driven, in part, by non-urgent patients, that resort to emergency services despite not having a medical emergency and which represent almost half of the total number of daily patients. This paper describes a novel deep learning architecture, the Temporal Fusion Transformer, that uses calendar and time-series covariates to forecast prediction intervals and point predictions for a 4 week period. We have concluded that patient volume can be forecasted with a Mean Absolute Percentage Error (MAPE) of 5.90% for Portugal's Health Regional Areas (HRA) and a Root Mean Squared Error (RMSE) of 84.4102 people/day. The paper shows empirical evidence supporting the use of a multivariate approach with static and time-series covariates while surpassing other models commonly found in the literature.

Francisco Caldas, Cláudia Soares

The increasing volume of space objects in Earth's orbit presents a significant challenge for Space Situational Awareness (SSA). And in particular, accurate orbit prediction is crucial to anticipate the position and velocity of space objects, for collision avoidance and space debris mitigation. When performing Orbit Prediction (OP), it is necessary to consider the impact of non-conservative forces, such as atmospheric drag and gravitational perturbations, that contribute to uncertainty around the future position of spacecraft and space debris alike. Conventional propagator methods like the SGP4 inadequately account for these forces, while numerical propagators are able to model the forces at a high computational cost. To address these limitations, we propose an orbit prediction algorithm utilizing machine learning. This algorithm forecasts state vectors on a spacecraft using past positions and environmental variables like atmospheric density from external sources. The orbital data used in the paper is gathered from precision ephemeris data from the International Laser Ranging Service (ILRS), for the period of almost a year. We show how the use of machine learning and time-series techniques can produce low positioning errors at a very low computational cost, thus significantly improving SSA capabilities by providing faster and reliable orbit determination for an ever increasing number of space objects.

Manuel Santos Pereira, Luís Tripa, Nélson Lima et al.

First formulated by Sir Isaac Newton in his work "Philosophiae Naturalis Principia Mathematica", the concept of the Three-Body Problem was put forth as a study of the motion of the three celestial bodies within the Earth-Sun-Moon system. In a generalized definition, it seeks to predict the motion for an isolated system composed of three point masses freely interacting under Newton's law of universal attraction. This proves to be analogous to a multitude of interactions between celestial bodies, and thus, the problem finds applicability within the studies of celestial mechanics. Despite numerous attempts by renowned physicists to solve it throughout the last three centuries, no general closed-form solutions have been reached due to its inherently chaotic nature for most initial conditions. Current state-of-the-art solutions are based on two approaches, either numerical high-precision integration or machine learning-based. Notwithstanding the breakthroughs of neural networks, these present a significant limitation, which is their ignorance of any prior knowledge of the chaotic systems presented. Thus, in this work, we propose a novel method that utilizes Physics-Informed Neural Networks (PINNs). These deep neural networks are able to incorporate any prior system knowledge expressible as an Ordinary Differential Equation (ODE) into their learning processes as a regularizing agent. Our findings showcase that PINNs surpass current state-of-the-art machine learning methods with comparable prediction quality. Despite a better prediction quality, the usability of numerical integrators suffers due to their prohibitively high computational cost. These findings confirm that PINNs are both effective and time-efficient open-form solvers of the Three-Body Problem that capitalize on the extensive knowledge we hold of classical mechanics.