arXiv subjects

Francisco Caldas

Publications and source records attributed to Francisco Caldas.

10 recordsLinked to original sources

arXiv2026

AdamX: Cosine similarity meets gradient descent

We introduce AdamX, a first-order optimizer that incorporates cosine similarity as an adaptive mechanism for controlling update magnitudes. The proposed method is scalable, model-agnostic, and straightforward to integrate into existing training pipelines. We further introduce a variance rectification scheme that promotes smoother optimization during the early stages of training. Overall, we provide empirical evidence that AdamX achieves competitive convergence rates across a range of benchmark datasets and architectures. Performance is evaluated in terms of the number of epochs required to reach predefined performance thresholds under a fixed hyperparameter budget. Code and Experiments available at: https://github.com/FranciscoCaldas/adamX.

cs.LG↗

arXiv2026

CIExplainer++: Generating Causal and Interpretable Explanations for Graph Neural Networks

Explainable Artificial Intelligence aims to make black-box models more trustworthy by presenting, in a human-understandable manner, the elements that lead to the model's output. This involves both (i) identifying components and connections with genuine causal influence on outputs and (ii) translating such structures into an interpretable representation. For the former, we introduce CIExplainer, a novel perturbation-based method grounded in causal inference for explaining Graph Neural Networks (GNNs). CIExplainer identifies the subgraph with the highest causal effects on GNN predictions using the Potential Outcome Framework. We evaluate and compare CIExplainer on various GNN architectures (GCN, GraphSAGE, GAT, GIN) and datasets. To bridge subgraph explanations with human interpretability, we further propose G2TeXplainer, a method that transforms causal subgraphs into natural language explanations that capture both feature-level and relational information.

cs.LG↗

arXiv2026

A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting

We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion. Unlike prior work that modifies the network architecture or diffuses directly in the frequency domain, our proposed method alters only the diffusion process itself, making it compatible with existing diffusion backbones (e.g., DiffWave, TimeGrad, CSDI). By staging noise injection according to component energy, it maintains high signal-to-noise ratios for dominant frequencies throughout the diffusion trajectory, thereby improving the recoverability of long-term patterns. This strategy enables the model to maintain the signal structure for a longer period in the forward process, leading to improved forecast quality. Across standard forecasting benchmarks, we show that applying spectral decomposition strategies, such as the Fourier or Wavelet transform, consistently improves upon diffusion models using the baseline forward process, with negligible computational overhead. The code for this paper is available at https://anonymous.4open.science/r/D-FDP-4A29.

stat.ML↗

arXiv2025

OrbitZoo: Real Orbital Systems Challenges for Reinforcement Learning

The increasing number of satellites and orbital debris has made space congestion a critical issue, threatening satellite safety and sustainability. Challenges such as collision avoidance, station-keeping, and orbital maneuvering require advanced techniques to handle dynamic uncertainties and multi-agent interactions. Reinforcement learning (RL) has shown promise in this domain, enabling adaptive, autonomous policies for space operations; however, many existing RL frameworks rely on custom-built environments developed from scratch, which often use simplified models and require significant time to implement and validate the orbital dynamics, limiting their ability to fully capture real-world complexities. To address this, we introduce OrbitZoo, a versatile multi-agent RL environment built on a high-fidelity industry standard library, that enables realistic data generation, supports scenarios like collision avoidance and cooperative maneuvers, and ensures robust and accurate orbital dynamics. The environment is validated against a real satellite constellation, Starlink, achieving a Mean Absolute Percentage Error (MAPE) of 0.16% compared to real-world data. This validation ensures reliability for generating high-fidelity simulations and enabling autonomous and independent satellite operations.

cs.LG↗

arXiv2025

Analyzing Data Quality and Decay in Mega-Constellations: A Physics-Informed Machine Learning Approach

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

astro-ph.EP↗

arXiv2025

Advancing Solutions for the Three-Body Problem Through Physics-Informed Neural Networks

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.

cs.LG↗

arXiv2024

Precise and Efficient Orbit Prediction in LEO with Machine Learning using Exogenous Variables

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.

cs.LG↗

arXiv2024

Machine Learning in Orbit Estimation: a Survey

Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with only thirty thousand larger than ten cm being tracked. To avert a chain reaction of collisions, known as Kessler Syndrome, it is essential to accurately track and predict debris and satellites' orbits. Current approximate physics-based methods have errors in the order of kilometers for seven-day predictions, which is insufficient when considering space debris, typically with less than one meter. This failure is usually due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, and unknown characteristics such as the mass or geometry of the space object. Operators can enhance Orbit Prediction accuracy by deriving unmeasured objects' characteristics and improving non-conservative forces' effects by leveraging data-driven techniques, such as Machine Learning. In this survey, we provide an overview of the work in applying Machine Learning for Orbit Determination, Orbit Prediction, and atmospheric density modeling.

astro-ph.EP↗

arXiv2023

Conjunction Data Messages for Space Collision Behave as a Poisson Process

Space debris is a major problem in space exploration. International bodies continuously monitor a large database of orbiting objects and emit warnings in the form of conjunction data messages. An important question for satellite operators is to estimate when fresh information will arrive so that they can react timely but sparingly with satellite maneuvers. We propose a statistical learning model of the message arrival process, allowing us to answer two important questions: (1) Will there be any new message in the next specified time interval? (2) When exactly and with what uncertainty will the next message arrive? The average prediction error for question (2) of our Bayesian Poisson process model is smaller than the baseline in more than 4 hours in a test set of 50k close encounter events.

stat.ML↗

arXiv2021

Conjunction Data Messages behave as a Poisson Process

astro-ph.IM↗