Gonzalo A. Ruz

Paul Escapil-Inchauspé, Gonzalo A. Ruz

We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO) procedure via Gaussian processes-based Bayesian optimization. We apply the HPO to Helmholtz equation for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density $r$ and (iii) the frequency $κ$, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.

Paul Escapil-Inchauspé, Gonzalo A. Ruz

We explore the data-parallel acceleration of physics-informed machine learning (PIML) schemes, with a focus on physics-informed neural networks (PINNs) for multiple graphics processing units (GPUs) architectures. In order to develop scale-robust and high-throughput PIML models for sophisticated applications which may require a large number of training points (e.g., involving complex and high-dimensional domains, non-linear operators or multi-physics), we detail a novel protocol based on $h$-analysis and data-parallel acceleration through the Horovod training framework. The protocol is backed by new convergence bounds for the generalization error and the train-test gap. We show that the acceleration is straightforward to implement, does not compromise training, and proves to be highly efficient and controllable, paving the way towards generic scale-robust PIML. Extensive numerical experiments with increasing complexity illustrate its robustness and consistency, offering a wide range of possibilities for real-world simulations.

Paul Escapil-Inchauspé, Gonzalo A. Ruz

We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of existing PINNs code, and enabling handling of non-linear and time-dependent operators. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations. Exhaustive numerical experiments are performed; demonstrating applicability and performance; raising a variety of new promising research avenues.

Carlos S. Sepúlveda, Gonzalo A. Ruz

Coverage path planning on irregular hexagonal grids is relevant to maritime surveillance, search and rescue and environmental monitoring, yet classical methods are often compared on small ad hoc examples or on rectangular grids. This paper presents a reproducible benchmark of deterministic single-vehicle coverage path planning heuristics on irregular hexagonal graphs derived from synthetic but maritime-motivated areas of interest. The benchmark contains 10,000 Hamiltonian-feasible instances spanning compact, elongated, and irregular morphologies, 17 heuristics from seven families, and a common evaluation protocol covering Hamiltonian success, complete-coverage success, revisits, path length, heading changes, and CPU latency. Across the released dataset, heuristics with explicit shortest-path reconnection solve the relaxed coverage task reliably but almost never produce zero-revisit tours. Exact Depth-First Search confirms that every released instance is Hamiltonian-feasible. The strongest classical Hamiltonian baseline is a Warnsdorff variant that uses an index-based tie-break together with a terminal-inclusive residual-degree policy, reaching 79.0% Hamiltonian success. The dominant design choice is not tie-breaking alone, but how the residual degree is defined when the endpoint is reserved until the final move. This shows that underreported implementation details can materially affect performance on sparse geometric graphs with bottlenecks. The benchmark is intended as a controlled testbed for heuristic analysis rather than as a claim of operational optimality at fleet scale.

Carlos S. Sepúlveda, Gonzalo A. Ruz

Maritime surveillance missions, such as search and rescue and environmental monitoring, rely on the efficient allocation of sensing assets over vast and geometrically complex areas. Traditional Coverage Path Planning (CPP) approaches depend on decomposition techniques that struggle with irregular coastlines, islands, and exclusion zones, or require computationally expensive re-planning for every instance. We propose a Deep Reinforcement Learning (DRL) framework to solve CPP on hexagonal grid representations of irregular maritime areas. Unlike conventional methods, we formulate the problem as a neural combinatorial optimization task where a Transformer-based pointer policy autoregressively constructs coverage tours. To overcome the instability of value estimation in long-horizon routing problems, we implement a critic-free Group-Relative Policy Optimization (GRPO) scheme. This method estimates advantages through within-instance comparisons of sampled trajectories rather than relying on a value function. Experiments on 1,000 unseen synthetic maritime environments demonstrate that a trained policy achieves a 99.0% Hamiltonian success rate, more than double the best heuristic (46.0%), while producing paths 7% shorter and with 24% fewer heading changes than the closest baseline. All three inference modes (greedy, stochastic sampling, and sampling with 2-opt refinement) operate under 50~ms per instance on a laptop GPU, confirming feasibility for real-time on-board deployment.

Gilber A. Corrales, Carlos Andrés Ferro Sánchez, Reinel Tabares-Soto et al.

ProfileXAI is a model- and domain-agnostic framework that couples post-hoc explainers (SHAP, LIME, Anchor) with retrieval - augmented LLMs to produce explanations for different types of users. The system indexes a multimodal knowledge base, selects an explainer per instance via quantitative criteria, and generates grounded narratives with chat-enabled prompting. On Heart Disease and Thyroid Cancer datasets, we evaluate fidelity, robustness, parsimony, token use, and perceived quality. No explainer dominates: LIME achieves the best fidelity-robustness trade-off (Infidelity $\le 0.30$, $L<0.7$ on Heart Disease); Anchor yields the sparsest, low-token rules; SHAP attains the highest satisfaction ($\bar{x}=4.1$). Profile conditioning stabilizes tokens ($σ\le 13\%$) and maintains positive ratings across profiles ($\bar{x}\ge 3.7$, with domain experts at $3.77$), enabling efficient and trustworthy explanations.