arXiv subjects

Roberto Morales

Publications and source records attributed to Roberto Morales.

18 recordsLinked to original sources

arXiv2026

Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations

Physical and synthetic models may describe complementary aspects of the same PDE-governed system while receiving different, possibly fragmented, observations. We propose Bi-Objective HYCO (Bi-HYCO), a cooperative framework that retains both representations and their local observational objectives while coupling their predicted states at unlabeled interaction points. These points contain no measurements and do not augment the data; they provide a communication mechanism in the common state space. The two criteria form a vector-valued objective, and weighted scalarizations provide computational realizations. For the deterministic shared-observation algorithm with fixed interaction points, we prove sufficient decrease and finite length of the whole alternating sequence, which converges to a mixed critical point under the stated Kurdyka-Lojasiewicz-type assumptions. Elliptic transmission and two-dimensional Navier-Stokes experiments assess parameter and state reconstruction, noise and scalarization effects, and PINN/XPINN references. Ablations show that removing state interaction while retaining aggregation deteriorates parameter recovery in the tested configurations, particularly for Navier-Stokes.

cs.LG↗

arXiv2026

Fair feature attribution for multi-output prediction: a Shapley-based perspective

In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the theoretical necessity of this practice has remained unclear. By extending the classical Shapley axioms to vector-valued cooperative games, we establish a rigidity theorem showing that any attribution rule satisfying efficiency, symmetry, dummy player, and additivity must necessarily decompose component-wise across outputs. Consequently, any joint-output attribution rule must relax at least one of the classical Shapley axioms. This result identifies a previously unformalized structural constraint in Shapley-based interpretability, clarifying the precise scope of fairness-consistent explanations in multi-output learning. Numerical experiments on a biomedical benchmark illustrate that multi-output models can yield computational savings in training and deployment, while producing SHAP explanations that remain fully consistent with the component-wise structure imposed by the Shapley axioms.

cs.LG↗

arXiv2025

Identification of Source Terms in the Ginzburg-Landau Equation from Final Data

In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's functional, deriving an explicit gradient formula via an adjoint system and proving its Lipschitz continuity. We then establish existence and uniqueness results for quasi-solutions, and validate the theory with numerical experiments based on iterative methods.

math.AP↗

arXiv2025

SHAP values through General Fourier Representations: Theory and Applications

This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to an orthonormalisation tensor-product basis constructed under a product probability measure. Within this setting, each SHAP attribution can be represented as a linear functional of the model's Fourier coefficients. Two complementary regimes are studied. In the deterministic regime, we derive quantitative stability estimates for SHAP values under Fourier truncation, showing that the attribution map is Lipschitz continuous with respect to the distance between predictors. In the probabilistic regime, we consider neural networks in their infinite-width limit and prove convergence of SHAP values toward those induced by the corresponding Gaussian process prior, with explicit error bounds in expectation and with high probability based on concentration inequalities. We also provide a numerical experiment on a clinical unbalanced dataset to validate the theoretical findings.

math.OC↗

arXiv2025

A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints

This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization problem, in which both distributed agents and a central coordinator contribute independent, potentially conflicting objectives over a shared model parameter space. Unlike traditional approaches that merge local losses under a common goal, our formulation explicitly incorporates coordinator-side criteria, enabling more flexible and structured training dynamics. To navigate the resulting trade-offs, we explore scalarization strategies, particularly weighted sums, to construct tractable surrogate problems. These yield solutions that are provably Pareto optimal under standard convexity and smoothness assumptions, while embedding global preferences directly into local updates. We propose a decentralized optimization algorithm with convergence guarantees, and demonstrate its empirical performance through simulations, highlighting the impact of the coordinator's influence on local agent behavior. The proposed approach offers a principled and customizable strategy for balancing personalization, fairness, and coordination in decentralized learning systems.

math.OC↗

arXiv2025

Simultaneous reconstruction of two potentials for a nonconservative Schr\"odinger equation with dynamic boundary conditions

In this article, we consider an inverse problem involving the simultaneous reconstruction of two real valued potentials for a Schr\"odinger equation with mixed boundary conditions: a dynamic boundary condition of Wentzell type and a Dirichler boundary condition. The main result of this paper is a Lipschitz stability estimate for such potentials from a single measurement of the flux. This result is deduced using the Bukhgeim-Klibanov method and a suitable Carleman estimate where the weight function depends on Minkowski's functional.

math.AP↗

arXiv2024

Numerical null controllability of parabolic PDEs using Lagrangian methods

In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the domain. The main goal is to compute numerically a control that drives a numerical approximation of the state from prescribed initial data exactly to zero. We introduce a methodology for solving numerical controllability problems that is new in some sense. The main idea is to apply classical Lagrangian and Augmented Lagrangian techniques to suitable constrained extremal formulations that involve unbounded weights in time that make global Carleman inequalities possible. The theoretical results are validated by satisfactory numerical experiments for spatially 2D and 3D problems.

math.OC↗

arXiv2024

Identification of source terms in the Schr\"odinger equation with dynamic boundary conditions from final data

In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the inverse source problem. By analyzing the associated Tikhonov functional, we prove a gradient formula of the functional in terms of the solution to a suitable adjoint system, allowing us to obtain the Lipschitz continuity of the gradient. Next, the existence and uniqueness of a quasi-solution are also investigated. Finally, our theoretical results are validated by numerical experiments in one dimension using the Landweber iteration method.

math.AP↗

arXiv2024

An Insensitizing control problem involving tangential gradient terms for a reaction-diffusion equation with dynamic boundary conditions

In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding controls such that a specific functional is insensitive for small perturbations of the initial data. More precisely, the functional considered here depends on the norm of the state in a subset of the bulk together with the norm of the tangential gradient of the state on the boundary. This problem is equivalent to a (relaxed) null controllability problem for an optimality system of cascade type, with a zeroth-order coupling term in the bulk and a second-order coupling term on the boundary. To achieve this result, we linearize the system around the origin and analyze it by the duality approach and we prove a new Carleman estimate for the corresponding adjoint system. Then, a local null controllability result for the nonlinear system is proven by using an inverse function theorem.

math.OC↗

arXiv2024

Drell-Yan Bounds on Gapped Continuum Spectra

Theories with gapped continuum spectra have gotten some attention, either as pure 4D models like unparticles, or in 5D realizations as certain soft walls constructions. In this paper, we derive experimental bounds from Drell-Yan processes ($pp \to \ell^+\ell^-$, $pp \to \ell^\pm \nu$) in a particular scenario where the electroweak bosons propagate in an extra dimension that produces a propagator with a continuum spectrum, on top of the isolated corresponding Standard Model pole. Using current LHC data we put a lower bound on the gap of 4.2 TeV (expected), 6.2 TeV (observed, bins with $< 10$ events combined) at 95\% CL, with some dependence in the observed limit on how low statistics bins are treated. We also study the limits for HL-LHC.

hep-ph↗

arXiv2023

Local null controllability of a cubic Ginzburg-Landau equation with dynamic boundary conditions

This paper deals with controllability properties of a cubic Ginzburg-Landau equation with dynamic boundary conditions. More precisely, we prove a local null controllability result by using a single control supported in a small subset of the domain. In order to achieve this result, we firstly linearize the system around the origin and we analyze it by the duality approach and an appropriate Carleman estimate. Then, by using an inverse function theorem, the local null controllability of the nonlinear system is proven.

math.AP↗

arXiv2023

Exact Controllability for a Schrödinger equation with dynamic boundary conditions

In this paper, we study the controllability of a Schrödinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type, and Dirichlet boundary condition. The main result of this article is given by new Carleman estimates for the associated adjoint system, where the weight function is constructed specially adapted to the geometry of the domain. Using these estimates, we prove the exact controllability of the system with a boundary control acting only in the part of the boundary where the Dirichlet condition is imposed. Also, we obtain a distributed exact controllability result for the system.

math.OC↗

arXiv2022

Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions

We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding adjoint system. This is done by using a suitable Carleman estimate for such models where the discrete parameters $h$ and $Δt$ are connected to the one of the large Carleman parameters.

math.AP↗

arXiv2017

Higgs effective $Hl_il_j$ vertex from heavy $ν_R$ and applications to LFV phenomenology

We present a new computation of the Lepton Flavor Violating effective vertex involving the Higgs boson and two leptons with different flavors. This vertex is generated from the integration to one-loop level of the heavy right handed neutrinos which are considered here within the context of the Low Scale Seesaw Models and with masses close to the TeV scale. We apply the Mass Insertion Approximation technique to compute the loop contributions from these heavy $ν_R$ and derive a symple analytical formula for the $Hl_il_j$ effective vertex in terms of the input $Y_ν$ Yukawa coupling matrix and right handed $M_R$ neutrino masses. Some interesting phenomenological applications of this $Hl_il_j$ effective vertex are also included.

hep-ph↗

arXiv2017

Four Tops for LHC

We design a search strategy for the Standard Model $t\bar t t \bar t$ production at the LHC in the same-sign dilepton and trilepton channels. We study different signal features and, given the small expected number of signal events, we scrutinize in detail all reducible and irreducible backgrounds. Our analysis shows that by imposing a set of basic jet and lepton selection criteria, the SM $pp \to t\bar t t \bar t$ process could be evidenced in the near future, within Run-II, when combining both multi-lepton search channels. We argue that this search strategy should also be used as a guideline to test New Physics coupling predominantly to top-quarks. In particular, we show that a non-resonant New Physics enhancement in the four-top final state would be detectable through this search strategy. We study two {\it top-philic} simplified models of this kind, a neutral scalar boson and a $Z^\prime$, and present current and future exclusion limits on their mass and couplings.

hep-ph↗

arXiv2016

Instantaneous charge state of Uranium projectiles in fully ionized plasmas from energy loss experiments

The instantaneous charge state of uranium ions traveling through a fully ionized hydrogen plasma has been theoretically studied and compared with one of the first energy loss experiments in plasmas, carried out at GSI-Darmstadt by Hoffmann \textit{et al.} in the 90's. For this purpose, two different methods to estimate the instantaneous charge state of the projectile have been employed: (1) rate equations using ionization and recombination cross sections, and (2) equilibrium charge state formulas for plasmas. Also, the equilibrium charge state has been obtained using these ionization and recombination cross sections, and compared with the former equilibrium formulas. The equilibrium charge state of projectiles in plasmas is not always reached, it depends mainly on the projectile velocity and the plasma density. Therefore, a non-equilibrium or an instantaneous description of the projectile charge is necessary. The charge state of projectile ions cannot be measured, except after exiting the target, and experimental data remain very scarce. Thus, the validity of our charge state model is checked by comparing the theoretical predictions with an energy loss experiment, as the energy loss has a generally quadratic dependence on the projectile charge state. The dielectric formalism has been used to calculate the plasma stopping power including the Brandt-Kitagawa (BK) model to describe the charge distribution of the projectile. In this charge distribution, the instantaneous number of bound electrons instead of the equilibrium number has been taken into account. Comparing our theoretical predictions with experiments, it is shown the necessity of including the instantaneous charge state and the BK charge distribution for a correct energy loss estimation. The results also show that the initial charge state has a strong influence in order to estimate the energy loss of the uranium ions.

physics.plasm-ph↗

arXiv2015

Calculations on the stopping power of a heterogeneous Warm Dense Matter

The stopping power of Warm Dense Matter (WDM) is estimated by means of the individual contributions of free electrons and bound electrons existing in this special kind of matter, located between classical and degenerate plasmas. For free electrons, the dielectric formalism, well described in our studies, is used to estimate the free electron stopping power. For bound electrons, the mean excitation energy of ions is used. Excitation energies are obtained through atomic calculations of the whole atom or, shell by shell in order to estimate their stopping power. Influence of temperature and density is analyzed in case of an impinging projectile. This influence becomes important for low projectile velocities and is negligible for high ones. Using free and bound electron analysis, the stopping power of an extended WDM is inferred from a dynamical calculation of energy transferred from the projectile to the plasma, where the Bragg peak and stopping range are calculated. Finally, this theoretical framework is used to study a typical plasma density profile of a WDM heated by lasers.

physics.plasm-ph↗

arXiv2014

Proton Stopping Power of Different Density Profile Plasmas

In this work, the stopping power of a partially ionized plasma is analyzed by means of free electron stopping and bound electron stopping. For the first one, the RPA dielectric function is used, and for the latter one, an interpolation of high and low projectile velocity formulas is used. The dynamical energy loss of an ion beam inside a plasma is estimated by using an iterative scheme of calculation. The Abel inversion is also applied when we have a plasma with radial symmetry. Finally, we compare our methods with two kind of plasmas. In the first one, we estimate the energy loss in a plasma created by a laser prepulse, whose density is approximated by a piecewise function. For the latter one, a radial electron density is supposed and the stopping is obtained as function of radius from the calculated lateral points. In both cases, the dependence with the density profile is observed.

physics.plasm-ph↗