arXiv subjects

Dajana Conte

Publications and source records attributed to Dajana Conte.

5 recordsLinked to original sources

arXiv2026

Integrating Artificial Intelligence, Physics, and Internet of Things: A Framework for Cultural Heritage Conservation

The conservation of cultural heritage increasingly relies on integrating technological innovation with domain expertise to ensure effective monitoring and predictive maintenance. This paper presents a novel framework to support the preservation of cultural assets, combining Internet of Things (IoT) and Artificial Intelligence (AI) technologies, enhanced with the physical knowledge of phenomena. The framework is structured into four functional layers that permit the analysis of 3D models of cultural assets and elaborate simulations based on the knowledge acquired from data and physics. A central component of the proposed framework consists of Scientific Machine Learning, particularly Physics-Informed Neural Networks (PINNs), which incorporate physical laws into deep learning models. To enhance computational efficiency, the framework also integrates Reduced Order Methods (ROMs), specifically Proper Orthogonal Decomposition (POD), and is also compatible with classical Finite Element (FE) methods. Additionally, it includes tools to automatically manage and process 3D digital replicas, enabling their direct use in simulations. The proposed approach offers three main contributions: a methodology for processing 3D models of cultural assets for reliable simulation; the application of PINNs to combine data-driven and physics-based approaches in cultural heritage conservation; and the integration of PINNs with ROMs to efficiently model degradation processes influenced by environmental and material parameters. The reproducible and open-access experimental phase exploits simulated scenarios on complex and real-life geometries to test the efficacy of the proposed framework in each of its key components, allowing the possibility of dealing with both direct and inverse problems. Code availability: https://github.com/valc89/PhysicsInformedCulturalHeritage

cs.LG↗

arXiv2025

Sparse Identification of Nonlinear Dynamics for Stochastic Delay Differential Equations

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse identification of nonlinear dynamics. The proposed methodology combines recently proposed high-order estimates of drift and covariance for dealing with stochastic problems with augmented libraries to handle delayed arguments. Three different strategies are discussed in view of exploiting only realistically available data. A thorough comparative numerical investigation is performed on different models, which helps guiding the choice of effective and possibly outperforming schemes.

math.NA↗

arXiv2025

Fast solution of a phase-field model of pitting corrosion

Excessive computational times represent a major challenge in the solution of corrosion models, limiting their practical applicability, e.g., as a support to predictive maintenance. In this paper, we propose an efficient strategy for solving a phase-field model for metal corrosion. Based on the Kronecker structure of the diffusion matrix in classical finite difference approximations on rectangular domains, time-stepping IMEX methods are efficiently solved in matrix form. However, when the domain is non-rectangular, the lack of the Kronecker structure prevents the direct use of the matrix-based approach. To address this issue, we reformulate the problem on an extended rectangular domain and introduce suitable iterative IMEX methods. The convergence of the iterations and the propagation of the numerical errors are analyzed. Test cases on two and three dimensional domains show that the proposed approach achieves accuracy comparable to existing methods, while significantly reducing the computational time, to the point of allowing actual predictions on standard workstations.

math.NA↗

arXiv2022

Exponentially fitted methods with a local energy conservation law

A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation, the new scheme has discrete conservation laws of charge and energy. The new method is compared with other conservative schemes from the literature on a benchmark problem whose solution is an oscillatory breather wave.

math.NA↗

arXiv2021

Exponentially fitted methods that preserve conservation laws

The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when applied to problems with oscillatory solutions. In this cases, compared to standard methods, they have proved to be very accurate even using large integration steps. In this paper we consider exponentially fitted Runge-Kutta methods and we give characterizations of those that preserve local conservation laws of linear and quadratic quantities. As benchmark problems we consider wave equations arising as models in several fields such as fluid dynamics and quantum physics, and derive exponentially fitted methods that preserve their conservation laws of mass (or charge) and momentum. The proposed methods are applied to approximate breather wave solutions and are compared to other known methods of the same order.

math.NA↗