arXiv subjects

Elias Cueto

Publications and source records attributed to Elias Cueto.

16 recordsLinked to original sources

arXiv2026

Data-free neural PDE solvers based on Graph Neural Networks and weak forms

We present a physics-informed, data-free neural solver for partial differential equations, built on a graph neural network architecture that utilises message passing. By relying on the weak form of the problem, we use gradients of finite-element shape functions (which are therefore polynomials) rather than automatic differentiation operators to compute the residuals of the equation from the displacements predicted by the network itself. Our approach generalises to previously unseen load cases and geometries, achieving easily convergence errors in the residuals of less than 1% and being capable of scaling up to models of considerable size and arbitrary geometries. To ensure compliance with the laws of physics and provide guarantees regarding the inference, it is possible to use the residual itself as an error indicator for the inference, and thus perform a refinement at the testing stage if the residual tolerance set in advance by the user is not met. Examples are provided to demonstrate the performance of the proposed method. This results in a method that avoids the costly process of obtaining, curating and storing high-fidelity synthetic data for training the neural network. Whilst this is not unique to our method, it is the first time it has been combined with a geometric machine learning technique capable of providing the necessary geometric bias to overcome the well-known difficulties of physics-informed neural networks.

cs.CE↗

arXiv2026

Physics-informed, Generative Adversarial Design of Funicular Shells

Shell structures are pivotal in the fields of architecture and engineering, due to their aesthetic appeal and structural efficiency. Recently, 3D concrete printing has reignited the interest in these structures. But, as printed concrete cannot be reinforced with steel, structures built in this way must be designed to withstand primarily pure compression: they must be funicular shells. Nevertheless, a fundamental challenge remains unsolved since Robert Hooke's discovered the catenary arch in 1675: it is not known whether the concept of a funicular polygon can be generalised to three-dimensional structures. Generative Adversarial Networks (GANs), have shown remarkable success in generating realistic data samples matching the distribution of the training data and have been shown to produce highly convincing synthetic images. This work proposes a physics-informed generative adversarial framework for the design of funicular shell structures. The approach employs a modified Deep Convolutional Generative Adversarial architecture physically guided by an auxiliary discriminator to generate realistic and structurally efficient shell geometries. Specifically, the model is constrained by the membrane factor to penalize geometries dominated by bending. An additional discriminator is also employed allowing the model to deal with more complex structures. Results show that the developed model is stable and capable of generating physically optimal, previously unseen, funicular shells with smooth forms and high membrane factor distributions.

cs.CE↗

arXiv2026

Variational Graph Neural Networks for Uncertainty Quantification in Inverse Problems

The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such as Digital Twins for engineering or medicine, fast responses are not enough; reliable results must also be provided. In certain cases, traditional deterministic methods may not be optimal as they do not provide a measure of confidence in their predictions or results, especially in inverse problems where the solution may not be unique or the initial data may not be entirely reliable due to the presence of noise, for instance. Classic deep neural networks also lack a clear measure to quantify the uncertainty of their predictions. In this work, we present a variational graph neural network (VGNN) architecture that integrates variational layers into its architecture to model the probability distribution of weights. Unlike computationally expensive full Bayesian networks, our approach strategically introduces variational layers exclusively in the decoder, allowing us to estimate cognitive uncertainty and statistical uncertainty at a relatively lower cost. In this work, we validate the proposed methodology in two cases of solid mechanics: the identification of the value of the elastic modulus with nonlinear distribution in a 2D elastic problem and the location and quantification of the loads applied to a 3D hyperelastic beam, in both cases using only the displacement field of each test as input data. The results show that the model not only recovers the physical parameters with high precision, but also provides confidence intervals consistent with the physics of the problem, as well as being able to locate the position of the applied load and estimate its value, giving a confidence interval for that experiment.

cs.LG↗

arXiv2026

MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics

We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets, while preserving a mesh-based graph representation. MGN-T overcomes a key limitation of standard MGN, the inefficient long-range information propagation caused by iterative message passing on large, high-resolution meshes. A physics-attention Transformer serves as a global processor, updating all nodal states simultaneously while explicitly retaining node and edge attributes. By directly capturing long-range physical interactions, MGN-T eliminates the need for deep message-passing stacks or hierarchical, coarsened meshes, enabling efficient learning on high-resolution meshes with varying geometries, topologies, and boundary conditions at an industrial scale. We demonstrate that MGN-T successfully handles industrial-scale meshes for impact dynamics, a setting in which standard MGN fails due message-passing under-reaching. The method accurately models self-contact, plasticity, and multivariate outputs, including internal, phenomenological plastic variables. Moreover, MGN-T outperforms state-of-the-art approaches on classical benchmarks, achieving higher accuracy while maintaining practical efficiency, using only a fraction of the parameters required by competing baselines.

cs.LG↗

arXiv2025

On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition

This paper proposes sharp lower bounds for the number of message passing iterations required in graph neural networks (GNNs) when solving partial differential equations (PDE). This significantly reduces the need for exhaustive hyperparameter tuning. Bounds are derived for the three fundamental classes of PDEs (hyperbolic, parabolic and elliptic) by relating the physical characteristics of the problem in question to the message-passing requirement of GNNs. In particular, we investigate the relationship between the physical constants of the equations governing the problem, the spatial and temporal discretisation and the message passing mechanisms in GNNs. When the number of message passing iterations is below these proposed limits, information does not propagate efficiently through the network, resulting in poor solutions, even for deep GNN architectures. In contrast, when the suggested lower bound is satisfied, the GNN parameterisation allows the model to accurately capture the underlying phenomenology, resulting in solvers of adequate accuracy. Examples are provided for four different examples of equations that show the sharpness of the proposed lower bounds.

cs.LG↗

arXiv2024

On the feasibility of foundational models for the simulation of physical phenomena

We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulators have shown some success when applied to specific tasks, it remains to be studied to what extent they are able to undergo severe changes in domain shape, boundary conditions and/or constitutive laws and still provide robust (i.e., hallucination-free) and accurate results. In this paper we perform an exhaustive study of these features, put ourselves in the worst-case scenario and study their resistance to such strong changes in their domain of application.

cs.CE↗

arXiv2023

Thermodynamics of learning physical phenomena

Thermodynamics could be seen as an expression of physics at a high epistemic level. As such, its potential as an inductive bias to help machine learning procedures attain accurate and credible predictions has been recently realized in many fields. We review how thermodynamics provides helpful insights in the learning process. At the same time, we study the influence of aspects such as the scale at which a given phenomenon is to be described, the choice of relevant variables for this description or the different techniques available for the learning process.

cs.LG↗

arXiv2022

A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluids

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a thermodynamics-informed active learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and analysis (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (grey box) modeling but also in the correction for real physics adaptation in low data regimes and partial observations of the dynamics. The method presented is extensible to other domains such as the development of cognitive digital twins, able to learn from observation of phenomena for which they have not been trained explicitly.

cs.CV↗

arXiv2022

Physics perception in sloshing scenes with guaranteed thermodynamic consistency

Physics perception very often faces the problem that only limited data or partial measurements on the scene are available. In this work, we propose a strategy to learn the full state of sloshing liquids from measurements of the free surface. Our approach is based on recurrent neural networks (RNN) that project the limited information available to a reduced-order manifold so as to not only reconstruct the unknown information, but also to be capable of performing fluid reasoning about future scenarios in real time. To obtain physically consistent predictions, we train deep neural networks on the reduced-order manifold that, through the employ of inductive biases, ensure the fulfillment of the principles of thermodynamics. RNNs learn from history the required hidden information to correlate the limited information with the latent space where the simulation occurs. Finally, a decoder returns data back to the high-dimensional manifold, so as to provide the user with insightful information in the form of augmented reality. This algorithm is connected to a computer vision system to test the performance of the proposed methodology with real information, resulting in a system capable of understanding and predicting future states of the observed fluid in real-time.

cs.CV↗

arXiv2021

MORPH-DSLAM: Model Order Reduction for PHysics-based Deformable SLAM

We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any ad-hoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually non-linear, is out of reach for current systems. To overcome this difficulty, we solve off-line a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the high-dimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.

cs.CV↗

arXiv2021

Monitoring weeder robots and anticipating their functioning by using advanced topological data analysis

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Topological Data Analysis will be used for extracting the trajectory descriptors, based on homology persistence. Then, appropriate metrics will be applied in order to compare that topological representation of the trajectories, for classifying them or for making efficient pattern recognition.

cs.RO↗

arXiv2021

Learning stable reduced-order models for hybrid twins

The concept of Hybrid Twin (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model-order reduction framework-to obtain real-time feedback rates-and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast and accurate corrections in the Hybrid Twin framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several sub-variants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.

cs.LG↗

arXiv2021

PGD-based advanced nonlinear multiparametric regressions for constructing metamodels at the scarce-data limit

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding multi-parametric solutions can be viewed as a sort of computational vademecum that, once computed offline, can be then used in a variety of real-time engineering applications including optimization, inverse analysis, uncertainty propagation or simulation based control. Sometimes, these multi-parametric problems can be solved by using advanced model order reduction -- MOR -- techniques. However, when the solution of these multi-parametric problems becomes cumbersome, one possibility consists in solving the problem for a sample of the parametric values, and then creating a regression from all the computed solutions, to finally infer the solution for any choice of the problem parameters. However, addressing high-dimensionality at the low data limit, ensuring accuracy and avoiding overfitting constitutes a difficult challenge. The present paper aims at proposing and discussing different PGD-based advanced regressions enabling the just referred features.

cs.CE↗

arXiv2021

Deep learning of thermodynamics-aware reduced-order models from data

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a so-called structure-preserving neural network. This data-based integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original full-dimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics.

cs.CE↗

arXiv2021

Learning Physics from Data: a Thermodynamic Interpretation

Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience collected in statistical mechanics and thermodynamics, the process of recognizing the pattern (the learning process) can be seen as a dissipative time evolution driven by entropy from a detailed level of description to less detailed. This is the way thermodynamics enters machine learning. On the other hand, reversible (typically Hamiltonian) evolution is propagation within the levels of description, that is also to be recognized. This is how Poisson geometry enters machine learning. Learning to handle free surface liquids and damped rigid body rotation serves as an illustration.

physics.data-an↗

arXiv2020

Structure-preserving neural networks

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E. 56 (6): 6620-6632]. The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that include conservative as well as dissipative systems, discrete as well as continuous ones.

cs.LG↗