Elías Cueto

Quercus Hernández, Alberto Badías, Francisco Chinesta et al.

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior with permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively, achieving relative mean errors of less than 3% in all the tested examples. Two ablation studies are provided based on recent works in both physics-informed and geometric deep learning.

Quercus Hernández, Alberto Badías, Francisco Chinesta et al.

The imminent impact of immersive technologies in society urges for active research in real-time and interactive physics simulation for virtual worlds to be realistic. In this context, realistic means to be compliant to the laws of physics. In this paper we present a method for computing the dynamic response of (possibly non-linear and dissipative) deformable objects induced by real-time user interactions in mixed reality using deep learning. The graph-based architecture of the method ensures the thermodynamic consistency of the predictions, whereas the visualization pipeline allows a natural and realistic user experience. Two examples of virtual solids interacting with virtual or physical solids in mixed reality scenarios are provided to prove the performance of the method.

Quercus Hernández, Alberto Badías, Francisco Chinesta et al.

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique.

Carlos Bermejo-Barbanoj, Beatriz Moya, Alberto Badías et al.

We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the dimensionality of the full order model to a set of latent variables that are enforced to match a prior, for example a normal distribution. Adversarial autoencoders are seen as generative models, and they can be trained to generate high-resolution samples from low-resoution inputs, meaning they can address the so-called super-resolution problem. Then, a second neural network is trained to learn the physical structure of the latent variables and predict their temporal evolution. This neural network is known as an structure-preserving neural network. It learns the metriplectic-structure of the system and applies a physical bias to ensure that the first and second principles of thermodynamics are fulfilled. The integrated trajectories are decoded to their original dimensionality, as well as to the higher dimensionality space produced by the adversarial autoencoder and they are compared to the ground truth solution. The method is tested with two examples of flow over a cylinder, where the fluid properties are varied between both examples.

Pau Urdeitx, Icíar Alfaro, David González et al.

The development of inductive biases has been shown to be a very effective way to increase the accuracy and robustness of neural networks, particularly when they are used to predict physical phenomena. These biases significantly increase the certainty of predictions, decrease the error made and allow considerably smaller datasets to be used. There are a multitude of methods in the literature to develop these biases. One of the most effective ways, when dealing with physical phenomena, is to introduce physical principles of recognised validity into the network architecture. The problem becomes more complex without knowledge of the physical principles governing the phenomena under study. A very interesting possibility then is to turn to the principles of thermodynamics, which are universally valid, regardless of the level of abstraction of the description sought for the phenomenon under study. To ensure compliance with the principles of thermodynamics, there are formulations that have a long tradition in many branches of science. In the field of rheology, for example, two main types of formalisms are used to ensure compliance with these principles: one-generator and two-generator formalisms. In this paper we study the advantages and disadvantages of each, using classical problems with known solutions and synthetic data.

Lucas Tesán, David González, Pedro Martins et al.

The growing importance of real-time simulation in the medical field has exposed the limitations and bottlenecks inherent in the digital representation of complex biological systems. This paper presents a novel methodology aimed at advancing current lines of research in soft tissue simulation. The proposed approach introduces a hybrid model that integrates the geometric bias of graph neural networks with the physical bias derived from the imposition of a metriplectic structure as soft and hard constrains in the architecture, being able to simulate hepatic tissue with dissipative properties. This approach provides an efficient solution capable of generating predictions at high feedback rate while maintaining a remarkable generalization ability for previously unseen anatomies. This makes these features particularly relevant in the context of precision medicine and haptic rendering. Based on the adopted methodologies, we propose a model that predicts human liver responses to traction and compression loads in as little as 7.3 milliseconds for optimized configurations and as fast as 1.65 milliseconds in the most efficient cases, all in the forward pass. The model achieves relative position errors below 0.15\%, with stress tensor and velocity estimations maintaining relative errors under 7\%. This demonstrates the robustness of the approach developed, which is capable of handling diverse load states and anatomies effectively. This work highlights the feasibility of integrating real-time simulation with patient-specific geometries through deep learning, paving the way for more robust digital human twins in medical applications.

Alicia Tierz, Iciar Alfaro, David González et al.

Thermodynamics-informed neural networks employ inductive biases for the enforcement of the first and second principles of thermodynamics. To construct these biases, a metriplectic evolution of the system is assumed. This provides excellent results, when compared to uninformed, black box networks. While the degree of accuracy can be increased in one or two orders of magnitude, in the case of graph networks, this requires assembling global Poisson and dissipation matrices, which breaks the local structure of such networks. In order to avoid this drawback, a local version of the metriplectic biases has been developed in this work, which avoids the aforementioned matrix assembly, thus preserving the node-by-node structure of the graph networks. We apply this framework for examples in the fields of solid and fluid mechanics. Our approach demonstrates significant computational efficiency and strong generalization capabilities, accurately making inferences on examples significantly different from those encountered during training.