Alicia Tierz

Alicia Tierz, Icíar Alfaro, David González et al.

Traditional Predictive Digital Twins often remain geometrically rigid, requiring extensive retraining or fine-tuning whenever the underlying physical domain or boundary conditions change. To overcome this limitation, we present a novel framework for \textit{Zero-Shot Digital Twins} that seamlessly couples real-time visual perception with a geometry-agnostic, physics-informed reasoning engine. At the core of our architecture is the Thermodynamics-Informed Graph Neural Network architecture, a Geometric Deep Learning solver grounded in a metriplectic thermodynamic formalism that enforces energy conservation and non-negative entropy production locally through graph message passing. The framework integrates an auxiliary Graph Neural Network to infer unobservable fields (such as stress tensors or velocity and energy distributions) directly from sparse initial visual boundaries, mitigating numerical start-up transients. To bridge the sim-to-real gap, we implement a continuous closed-loop data assimilation mechanism; the pipeline tracks macroscopic deformations and free-surface fluid boundaries in real-time using deep segmentation networks combined with sparse optical flow, dynamically correcting the autoregressive simulation rollout and eliminating numerical drift. To test the validity of our approach, we demonstrate the extreme generalization capabilities of our approach across two disparate physical regimes: the large deformations of a viscoelastic beam and the non-linear sloshing of a viscous fluid. In both scenarios, the unified framework instantiates physically accurate simulations on novel, unseen geometries without case-specific retraining, operating well within real-time latency budgets (approximately 25 ms per frame) and enabling the direct projection of latent mechanical variables via Augmented Reality.

Jad Mounayer, Alicia Tierz, Jerome Tomezyk et al.

Deterministic Rank Reduction Autoencoders (RRAEs) enforce by construction a regularization on the latent space by applying a truncated SVD. While this regularization makes Autoencoders more powerful, using them for generative purposes is counter-intuitive due to their deterministic nature. On the other hand, Variational Autoencoders (VAEs) are well known for their generative abilities by learning a probabilistic latent space. In this paper, we present Variational Rank Reduction Autoencoders (VRRAEs), a model that leverages the advantages of both RRAEs and VAEs. Our claims and results show that when carefully sampling the latent space of RRAEs and further regularizing with the Kullback-Leibler (KL) divergence (similarly to VAEs), VRRAEs outperform RRAEs and VAEs. Additionally, we show that the regularization induced by the SVD not only makes VRRAEs better generators than VAEs, but also reduces the possibility of posterior collapse. Our results include a synthetic dataset of a small size that showcases the robustness of VRRAEs against collapse, and three real-world datasets; the MNIST, CelebA, and CIFAR-10, over which VRRAEs are shown to outperform both VAEs and RRAEs on many random generation and interpolation tasks based on the FID score. We developed an open-source implementation of VRRAEs in JAX (Equinox), available at https://github.com/JadM133/RRAEs.git.

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.