Chady Ghnatios

Jad Mounayer, Sebastian Rodriguez, Jerome Tomezyk et al.

Most existing latent-space models for dynamical systems require fixing the latent dimension in advance, they rely on complex loss balancing to approximate linear dynamics, and they don't regularize the latent variables. We introduce RRAEDy, a model that removes these limitations by discovering the appropriate latent dimension, while enforcing both regularized and linearized dynamics in the latent space. Built upon Rank-Reduction Autoencoders (RRAEs), RRAEDy automatically rank and prune latent variables through their singular values while learning a latent Dynamic Mode Decomposition (DMD) operator that governs their temporal progression. This structure-free yet linearly constrained formulation enables the model to learn stable and low-dimensional dynamics without auxiliary losses or manual tuning. We provide theoretical analysis demonstrating the stability of the learned operator and showcase the generality of our model by proposing an extension that handles parametric ODEs. Experiments on canonical benchmarks, including the Van der Pol oscillator, Burgers' equation, 2D Navier-Stokes, and Rotating Gaussians, show that RRAEDy achieves accurate and robust predictions. Our code is open-source and available at https://github.com/JadM133/RRAEDy. We also provide a video summarizing the main results at https://youtu.be/ox70mSSMGrM.

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.

Chady Ghnatios, Kazem Fayazbakhsh

Feedstock deformation during 3D printing of continuous fiber composites is a critical challenge in path planning and a main driver in the generation of manufacturing defects. The proposed work addressed the feedstock deformation during the deposition through several experimental and numerical pathways. The experimental setups and numerical simulations are used to identify the main driving phenomena in the deformation of feedstock through residual stress relief and drying, crystallization, and thermal stresses. A hybrid physics-based and data-driven modeling effort is performed, using Kelvin-Voigt viscoelastic modeling of the composite prepregs and a stabilized neural ODE for the modeling of drying and crystallization. The identified hybrid models from DMA and DSC experiments are used in robotic 3D printing to validate the deposition of a composite prepreg in real printing settings. The results show the ability of the model to reproduce the prepreg behavior far above the temperature used in the training, showcasing its robustness and generalization capability.

Jad Mounayer, Sebastian Rodriguez, Chady Ghnatios et al.

The choice of an appropriate bottleneck dimension and the application of effective regularization are both essential for Autoencoders to learn meaningful representations from unlabeled data. In this paper, we introduce a new class of deterministic autoencoders, Rank Reduction Autoencoders (RRAEs), which regularize their latent spaces by employing a truncated singular value decomposition (SVD) during training. In RRAEs, the bottleneck is defined by the rank of the latent matrix, thereby alleviating the dependence of the encoder/decoder architecture on the bottleneck size. This approach enabled us to propose an adaptive algorithm (aRRAEs) that efficiently determines the optimal bottleneck size during training. We empirically demonstrate that both RRAEs and aRRAEs are stable, scalable, and reliable, as they do not introduce any additional training hyperparameters. We evaluate our proposed architecture on a synthetic data set, as well as on MNIST, Fashion MNIST, and CelebA. Our results show that RRAEs offer several advantages over Vanilla AEs with both large and small latent spaces, and outperform other regularizing AE architectures.

Elias Al Ghazal, Jad Mounayer, Beatriz Moya et al.

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods that fail to capture high frequency behaviours. To overcome these difficulties, we propose three approaches for multiscale learning. The first leverages the Partition of Unity (PU) method, integrated with neural networks, to decompose the dynamics into local components and directly predict both macro- and micro-scale behaviors. The second applies the Singular Value Decomposition (SVD) to extract dominant modes that explicitly separate macro- and micro-scale dynamics. Since full access to the data matrix is rarely available in practice, we further employ a Sparse High-Order SVD to reconstruct multiscale dynamics from limited measurements. Together, these approaches ensure that both coarse and fine dynamics are accurately captured, making the framework effective for real-world applications involving complex, multi-scale phenomena and adaptable to higher-dimensional systems with incomplete observations, by providing an approximation and interpretation in all time scales present in the phenomena under study.