Related papers: Beyond the Kolmogorov Barrier: A Learnable Weighte…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…

Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…

The paper introduces a very simple and fast computation method for high-dimensional integrals to solve high-dimensional Kolmogorov partial differential equations (PDEs). The new machine learning-based method is obtained by solving a…

Variational autoencoders (VAEs) are a standard framework for inducing latent variable models that have been shown effective in learning text representations as well as in text generation. The key challenge with using VAEs is the {\it…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

Variational Autoencoders and their many variants have displayed impressive ability to perform dimensionality reduction, often achieving state-of-the-art performance. Many current methods however, struggle to learn good representations in…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…

Data representation techniques have made a substantial contribution to advancing data processing and machine learning (ML). Improving predictive power was the focus of previous representation techniques, which unfortunately perform rather…

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

In this work, we propose a modified Hybrid Parallel Kolmogorov--Arnold Network and Multilayer Perceptron Physics-Informed Neural Network to overcome the high-frequency and multiscale challenges inherent in Physics-Informed Neural Networks.…

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or…

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics…