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This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…

This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…

Machine learning (ML) tools such as encoder-decoder deep convolutional neural networks (CNN) are able to extract relationships between inputs and outputs of large complex systems directly from raw data. For time-varying systems the…

Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman framework. In eDMD a compression of the lifted system…

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

For safely applying reinforcement learning algorithms on high-dimensional nonlinear dynamical systems, a simplified system model is used to formulate a safe reinforcement learning framework. Based on the simplified system model, a…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

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…

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…

Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the…

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…

A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…

This work presents, to the best of the authors' knowledge, the first generalizable and fully data-driven adaptive framework designed to stabilize deep learning (DL) autoregressive forecasting models over long time horizons, with the goal of…

An additive autoencoder for dimension reduction, which is composed of a serially performed bias estimation, linear trend estimation, and nonlinear residual estimation, is proposed and analyzed. Computational experiments confirm that an…

Predicting the dynamics of complex systems is crucial for various scientific and engineering applications. The accuracy of predictions depends on the model's ability to capture the intrinsic dynamics. While existing methods capture key…

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…

In this work, a data-driven framework based on Phase-Field simulations data is proposed to highlight the capabilities of neural networks to ensure accurate low dimensionality reduction of simulated microstructural images and to provide…

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,…