Related papers: Reduced-Order Surrogates for Forced Flexible Mesh …

Forecasting physical systems over long horizons from irregularly sampled observations demands models that are stable, computationally efficient, and free of fixed-timestep assumptions. We address this with a continuous-time Koopman…

We investigate the Continuous-Time Koopman Autoencoder (CT-KAE) as a lightweight surrogate model for long-horizon ocean state forecasting in a two-layer quasi-geostrophic (QG) system. By projecting nonlinear dynamics into a latent space…

Reduced-order models (ROMs) are very popular for surrogate modeling of full-order computational fluid dynamics (CFD) simulations, allowing for real-time approximation of complex flow phenomena. However, their application to CFD models…

We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…

Several related works have introduced Koopman-based Machine Learning architectures as a surrogate model for dynamical systems. These architectures aim to learn non-linear measurements (also known as observables) of the system's state that…

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

Reliable long-horizon prediction remains a challenge for data-driven CFD surrogates, because offline-trained models accumulate autoregressive errors and lose accuracy when operating conditions change. This work develops a divergence-aware…

Accurate and robust surrogate modeling is essential for the real-time control and optimization of large-scale subsurface systems, such as geological CO2 storage and waterflood management. This study investigates the limits of classical…

Predicting and simulating aerodynamic fields for civil aircraft over wide flight envelopes represent a real challenge mainly due to significant numerical costs and complex flows. Surrogate models and reduced-order models help to estimate…

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

Robotic cloth folding is a challenging task, particularly when considering dynamic folding tasks, which aim at folding cloth by fast motions that leverage its dynamics. When subject to such fast motions, the complexity of cloth dynamics…

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

In this work, a terrain estimation framework is developed for autonomous vehicles operating on deformable terrains. Previous work in this area usually relies on steady state tire operation, linearized classical terramechanics models, or on…

We develop two deep learning surrogate autoregressive models for the prediction of the temporal evolution of two-dimensional ideal magnetohydrodynamic (MHD) Kelvin-Helmholtz instabilities across a range of magnetic field strengths. Using…

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

Training reinforcement learning (RL) agents to control fluid dynamics systems is computationally expensive due to the high cost of direct numerical simulations (DNS) of the governing equations. Surrogate models offer a promising alternative…

A machine-learning-based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (e.g., random forests, LASSO)…