Related papers: Reduced-Order Surrogates for Forced Flexible Mesh …
While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A…
Following the introduction of Dynamic Mode Decomposition and its numerous extensions, many neural autoencoder-based implementations of the Koopman operator have recently been proposed. This class of methods appears to be of interest for…
In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is…
The solar wind, a continuous outflow of charged particles from the Sun's corona, shapes the heliosphere and impacts space systems near Earth. Accurate prediction of features such as high-speed streams and coronal mass ejections is critical…
This paper derives conditions under which Model Predictive Control (MPC) with terminal conditions, using a data-driven surrogate model as a prediction model, asymptotically stabilizes the plant despite approximation errors. In particular,…
In this paper, we analyze stability of nonlinear model predictive control (MPC) using data-driven surrogate models in the optimization step. First, we establish asymptotic stability of the origin, a controlled steady state, w.r.t. the MPC…
Analyzing the spectral properties of the Koopman operator is crucial for understanding and predicting the behavior of complex stochastic dynamical systems. However, the accuracy of data-driven estimation methods, such as Extended Dynamic…
Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be…
We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to…
The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical…
Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited…
The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
The prediction of photon echoes is a crucial technique for understanding optical quantum systems. However, it typically requires numerous simulations with varying parameters and input pulses, rendering numerical studies computationally…
Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this…
Imitation learning (IL) enables efficient skill acquisition from demonstrations but often struggles with long-horizon tasks and high-precision control due to compounding errors. Residual policy learning offers a promising, model-agnostic…
The two-layer quasi-geostrophic equations (2QGE) is a simplified model that describes the dynamics of a stratified, wind-driven ocean in terms of potential vorticity and stream function. Its numerical simulation is plagued by a high…
This paper develops a surrogate model refinement approach for the simulation of dynamical systems and the solution of optimization problems governed by dynamical systems in which surrogates replace expensive-to-compute state- and…