Related papers: Data-Driven Reduction for Multiscale Stochastic Dy…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
We address the question of parameterizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one-dimensional stochastically forced shallow water equations. The problem is formulated in…
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…
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 propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Modern deep models are trained on large real-world datasets, where data quality varies and redundancy is common. Data-centric approaches such as dataset pruning have shown promise in improving training efficiency and model performance.…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Chemical kinetic models in terms of ordinary differential equations correspond to finite dimensional dissipative dynamical systems involving a multiple time scale structure. Most dimension reduction approaches aimed at a slow…
A variety of established approaches exist for the detection of dynamic bottlenecks. Furthermore, the prediction of bottlenecks is experiencing a growing scientific interest, quantifiable by the increasing number of publications in recent…
Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a…