Related papers: Physics-informed dynamic mode decomposition (piDMD…
Dynamic mode decomposition (DMD) has proven to be a valuable tool for the analysis of complex flow-fields but the application of this technique to flows with moving boundaries is not straightforward. This is due to the difficulty in…
Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…
Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
We propose exploiting symmetries (exact or approximate) of the Standard Model (SM) to search for physics Beyond the Standard Model (BSM) using the data-directed paradigm (DDP). Symmetries are very powerful because they provide two samples…
Dynamic Mode Decomposition (DMD) is a data-driven modeling tool that generates a model from spatio-temporal data. The data needs to be as clean as possible for DMD to come up with a faithful model. We review a few data-filtering methods to…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis,…
Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models…
Goal-conditioned dynamic manipulation is inherently challenging due to complex system dynamics and stringent task constraints, particularly in deformable object scenarios characterized by high degrees of freedom and underactuation. Prior…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…
A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many…
We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…
In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…