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Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems.…
Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…
This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment…
Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing computational costs for simulation as well as for model-based control approaches. This work presents a data-driven framework for minimal-dimensional…
Many computer vision applications involve modeling complex spatio-temporal patterns in high-dimensional motion data. Recently, restricted Boltzmann machines (RBMs) have been widely used to capture and represent spatial patterns in a single…
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…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure…
We propose the time-delayed transformer (TD-TF), a simplified transformer architecture for data-driven modeling of unsteady spatio-temporal dynamics. TD-TF bridges linear operator-based methods and deep sequence models by showing that a…
The self-attention mechanism utilizes large implicit weight matrices, programmed through dot product-based activations with very few trainable parameters, to enable long sequence modeling. In this paper, we investigate the possibility of…
Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…
We investigate the applicability of machine learning based reduced order model (ML-ROM) to three-dimensional complex flows. As an example, we consider a turbulent channel flow at the friction Reynolds number of $Re_\tau=110$ in a minimum…
Estimating intervention effects in dynamical systems is crucial for outcome optimization. In medicine, such interventions arise in physiological regulation (e.g., cardiovascular system under fluid administration) and pharmacokinetics, among…
Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
Understanding the dynamics of a system is important in many scientific and engineering domains. This problem can be approached by learning state transition rules from observations using machine learning techniques. Such observed time-series…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…