Related papers: Making it possible: constructing a reliable mechan…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
A dynamical low-rank approximation is developed for reduced-order modeling (ROM) of the filtered density function (FDF) transport equation, which is utilized for large eddy simulation (LES) of turbulent reacting flows. In this methodology,…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville…
Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Knowledge Distillation (KD) emerges as one of the most promising compression technologies to run advanced deep neural networks on resource-limited devices. In order to train a small network (student) under the guidance of a large network…
The importance of state estimation in fluid mechanics is well-established; it is required for accomplishing several tasks including design/optimization, active control, and future state prediction. A common tactic in this regards is to rely…
Defect phase diagrams provide a unified description of crystal defect states for materials design and are central to the scientific objectives of the Collaborative Research Centre (CRC) 1394. Their construction requires the systematic…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…
We discuss the computational complexity of finding the ground state of the two-dimensional array of quantum bits that interact via strong van der Waals interactions. Specifically, we focus on systems where the interaction strength between…
Sparse Representation (SR) techniques encode the test samples into a sparse linear combination of all training samples and then classify the test samples into the class with the minimum residual. The classification of SR techniques depends…
Simulating many-body quantum systems poses significant challenges due to the large size of the state space. To address this issue, we propose using an SU(2) coherent state for individual spins to simulate spins on a lattice and derive…
In this work, we consider the problem of network parameter optimization for rate maximization. We frame this as a joint optimization problem of power control, beam forming, and interference cancellation. We consider the setting where…
We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost.…
This paper presents methods for dramatically improving the performance of sampling-based kinodynamic planners. The key component is the first-known complete, exact steering method that produces a time-optimal trajectory between any states…
The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally simulate or intuitively comprehend the…
Medical image reconstruction from measurement data is a vital but challenging inverse problem. Deep learning approaches have achieved promising results, but often requires paired measurement and high-quality images, which is typically…
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)…