Related papers: Statistical Treatment, Fourier and Modal Decomposi…
The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…
Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases can not be uniquely…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatio-temporal transport mechanisms are uncovered…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…
This work aims to improve fuel chamber injectors' performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of…
Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…
Particle-based velocimetry (PV) is a widely used technique for non-invasive flow field measurements in fluid mechanics. Existing PV measurements typically rely on a single type of particle recording. With advancements in deep learning and…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
Particle Image Velocimetry (PIV) is a widely adopted non-invasive imaging technique that tracks the motion of tracer particles across image sequences to capture the velocity distribution of fluid flows. It is commonly employed to analyze…
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in LCDM models. From N-body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
The research community has witnessed the powerful potential of self-supervised Masked Image Modeling (MIM), which enables the models capable of learning visual representation from unlabeled data. In this paper, to incorporate both the…
Accurate skin lesion segmentation from dermoscopic images is of great importance for skin cancer diagnosis. However, automatic segmentation of melanoma remains a challenging task because it is difficult to incorporate useful texture…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
Recently, several single-pixel imaging (SPI) schemes have emerged for imaging fast-moving objects and have shown dramatic results. However, fast image reconstruction of a moving object with high quality is still challenging for SPI, thereby…
These are notes for a set of 7 two-hour lectures given at the 2010 Summer School on Quantitative Evolutionary and Comparative Genomics at OIST, Okinawa, Japan. The emphasis is on understanding how biological systems process information. We…