Related papers: Parameter estimation for fractional autoregressive…
We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…
Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…
The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex…
Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…
In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory…
We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
We improve upon the two-stage sparse vector autoregression (sVAR) method in Davis et al. (2016) by proposing an alternative two-stage modified sVAR method which relies on time series graphical lasso to estimate sparse inverse spectral…
Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Reconstructing continuous flow fields from sparse surface-mounted sensors is central to aerodynamic design, flow control, and digital-twin instrumentation. Existing neural methods for this task typically encode sensor readings into implicit…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
This paper presents a new fuel cycle benchmarking analysis methodology by coupling Gaussian process regression, a popular technique in Machine Learning, to dynamic time warping, a mechanism widely used in speech recognition. Together they…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
Autoregressive models have demonstrated remarkable success in sequential data generation, particularly in NLP, but their extension to continuous-domain image generation presents significant challenges. Recent work, the masked autoregressive…
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…
In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…