Related papers: Greatly enhancing the modeling accuracy for distri…

We have previously introduced Spectral Diffusion Posterior Sampling (Spectral DPS) as a framework for accurate one-step material decomposition by integrating analytic spectral system models with priors learned from large datasets. This work…

This study introduces an approach for modeling unsteady transonic aerodynamics within a parametric space, using Volterra series to capture aerodynamic responses and machine learning to enable interpolation. The first- and second-order…

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…

The Volterra integral-functional series is the classic approach for nonlinear black box dynamical systems modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many…

Numerous industrial thermal processes and fluid processes can be described by distributed parameter systems (DPSs), wherein many process parameters and variables vary in space and time. Early internal abnormalities in the DPS may develop…

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The…

Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…

Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

This computer science master thesis aims at modelling the nonlinearities of a loudspeaker. A piecewise linear approximation is initially explored and then we present a nonlinear Volterra model to simulate the behavior of the system. The…

This paper presents detailed insights of embedding Carleman linearization into nonlinear systems for designing Volterra model-based control technique. Volterra series method is a competent mathematical tool, which extends the convolution…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

We establish a comprehensive sample path large deviation principle (LDP) for log-processes associated with multivariate time-inhomogeneous stochastic volatility models. Examples of models for which the new LDP holds include Gaussian models,…

In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…