Related papers: Manifold-constrained Gaussian process inference fo…
Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, choosing an appropriate prior distribution is an important task. In…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
We present Flow-Induced Diagonal Gaussian Processes (FiD-GP), a compression framework that incorporates a compact inducing weight matrix to project a neural network's weight uncertainty into a lower-dimensional subspace. Critically, FiD-GP…
Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of…
Identifying and calibrating quantitative dynamical models for physical quantum systems is important for a variety of applications. Here we present a closed-loop Bayesian learning algorithm for estimating multiple unknown parameters in a…
Out-of-distribution (OOD) generalization remains a central challenge in deploying deep learning models to real-world scenarios, particularly in domains such as biomedical images, where distribution shifts are both subtle and pervasive.…
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…
Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…
Extracting meaningful information from high-dimensional data poses a formidable modeling challenge, particularly when the data is obscured by noise or represented through different modalities. This research proposes a novel non-parametric…
Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how the distribution of a biomarker, such as glucose, changes over…
Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms…
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…
Practitioners deploying time series forecasting models face a dilemma: exhaustively validating dozens of models is computationally prohibitive, yet choosing the wrong model risks poor performance. We show that spectral…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…