Related papers: EFiGP: Eigen-Fourier Physics-Informed Gaussian Pro…
Differential equations (DEs) are crucial for modeling the evolution of natural or engineered systems. Traditionally, the parameters in DEs are adjusted to fit data from system observations. However, in fields such as politics, economics,…
Recent advances in generative AI offer promising solutions for synthetic data generation but often rely on large datasets for effective training. To address this limitation, we propose a novel generative model that learns from limited data…
The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build…
Gaussian processes (GPs) are widely used as surrogate models for emulating computer code, which simulate complex physical phenomena. In many problems, additional boundary information (i.e., the behavior of the phenomena along input…
Remote sensing data have been widely used to study various geophysical processes. With the advances in remote-sensing technology, massive amount of remote sensing data are collected in space over time. Different satellite instruments…
Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…
Understanding the structure of our universe and the distribution of matter is an area of active research. As cosmological surveys grow in complexity, the development of emulators to efficiently and effectively predict matter power spectra…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
There is significant interest in learning and optimizing a complex system composed of multiple sub-components, where these components may be agents or autonomous sensors. Among the rich literature on this topic, agent-based and…
Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…
We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on…
An important issue in quadcopter control is that an accurate dynamic model of the system is nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based estimation is an…
In many areas of science and engineering, computer simulations are widely used as proxies for physical experiments, which can be infeasible or unethical. Such simulations can often be computationally expensive, and an emulator can be…
This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style…
This paper proposes a receding horizon active learning and control problem for dynamical systems in which Gaussian Processes (GPs) are utilized to model the system dynamics. The active learning objective in the optimization problem is…
Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations,…
Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…
Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…
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…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…