Related papers: GPLaSDI: Gaussian Process-based Interpretable Late…

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric…

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

The exact quantum dynamics of lattice models can be computationally intensive, especially when aiming for large system sizes and extended simulation times necessary to converge transport coefficients. By leveraging finite memory times to…

Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

In recent years, deep learning has successfully been applied to automate a wide variety of tasks in diagnostic histopathology. However, fast and reliable localization of small-scale regions-of-interest (ROI) has remained a key challenge, as…

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. In this paper, we introduce latent map Gaussian processes (LMGPs) that…

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…

Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…

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…

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

Capturing 4D spatiotemporal surroundings is crucial for the safe and reliable operation of robots in dynamic environments. However, most existing methods address only one side of the problem: they either provide coarse geometric tracking…

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

Diffusion models generate data by learning to reverse a forward process, where samples are progressively perturbed with Gaussian noise according to a predefined noise schedule. From a geometric perspective, each noise schedule corresponds…

We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observations. Identifying unknown differential equations from noisy…