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Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven models are pervasive, physical knowledge -- often expressed as…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…

The proliferation of unmanned vehicles offers many opportunities for solving environmental sampling tasks with applications in resource monitoring and precision agriculture. Informative path planning (IPP) includes a family of methods which…

A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for many robot manipulators. Existing numerical solvers are broadly applicable but typically only produce a single solution and rely on…

Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g.,…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High-dimensionality of the robot configuration space often leads to difficulties in utilizing the…

Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

This paper presents a novel approach for incremental semiparametric inverse dynamics learning. In particular, we consider the mixture of two approaches: Parametric modeling based on rigid body dynamics equations and nonparametric modeling…

In this paper, we consider the use of black-box Gaussian process (GP) models for trajectory tracking control based on feedback linearization, in the context of mechanical systems. We considered two strategies. The first computes the control…

The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…

In this paper, we introduce a novel bond-based peridynamic model that utilizes a Gaussian kernel function. Previous peridynamic models, when directly discretized, have exhibited a lack of asymptotically compatibility with their…

Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these problems require optimization of functions defined on…

We study a prototypical situation when a learned predictor can discover useful low-dimensional structure in data, while using fewer samples than are needed for accurate prediction. Specifically, we consider the problem of recovering a…