Related papers: Compliance Minimization via Physics-Informed Gauss…

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in…

We introduce a simultaneous and meshfree topology optimization (TO) framework based on physics-informed Gaussian processes (GPs). Our framework endows all design and state variables via GP priors which have a shared, multi-output mean…

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of…

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…

A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

Physics-informed neural networks (PINNs) offer a mesh-free framework for solving partial differential equations (PDEs), yet training often suffers from gradient pathologies, spectral bias, and poor convergence, especially for problems with…

Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear controlsystems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and…

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 a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can be used as a pretraining stage to find initial conditions for…

We propose a method to encourage safety in Model Predictive Control (MPC)-based Reinforcement Learning (RL) via Gaussian Process (GP) regression. This framework consists of 1) a parametric MPC scheme that is employed as model-based…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…