Related papers: APIK: Active Physics-Informed Kriging Model with P…

The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty…

Autonomous aerial vehicles necessitate control strategies that balance computational efficiency with robust performance in dynamic operational environments. This paper proposes a model predictive control (MPC) framework for aerial platforms…

Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to…

In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…

PDE discovery shows promise for uncovering predictive models of complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a…

We present a new analytical and numerical framework for solution of Partial Differential Equations (PDEs) that is based on an exact transformation that moves the boundary constraints into the dynamics of the corresponding governing…

Spatio-temporal kriging is an important problem in web and social applications, such as Web or Internet of Things, where things (e.g., sensors) connected into a web often come with spatial and temporal properties. It aims to infer knowledge…

Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical…

We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to prioritize the parsimonious partial differential equation (PDE) that sufficiently governs noisy spatial-temporal observed data with few…

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…

Wire-arc directed energy deposition (DED) has emerged as a promising additive manufacturing (AM) technology for large-scale structural engineering applications. However, the complex thermal dynamics inherent to the process present…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…

Spatial prediction in an arbitrary location, based on a spatial set of observations, is usually performed by Kriging, being the best linear unbiased predictor (BLUP) in a least-square sense. In order to predict a continuous surface over a…

Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data,…

We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diffusion type PDE. We first conduct theoretical analysis and…

We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…

Reinforcement learning of real-world tasks is very data inefficient, and extensive simulation-based modelling has become the dominant approach for training systems. However, in human-robot interaction and many other real-world settings,…

This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and…