Related papers: Physics-informed machine learning as a kernel meth…

The development of robust and reliable modeling approaches for crystallization processes is often challenging because of non-idealities in real data arising from various sources of uncertainty. This study investigated the effectiveness of…

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…

Recent advances in machine learning have inspired a surge of research into reconstructing specific quantities of interest from measurements that comply with certain physical laws. These efforts focus on inverse problems that are governed by…

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a…

This paper proposed a novel radial basis function neural network (RBFNN) to solve various partial differential equations (PDEs). In the proposed RBF neural networks, the physics-informed kernel functions (PIKFs), which are derived according…

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…

We present a new efficient hybrid parameter estimation method based on the idea, that if nonlinear dynamic models are stated in terms of a system of equations that is linear in terms of the parameters, then regularized ordinary least…

Melt pool dynamics in metal additive manufacturing (AM) is critical to process stability, microstructure formation, and final properties of the printed materials. Physics-based simulation including computational fluid dynamics (CFD) is the…

Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

Modeling thermal states for complex space missions, such as the surface exploration of airless bodies, requires high computation, whether used in ground-based analysis for spacecraft design or during onboard reasoning for autonomous…

In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informed neural networks. They solve forward and inverse problems…

Physics-based models of dynamical systems are often used to study engineering and environmental systems. Despite their extensive use, these models have several well-known limitations due to simplified representations of the physical…

The mass loss of the polar ice sheets contributes considerably to ongoing sea-level rise and changing ocean circulation, leading to coastal flooding and risking the homes and livelihoods of tens of millions of people globally. To address…

Prognostics and Health Management ensures the reliability, safety, and efficiency of complex engineered systems by enabling fault detection, anticipating equipment failures, and optimizing maintenance activities throughout an asset…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

While balancing covariates between groups is central for observational causal inference, selecting which features to balance remains a challenging problem. Kernel balancing is a promising approach that first estimates a kernel that captures…

We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…

This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques…

Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…