Related papers: Physics Informed Deep Kernel Learning
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…
A recent development in machine learning - physics-informed deep learning (PIDL) - presents unique advantages in transportation applications such as traffic state estimation. Consolidating the benefits of deep learning (DL) and the…
In a lot of real-world data mining and machine learning applications, data are provided by multiple providers and each maintains private records of different feature sets about common entities. It is challenging to train these vertically…
Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in…
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications,…
Physics-informed machine learning (PIML), referring to the combination of prior knowledge of physics, which is the high level abstraction of natural phenomenons and human behaviours in the long history, with data-driven machine learning…
Physics-Informed Neural Networks have become a powerful mesh-free method for solving partial differential equations, but their performance is often limited by spectral bias. Specifically, in standard MLPs used in PINNs, the global parameter…
Physics-informed deep learning has been developed as a novel paradigm for learning physical dynamics recently. While general physics-informed deep learning methods have shown early promise in learning fluid dynamics, they are difficult to…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…
While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the…
Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some…
We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…
Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2)…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…
Neural models, with their ability to provide novel representations, have shown promising results in prediction tasks in healthcare. However, patient demographics, medical technology, and quality of care change over time. This often leads to…
Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We introduce a…