Related papers: Physics-informed kernel learning

Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology,…

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

Physics informed neural networks (PINNs) have recently been proposed as surrogate models for solving process optimization problems. However, in an active learning setting collecting enough data for reliably training PINNs poses a challenge.…

Physics-informed Kolmogorov-Arnold Networks (PIKANs), and in particular their Chebyshev-based variants (cPIKANs), have recently emerged as promising models for solving partial differential equations (PDEs). However, their training dynamics…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…

Intensive studies have been conducted in recent years to integrate neural networks with physics models to balance model accuracy and interpretability. One recently proposed approach, named Physics-Enhanced Residual Learning (PERL), is to…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…

Physics-Informed Neural Networks (PINNs) integrate machine learning with differential equations to solve forward and inverse problems while ensuring that predictions adhere to physical laws. Physiologically based pharmacokinetic (PBPK)…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

The prevailing data-driven machine learning has been plagued by the absence of physics knowledge and the scarcity of data. We implement the physics-model informed prior into Bayesian machine learning to evaluate the energy dependence of…

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…