Related papers: Physics informed operator learning of parameter de…

Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

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…

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor…

Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters 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…

Deep learning with artificial neural networks is increasingly gaining attention, because of its potential for data-driven astronomy. However, this methodology usually does not provide uncertainties and does not deal with incompleteness and…

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 neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them…

For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…

Machine learning and neural networks have advanced numerous research domains, but challenges such as large training data requirements and inconsistent model performance hinder their application in certain scientific problems. To overcome…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear…

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…

Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…