Related papers: A data-driven model-free physical-informed deep op…
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…
In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…
Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly…
The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…
Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…
The goal of this work is to investigate the capability of a neural operator (DeepONet) to accurately capture the complex deformation of a platelet's membrane under shear flow. The surrogate model approximated by the neural operator predicts…
Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are…
Deep learning is the backbone of artificial intelligence technologies, and it can be regarded as a kind of multilayer feedforward neural network. An essence of deep learning is information propagation through layers. This suggests that…
We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…
Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses…
Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by…
We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…
Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…