Related papers: White-box machine learning for uncovering physical…
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 second…
Fine particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Recent examination of these mixtures in…
Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…
Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…
Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…
Polar sea ice is crucial to Earth's climate system. Its dynamics also affect coastal communities, wildlife, and global shipping. Sea ice is typically modeled as a continuum fluid using a model proposed almost 50 years ago, which is…
Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural network-based methods. However, the…
While machine learning (ML) in experimental research has demonstrated impressive predictive capabilities, inductive reasoning and knowledge extraction remain elusive tasks, in part because of the difficulty extracting fungible knowledge…
The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…
Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…
We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth, frictional walls, moving with opposite velocities $\pm$V . Discrete…
PDE discovery shows promise for uncovering predictive models of complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a…
Differentiable physics modeling combines physics models with gradient-based learning to provide model explicability and data efficiency. It has been used to learn dynamics, solve inverse problems and facilitate design, and is at its…