Related papers: A data-driven approach to viscous fluid mechanics …
Fluid data completion is a research problem with high potential benefit for both experimental and computational fluid dynamics. An effective fluid data completion method reduces the required number of sensors in a fluid dynamics experiment,…
Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a…
We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of…
Data-Driven Continuum Mechanics -- the continuous counterpart of Data-Driven Computational Mechanics -- is a modern paradigm that enhances classical continuum mechanics by incorporating finite sets of experimental material data directly,…
We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…
We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by means of fully coupled, grain-resolved direct numerical…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…
We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as…
There has been recent progress in developing well-posed theories of relativistic viscous hydrodynamics and of gravitational effective field theories. These have in common the feature that they introduce unphysical degrees of freedom. We…
The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie…
Data-driven approaches offer novel opportunities for improving the performance of turbulent flow simulations, which are critical to wide-ranging applications from wind farms and aerodynamic designs to weather and climate forecasting. While…
Two-dimensional active nematics are often modeled using phenomenological continuum theories that describe the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
A data-driven turbulence model for coarse-grained numerical simulations of two-dimensional Rayleigh-B\'enard convection is proposed. The model starts from high-fidelity data and is based on adjusting the Fourier coefficients of the…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
With the growing size and complexity of turbulent flow models, data compression approaches are of the utmost importance to analyze, visualize, or restart the simulations. Recently, in-situ autoencoder-based compression approaches have been…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…