Related papers: Learning-based Multi-continuum Model for Multiscal…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
Learning with neural networks from a continuous stream of visual information presents several challenges due to the non-i.i.d. nature of the data. However, it also offers novel opportunities to develop representations that are consistent…
The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which address this problem by keeping the…
This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…
Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Systems comprising a turbulent channel flow overlaying a permeable bed can be found in a variety of industrial and natural applications (e.g. urban planning, fracking, submerged vegetation). One important realization of this system is at…
In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to…
The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…
Data-driven methods demonstrate considerable potential for accelerating the inherently expensive computational fluid dynamics (CFD) solvers. Nevertheless, pure machine-learning surrogate models face challenges in ensuring physical…
Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…
Multi-task learning solves multiple correlated tasks. However, conflicts may exist between them. In such circumstances, a single solution can rarely optimize all the tasks, leading to performance trade-offs. To arrive at a set of optimized…
Many real-world problems are naturally modeled as heterogeneous graphs, where nodes and edges represent multiple types of entities and relations. Existing learning models for heterogeneous graph representation usually depend on the…
Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of…
In this research, we address Darcy flow problems with random permeability using iterative solvers, enhanced by a two-grid preconditioner based on a generalized multiscale prolongation operator, which has been demonstrated to be stable for…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…