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Stellar streams retain a memory of their gravitational interactions with small-scale perturbations. While perturbative models for streams have been formulated in action-angle coordinates, a direct transformation to these coordinates is only…
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…
The modeling and simulation of multiphase fluid flow receive significant attention in reservoir engineering. Many time discretization schemes for multiphase flow equations are either explicit or semi-implicit, relying on the decoupling…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
Fluid-induced slip of fractures is characterized by strong multiphysics couplings. Three physical processes are considered: Flow, rock deformation and fracture deformation. The fractures are represented as lower-dimensional objects embedded…
Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…
In finite-volume-based flow-simulations with free-surface waves, wave reflections at the domain boundaries can cause substantial errors in the results and must therefore be minimized. This can be achieved via `implicit relaxation zones',…
We propose a high resolution finite volume scheme for a (m+1)x(m+1) system of non strictly hyperbolic conservation laws which models multicomponent polymer flooding in enhanced oil-recovery process in two dimensions. In the presence of…
In this paper we study the use of Virtual Element method for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes that form the reservoirs, such as sedimentation, erosion and faulting, lead to…
Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly…
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…
The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging numerically for large-scale sparse/dense system, especially when it has zero eigenvalues. Based on a direct sum…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…