Related papers: Differential Geometric Foundations for Power Flow …
Performance variability management is an active research area in high-performance computing (HPC). We focus on input/output (I/O) variability. To study the performance variability, computer scientists often use grid-based designs (GBDs) to…
Power flow calculation in EMS is required to accommodate a large and complex power system. To achieve a faster than real-time calculation, a graph based power flow calculation is proposed in this paper. Graph database and graph computing…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy…
Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the…
We formulate and implement the Euler equations with SGS dynamics and provide numerical tests of an SGS turbulence energy model that predicts the turbulent pressure of unresolved velocity fluctuations and the rate of dissipation for highly…
Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible…
Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
Differentiable physics is a powerful tool in computer vision and robotics for scene understanding and reasoning about interactions. Existing approaches have frequently been limited to objects with simple shape or shapes that are known in…
Hydrodynamics describes the evolution of macroscopic states in non--equilibrium thermodynamics. Following Onsager reciprocal relations, one can formulate a large class of hydrodynamic equations as gradient flows of free energies. In recent…
The geometric quantization of the geodesic flow on a compact Riemannian manifold via the BKS "dragging projection" yields the Laplacian plus a scalar curvature term. To avoid convergence issues, the standard construction involves somewhat…
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges…
Implicit neural representations have emerged as a powerful approach for encoding complex geometries as continuous functions. These implicit models are widely used in computer vision and 3D content creation, but their integration into…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…