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The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea interface at geophysically relevant Reynolds numbers. It…
Penetration depth (PD) is essential for robotics due to its extensive applications in dynamic simulation, motion planning, haptic rendering, etc. The Expanding Polytope Algorithm (EPA) is the de facto standard for this problem, which…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most…
We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two…
Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
The rapid rise of deep learning (DL) in numerical weather prediction (NWP) has led to a proliferation of models which forecast atmospheric variables with comparable or superior skill than traditional physics-based NWP. However, among these…
We introduce a class of explicit exponential Rosenbrock methods for the time integration of large systems of stiff differential equations. Their application with respect to simulation tasks in the field of visual computing is discussed…
Data-driven emulators are increasingly being used to learn and emulate physics-based simulations, reducing computational expense and run time. Here, we present a structured way to improve the quality of these high-dimensional emulated…
Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather…
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler…
We propose a neural network approach to produce probabilistic weather forecasts from a deterministic numerical weather prediction. Our approach is applied to operational surface temperature outputs from the Global Deterministic Prediction…
Accurate prediction of global sea surface temperature at sub-seasonal to seasonal (S2S) timescale is critical for drought and flood forecasting, as well as for improving disaster preparedness in human society. Government departments or…
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave…
The reliable integration of wind energy into modern-day electricity systems heavily relies on accurate short-term wind forecasts. We propose a spatio-temporal model called AIRU-WRF (short for the AI-powered Rutgers University Weather…
Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques…
The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for various flow problems. A guided diffusion…