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Lagrangian averaging plays an important role in the analysis of wave--mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is however challenging. Typical…
Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…
Fluid flow simulation is a highly active area with applications in a wide range of engineering problems and interactive systems. Meshless methods like the Moving Particle Semi-implicit (MPS) are a great alternative to deal efficiently with…
Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…
In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…
In this study, we propose a graph neural network (GNN) model for efficiently predicting the flow behavior of non-Newtonian fluids with free surface dynamics. The numerical analysis of non-Newtonian fluids presents significant challenges, as…
Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…
We present a computational framework for modeling large-scale particle-laden flows in complex domains with the goal of enabling simulations in medical-image derived patient specific geometries. The framework is based on a volume-filtered…
The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal…
Machine learning techniques have emerged as powerful tools to tackle various challenges. The integration of machine learning methods with Physics has led to innovative approaches in understanding, controlling, and simulating physical…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
Partial differential equations (PDEs) are central to dynamical systems modeling, particularly in hydrodynamics, where traditional solvers often struggle with nonlinearity and computational cost. Lagrangian neural surrogates such as GNS and…
This project aims to create 3d model of the natural world and model changes in it instantaneously. A framework for modeling instantaneous changes natural scenes in real time using Lagrangian Particle Framework and a fluid-particle grid…
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial…
Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…