相关论文: Localized Nonlinear Solution Strategies for Effici…

Simulation of fluid flows is crucial for modeling physical phenomena like meteorology, aerodynamics, and biomedicine. Classical numerical solvers often require fine spatiotemporal grids to satisfy stability, consistency, and convergence…

Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolution equations, the nature of multiscale spatio-temporal…

Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that integrates…

Decentralized optimization for non-convex problems are now demanding by many emerging applications (e.g., smart grids, smart building, etc.). Though dramatic progress has been achieved in convex problems, the results for non-convex cases,…

Recently, a family of models that couple multifluid systems to the full Maxwell equations draw a lot of attention in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than…

Deep Learning (DL) algorithms are becoming increasingly popular for the reconstruction of high-resolution turbulent flows (aka super-resolution). However, current DL approaches perform spatially uniform super-resolution - a key performance…

Reservoir computing (RC) is a state-of-the-art machine learning method that makes use of the power of dynamical systems (the reservoir) for real-time inference. When using biological complex systems as reservoir substrates, it serves as a…

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping…

Reservoir computing is a very promising approach for the prediction of complex nonlinear dynamical systems. Besides capturing the exact short-term trajectories of nonlinear systems, it has also proved to reproduce its characteristic…

A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order…

Physical reservoir computing is a computational framework that offers an energy- and computation-efficient alternative to conventional training of neural networks. In reservoir computing, input signals are mapped into the high-dimensional…

The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

The growing interest in creating a parametric representation of liquid sloshing inside a container stems from its practical applications in modern engineering systems. The resonant excitation, on the other hand, can cause unstable and…

We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…

Our goal of this paper is to develop a new upscaling method for multicontinua flow problems in fractured porous media. We consider a system of equations that describes flow phenomena with multiple flow variables defined on both matrix and…

We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…

This paper develops a helicity-aware physics-informed neural network framework for incompressible non-Newtonian flow in rotational form. In addition to the energy law and the incompressibility constraint, helicity is a fundamental geometric…

We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…

In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…