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We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the…
The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…
To investigate the effect and ability of FACTS devices using the Fast and Flexible Holomorphic Embedding technique (FFHE), it is necessary to develop an embedded system for these devices. Therefore, this paper presents FFHE based embedded…
Hierarchical multi-label classification (HMLC) is essential for modeling complex label dependencies in remote sensing. Existing methods, however, struggle with multi-path hierarchies where instances belong to multiple branches, and they…
Part I of this paper embeds the AC power flow problem with voltage control and exponential load model in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in…
Traditional dynamic security assessment faces challenges as power systems are experiencing a transformation to inverter-based-resource (IBR) dominated systems, for which electromagnetic transient (EMT) dynamics have to be considered.…
The HELM algorithm was used in this project to solve the optimal power flow problem introduced by a radial PandaPower network formulated from the data given by AEMO on the NEM network. Large losses were observed in the transmission…
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…
The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and…
Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…
Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat…
Membranes holomorphically embedded in flat noncompact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static…
Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However,…
A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through…
There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational…
Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an…
In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
Efficiently solving Optimal Power Flow (OPF) problems in power systems is crucial for operational planning and grid management. There is a growing need for scalable algorithms capable of handling the increasing variability, constraints, and…