Related papers: Designing Neural Networks for Hyperbolic Conservat…

We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…

We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…

In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network…

Fluid dynamics spans phenomena from the Cheerios effect to cosmic evolution and has been called the 'queen mother' of science. Traditional modelling relies on numerical methods, including finite differences, volumes, and elements, that…

This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon the prior research incorporating a data-driven finite-difference approximation of smooth solutions…

The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…

Physics-informed neural networks have gained popularity as a deep-learning based parametric partial differential equation solver. Especially for engineering applications, this approach is promising because a single neural network could…

We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection. Our model is formulated as a hypernetwork: it…

Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al.…

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…

To reliably project future sea level rise, ice sheet models require inputs that respect physics. Embedding physical principles like mass conservation into models that interpolate Antarctic ice flow vector fields from sparse & noisy…

In this paper, we aim at developing scalable neural network-type learning systems. Motivated by the idea of "constructive neural networks" in approximation theory, we focus on "constructing" rather than "training" feed-forward neural…

We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…

Deep convolutional neural networks (CNNs) have delivered superior performance in many computer vision tasks. In this paper, we propose a novel deep fully convolutional network model for accurate salient object detection. The key…

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…

Power flow analysis plays a critical role in the control and operation of power systems. The high computational burden of traditional solution methods led to a shift towards data-driven approaches, exploiting the availability of digital…

We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key…