Related papers: Deep learning observables in computational fluid d…

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

It has been shown that deep learning models can under certain circumstances outperform traditional statistical methods at forecasting. Furthermore, various techniques have been developed for quantifying the forecast uncertainty (prediction…

Machine learning methods have been successful in many areas, like image classification and natural language processing. However, it still needs to be determined how to apply ML to areas with mathematical constraints, like solving PDEs.…

Deep learning has been successful in automating the design of features in machine learning pipelines. However, the algorithms optimizing neural network parameters remain largely hand-designed and computationally inefficient. We study if we…

A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…

Underwater explosions produce complex fluid phenomena relevant to diverse applications including maritime engineering, medical therapeutics, and inertial confinement fusion. These systems exhibit multiphase flows, chemical kinetics, and…

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…

Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve…

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as…

Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for…

This paper presents two novel, physics-informed extreme learning machine (PIELM)-based algorithms for solving steady and unsteady nonlinear partial differential equations (PDEs) related to fluid flow. Although single-hidden-layer PIELMs…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Obtaining accurate solutions to the Schr\"odinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy,…

Computational complexity has been the bottleneck of applying physically-based simulations on large urban areas with high spatial resolution for efficient and systematic flooding analyses and risk assessments. To address this issue of long…

Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…