Related papers: Physics-Informed Deep Operator Learning for Comput…

A physics-informed neural network is presented for poroelastic problems with coupled flow and deformation processes. The governing equilibrium and mass balance equations are discussed and specific derivations for two-dimensional cases are…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…

Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

The simulation of fluid flows is computationally expensive due to the complexity of its governing partial differential equations. Machine learning models offer a potential surrogate, enabling learning from simulations and significantly…

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…

Shallow water equations (SWEs) are the backbone of most hydrodynamics models for flood prediction, river engineering, and many other water resources applications. The estimation of flow resistance, i.e., the Manning's roughness coefficient…

Spatio-temporal data, which consists of responses or measurements gathered at different times and positions, is ubiquitous across diverse applications of civil infrastructure. While SciML methods have made significant progress in tackling…

Optimizing fluid-dynamic performance is an important engineering task. Traditionally, experts design shapes based on empirical estimations and verify them through expensive experiments. This costly process, both in terms of time and space,…

The shallow water equations (SWE) model a variety of geophysical flows. Flows in channels with rectangular cross sections may be modelled with a simplified one-dimensional SWE with varying width. Among other model parameters, information…

Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…

This paper introduces wavelet-physics-informed residual neural networks (W-PIRNNs) to study complex fluid flow problems by reconstructing the flow field from highly sparse, supervised data. Our W-PIRNNs fundamentally integrate ResNet and…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

Fast and accurate predictions of turbulent flows are of great importance in the science and engineering field. In this paper, we investigate the implicit U-Net enhanced Fourier neural operator (IUFNO) in the stable prediction of long-time…

Traditional computational fluid dynamics and physics-informed neural networks (PINNs) often suffer from high computational cost, mesh sensitivity, and reduced accuracy for strongly nonlinear and time-dependent flows. To address these…

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections…

DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

The pressure Poisson equation, central to the fractional step method in incompressible flow simulations, incurs high computational costs due to the iterative solution of large-scale linear systems. To address this challenge, we introduce…