Related papers: Convolution Operator Network for Forward and Inver…
We consider ill-posed inverse problems where the forward operator $T$ is unknown, and instead we have access to training data consisting of functions $f_i$ and their noisy images $Tf_i$. This is a practically relevant and challenging…
We have formulated elastic seismic full waveform inversion (FWI) within a deep learning environment. In our formulation, a recurrent neural network is set up with rules enforcing elastic wave propagation, with the wavefield projected onto a…
Ionic models, described by systems of stiff ordinary differential equations, are fundamental tools for simulating the complex dynamics of excitable cells in both Computational Neuroscience and Cardiology. Approximating these models using…
Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows…
Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…
Convolutional architectures have emerged as powerful alternatives to Transformers for sequence modeling. The primary advantage is that they offer improved theoretical sequence length complexity by leveraging the Fast Fourier Transform…
Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…
High-fidelity modeling of turbulent flows is one of the major challenges in computational physics, with diverse applications in engineering, earth sciences and astrophysics, among many others. The rising popularity of high-fidelity…
We propose a novel convolutional neural network (CNN), called $\Psi$DONet, designed for learning pseudodifferential operators ($\Psi$DOs) in the context of linear inverse problems. Our starting point is the Iterative Soft Thresholding…
Advanced nuclear reactors often exhibit complex thermal-fluid phenomena during transients. To accurately capture such phenomena, a coarse-mesh three-dimensional (3-D) modeling capability is desired for modern nuclear-system code. In the…
Machine learning algorithms have been successfully used to approximate nonlinear maps under weak assumptions on the structure and properties of the maps. We present deep neural networks using dense and convolutional layers to solve an…
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by…
Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as…
Accurate and interpretable bearing fault classification is critical for ensuring the reliability of rotating machinery, particularly under variable operating conditions where domain shifts can significantly degrade model performance. This…
An accurate velocity model is essential to make a good seismic image. Conventional methods to perform Velocity Model Building (VMB) tasks rely on inverse methods, which, despite being widely used, are ill-posed problems that require intense…
This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit…
High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as…
Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…
Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…
We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment,…