Related papers: A Filtered MgNet Solver For Radiative Transfer Equ…

We present MorphNet, an approach to automate the design of neural network structures. MorphNet iteratively shrinks and expands a network, shrinking via a resource-weighted sparsifying regularizer on activations and expanding via a uniform…

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…

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of…

The parametric radiative transfer equation (RTE) arises in multi-query applications, such as design optimization, inverse problems, and uncertainty quantification, which require solving the RTE multiple times for various parameters.…

Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…

To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…

MRI is an inherently slow process, which leads to long scan time for high-resolution imaging. The speed of acquisition can be increased by ignoring parts of the data (undersampling). Consequently, this leads to the degradation of image…

In this paper, we investigate learning-based MIMO-OFDM symbol detection strategies focusing on a special recurrent neural network (RNN) -- reservoir computing (RC). We first introduce the Time-Frequency RC to take advantage of the…

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a…

Preconditioned adaptive methods have gained significant attention for training deep neural networks, as they capture rich curvature information of the loss landscape. The central challenge in this field lies in balancing preconditioning…

This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

In this work, we introduce a novel neural operator, the Solute Transport Operator Network (STONet), to efficiently model contaminant transport in micro-cracked porous media. STONet's model architecture is specifically designed for this…

The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural…

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…

Operator learning has emerged as a promising paradigm for approximating solution operators of partial differential equations (PDEs). However, conventional approaches typically rely on pointwise function discretizations, which often suffer…