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

Ultrashort-pulse propagation in graded-index multimode fibers is a highly nonlinear phenomenon driven by several physical processes. Although conventional numerical solvers can reproduce this behavior with high fidelity, their computational…

This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…

This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…

Classical orthogonal wavelets guarantee perfect reconstruction but rely on fixed bases optimized for polynomial smoothness, achieving suboptimal compression on signals with fractal spectral signatures. Conversely, learned methods offer…

Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…

Coarse resolution, imperfect parameterizations, and uncertain initial states and forcings limit Earth-system model (ESM) predictions. Traditional bias correction via data assimilation improves constrained simulations but offers limited…

All-in-one image restoration aims to handle diverse degradations within a single model. However, existing methods often suffer from three key limitations: 1) per-input computational overhead from dynamic degradation estimation; 2)…

We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output…

Reinforcement learning (RL) is a classical tool to solve network control or policy optimization problems in unknown environments. The original Q-learning suffers from performance and complexity challenges across very large networks. Herein,…

This work presents a systematic analysis and extension of the sparse radial basis function network (SparseRBFnet) previously introduced for solving nonlinear partial differential equations (PDEs). Based on its adaptive-width shallow kernel…

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

We describe an approach for estimating the statistical risk of deep networks that contain a mix of learned and known operators. Building on the maximal training error bounds previously established for known operator learning, we derive a…

We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms, we train an autoencoder network $D \circ E$ with $E$…

This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, we proposed an approach to directly learn the…

We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…

Transfer Learning enables Convolutional Neural Networks (CNN) to acquire knowledge from a source domain and transfer it to a target domain, where collecting large-scale annotated examples is time-consuming and expensive. Conventionally,…