Related papers: Uniformly accurate structure-preserving neural sur…

This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…

Boundary incompleteness raises great challenges to automatic prostate segmentation in ultrasound images. Shape prior can provide strong guidance in estimating the missing boundary, but traditional shape models often suffer from hand-crafted…

Multi-fidelity surrogate modeling aims to learn an accurate surrogate at the highest fidelity level by combining data from multiple sources. Traditional methods relying on Gaussian processes can hardly scale to high-dimensional data. Deep…

This paper concerns solving the steady radiative transfer equation with diffusive scaling, using the physics informed neural networks (PINNs). The idea of PINNs is to minimize a least-square loss function, that consists of the residual from…

We propose a novel learnable representation for detail-preserving shape deformation. The goal of our method is to warp a source shape to match the general structure of a target shape, while preserving the surface details of the source. Our…

U-Nets are a go-to, state-of-the-art neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper,…

Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop…

In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…

Biophysical neural system simulations are among the most computationally demanding scientific applications, and their optimization requires navigating high-dimensional parameter spaces under numerous constraints that impose a binary…

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

Objective: Deep learning-based deformable image registration has achieved strong accuracy, but remains sensitive to variations in input image characteristics such as artifacts, field-of-view mismatch, or modality difference. We aim to…

Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…

There is renewed interest in developing small modular reactors and micro-reactors. Innovation is necessary in both construction and operation methods of these reactors to be financially attractive. For operation, an area of interest is the…

We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a…

Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…

Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not…

Neural operators, serving as physics surrogate models, have recently gained increased interest. With ever increasing problem complexity, the natural question arises: what is an efficient way to scale neural operators to larger and more…

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…