Related papers: Accelerated replica exchange stochastic gradient L…

Accelerating the solution of nonlinear partial differential equations (PDEs) while maintaining accuracy at coarse spatiotemporal resolution remains a key challenge in scientific computing. Physics-informed machine learning (ML) methods such…

Diffusion models demonstrate remarkable capabilities in capturing complex data distributions and have achieved compelling results in many generative tasks. While they have recently been extended to dense prediction tasks such as depth…

We develop a class of data-driven generative models that approximate the solution operator for parameter-dependent partial differential equations (PDE). We propose a novel probabilistic formulation of the operator learning problem based on…

This paper introduces Progressively Diffused Networks (PDNs) for unifying multi-scale context modeling with deep feature learning, by taking semantic image segmentation as an exemplar application. Prior neural networks, such as ResNet, tend…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

We introduce Discontinuous Galerkin Finite Element Operator Network (DG--FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin (DG) method with neural networks to solve parametric partial…

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and…

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…

As overparameterized models become increasingly prevalent, training loss alone offers limited insight into generalization performance. While smoothness has been linked to improved generalization across various settings, directly enforcing…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

We study Bayesian hypernetworks: a framework for approximate Bayesian inference in neural networks. A Bayesian hypernetwork $\h$ is a neural network which learns to transform a simple noise distribution, $p(\vec\epsilon) = \N(\vec 0,\mat…

Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms:…

In this paper, we propose a deep neural network approximation to the evolution operator for time dependent PDE systems over long time period by recursively using one single neural network propagator, in the form of POD-DeepONet with…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be…

Deep Learning (DL) holds great promise in reshaping the industry owing to its precision, efficiency, and objectivity. However, the brittleness of DL models to noisy and out-of-distribution inputs is ailing their deployment in sensitive…

The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond…

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…

Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new…

Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…