Related papers: Bayesian Inversion with Neural Operator (BINO) for…
Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…
Bagging has achieved great success in the field of machine learning by integrating multiple base classifiers to build a single strong classifier to reduce model variance. The performance improvement of bagging mainly relies on the number…
Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…
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…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…
Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, the Fourier-based neural operator framework inherently truncates high-frequency…
We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…
Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…
We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…
Neural channel decoder, as a data-driven channel decoding strategy, has shown very promising improvement on error-correcting capability over the classical methods. However, the success of those deep learning-based decoder comes at the cost…
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…
The backwards diffusion equation is one of the classical ill-posed inverse problems, related to a wide range of applications, and has been extensively studied over the last 50 years. One of the first methods was that of {\it…
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with…
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…
Bayesian optimization (BO) is a popular framework to optimize black-box functions. In many applications, the objective function can be evaluated at multiple fidelities to enable a trade-off between the cost and accuracy. To reduce the…
Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is…
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…