This paper is a basic tutorial on the adjoint method when used in a computational scheme
for solving an inverse problem. The adjoint method is a technique for the efficient calculation …

Data-driven science and technology offer transformative tools and methods to science. This
review article highlights the latest development and progress in the interdisciplinary field of …

Here we employ and adapt the image-to-image translation concept based on conditional
generative adversarial networks (cGAN) for learning a forward and an inverse solution …

We propose derivative-informed neural operators (DINOs), a general family of neural
networks to approximate operators as infinite-dimensional map**s from input function …

Many-query problems–arising from, eg, uncertainty quantification, Bayesian inversion,
Bayesian optimal experimental design, and optimization under uncertainty–require …

We explore using neural operators, or neural network representations of nonlinear maps
between function spaces, to accelerate infinite-dimensional Bayesian inverse problems …

Rock strength has long been linked to lithospheric deformation and seismicity. However,
independent constraints on the related elastic heterogeneity are missing, yet could provide …

We develop a fast and scalable computational framework to solve Bayesian optimal
experimental design problems governed by partial differential equations (PDEs) with …

We consider a mixture-theoretic continuum model of the spread of COVID-19 in Texas. The
model consists of multiple coupled partial differential reaction–diffusion equations governing …

Bayesian inference provides a systematic framework for integration of data with
mathematical models to quantify the uncertainty in the solution of the inverse problem …