Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …

In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

In this article, 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 …

The classical development of neural networks has primarily focused on learning map**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

Machine learning develops rapidly, which has made many theoretical breakthroughs and is
widely applied in various fields. Optimization, as an important part of machine learning, has …

We introduce a simple, rigorous, and unified framework for solving nonlinear partial
differential equations (PDEs), and for solving inverse problems (IPs) involving the …

Climate projections continue to be marred by large uncertainties, which originate in
processes that need to be parameterized, such as clouds, convection, and ecosystems. But …

Questions of 'how best to acquire data'are essential to modelling and prediction in the
natural and social sciences, engineering applications, and beyond. Optimal experimental …

In this paper, we study a method to sample from a target distribution π over R^d having a
positive density with respect to the Lebesgue measure, known up to a normalisation factor …