Particle filters contain the promise of fully nonlinear data assimilation. They have been
applied in numerous science areas, including the geosciences, but their application to high …

Artificial intelligence‐based methods such as chemometrics, machine learning, and deep
learning are promising tools that lead to a clearer and better understanding of data. Only …

Representation, representativity, representativeness error, forward interpolation error,
forward model error, observation‐operator error, aggregation error and sampling error are …

The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

Mathematical models of the most physical phenomena are governed by initial and boundary
value problems for partial differential equations (PDEs). Inverse problems governed by …

We propose a novel approach to model viscoelasticity materials, where rate-dependent and
non-linear constitutive relationships are approximated with deep neural networks. We …

Cardiovascular (CV) disease impacts tens of millions of people annually and carries a
massive global economic burden. Continued advances in medical imaging, hardware and …

Inverse problems associated with designing cylindrical thermal layered shielding and
cloaking shells are studied. Using the optimization method these inverse problems are …

Particle filters are well known in statistics. They have a long tradition in the framework of
ensemble data assimilation (EDA) as well as Markov chain Monte Carlo (MCMC) methods …

Despite their remarkable success in approximating a wide range of operators defined by
PDEs, existing neural operators (NOs) do not necessarily perform well for all physics …