Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep surrogate accelerated delayed-acceptance HMC for Bayesian inference
  of spatio-temporal heat fluxes in rotating disc systems   We study the Bayesian inverse problem of inferring the Biot number, a
spatio-temporal heat-flux parameter in a PDE model. This is an ill-posed
problem where standard optimisation yields unphysical inferences. We introduce
a training scheme that uses temperature data to adaptively train a
neural-network surrogate to simulate the parametric forward model. This
approach approximates forward and inverse solution together, by simultaneously
identifying an approximate posterior distribution over the Biot number, and
weighting the forward training loss according to this approximation. Utilising
random Chebyshev series, we outline how to approximate an arbitrary Gaussian
process prior, and using the surrogate we apply Hamiltonian Monte Carlo (HMC)
to efficiently sample from the corresponding posterior distribution. We derive
convergence of the surrogate posterior to the true posterior distribution in
the Hellinger metric as our adaptive loss function approaches zero.
Furthermore, we describe how this surrogate-accelerated HMC approach can be
combined with a traditional PDE solver in a delayed-acceptance scheme to
a-priori control the posterior accuracy, thus overcoming a major limitation of
deep learning-based surrogate approaches, which do not achieve guaranteed
accuracy a-priori due to their non-convex training. Biot number calculations
are involved turbo-machinery design, which is safety critical and highly
regulated, therefore it is important that our results have such mathematical
guarantees. Our approach achieves fast mixing in high-dimensional parameter
spaces, whilst retaining the convergence guarantees of a traditional PDE
solver, and without the burden of evaluating this solver for proposals that are
likely to be rejected. Numerical results compare the accuracy and efficiency of
the adaptive and general training regimes, as well as various Markov chain
Monte Carlo proposals strategies.

16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio