Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast and accurate multidimensional free energy integration   Enhanced sampling and free energy calculation algorithms of the Thermodynamic
Integration family (such as the Adaptive Biasing Force method, ABF) are not
based on the direct computation of a free energy surface, but rather of its
gradient. Integrating the free energy surface is non-trivial in dimension
higher than one. Here the author introduces a flexible, portable implementation
of a Poisson equation formalism to integrate free energy surfaces from
estimated gradients in dimension 2 and 3, using any combination of periodic and
non-periodic (Neumann) boundary conditions. The algorithm is implemented in
portable C++, and provided as a standalone tool that can be used to integrate
multidimensional gradient fields estimated on a grid using any algorithm, such
as Umbrella Integration as a post-treatment of Umbrella Sampling simulations.
It is also included in the implementation of ABF (and its extended-system
variant eABF) in the Collective Variables Module, enabling the seamless
computation of multidimensional free energy surfaces within ABF and eABF
simulations. A Python-based analysis toolchain is provided to easily plot and
analyze multidimensional ABF simulation results, including metrics to assess
their convergence. The Poisson integration algorithm can also be used to
perform Helmholtz decomposition of noisy gradients estimates on the fly,
resulting in an efficient implementation of the projected ABF (pABF) method
proposed by Leli\`evre and co-workers. In numerical tests, pABF is found to
lead to faster convergence with respect to ABF in simple cases of low intrinsic
dimension, but seems detrimental to convergence in a more realistic case
involving degenerate coordinates and hidden barriers, due to slower
exploration. This suggests that variance reduction schemes do not always yield
convergence improvements when applied to enhanced sampling methods.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
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The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex