Neural networks: solving the chemistry of the interstellar medium by Lorenzo Branca et al. on Wednesday 30 November

Non-equilibrium chemistry is a key process in the study of the InterStellar

Medium (ISM), in particular the formation of molecular clouds and thus stars.

However, computationally it is among the most difficult tasks to include in

astrophysical simulations, because of the typically high (>40) number of

reactions, the short evolutionary timescales (about $10^4$ times less than the

ISM dynamical time) and the characteristic non-linearity and stiffness of the

associated Ordinary Differential Equations system (ODEs). In this proof of

concept work, we show that Physics Informed Neural Networks (PINN) are a viable

alternative to traditional ODE time integrators for stiff thermo-chemical

systems, i.e. up to molecular hydrogen formation (9 species and 46 reactions).

Testing different chemical networks in a wide range of densities ($-2< \log

n/{\rm cm}^{-3}< 3$) and temperatures ($1 < \log T/{\rm K}< 5$), we find that a

basic architecture can give a comfortable convergence only for simplified

chemical systems: to properly capture the sudden chemical and thermal

variations a Deep Galerkin Method is needed. Once trained ($\sim 10^3$ GPUhr),

the PINN well reproduces the strong non-linear nature of the solutions (errors

$\lesssim 10\%$) and can give speed-ups up to a factor of $\sim 200$ with

respect to traditional ODE solvers. Further, the latter have completion times

that vary by about $\sim 30\%$ for different initial $n$ and $T$, while the

PINN method gives negligible variations. Both the speed-up and the potential

improvement in load balancing imply that PINN-powered simulations are a very

palatable way to solve complex chemical calculation in astrophysical and

cosmological problems.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.15688v1