Neural networks: solving the chemistry of the interstellar medium

Abstract

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 ($-2<\log n/{\mathrm{cm}}^{-3}<3$) and temperatures ($1<\log T/\mathrm{K}<5$), 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.

16 pages, 12 figures, accepted for publication on MNRAS

References in corpus (17)

• The NumPy array: a structure for efficient numerical computation
• Grackle: a Chemistry and Cooling Library for Astrophysics
• Uncertainties in H2 and HD Chemistry and Cooling and their Role in Early Structure Formation
• Physics Informed Neural Networks for Simulating Radiative Transfer
• Metal and molecule cooling in simulations of structure formation
• Metal and molecule cooling in simulations of structure formation
• Deep into the structure of the first galaxies: SERRA views
• UCLCHEM: A Gas-Grain Chemical Code
• When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
• The impact of chemistry on the structure of high-z galaxies
• A survey of high-$z$ galaxies: SERRA simulations
• Machine learning astrophysics from 21 cm lightcones: impact of network architectures and signal contamination
• Photoevaporation of Jeans-unstable molecular clumps
• Chemulator: Fast, accurate thermochemistry for dynamical models through emulation
• Shaping the structure of a GMC with radiation and winds
• Machine Learning the 6th Dimension: Stellar Radial Velocities from 5D Phase-Space Correlations
• The Astrochemical Evolution of Turbulent Giant Molecular Clouds : I - Physical Processes and Method of Solution for Hydrodynamic, Embedded Starless Clouds

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• Neural Infalling Cloud Equations (NICE): Increasing the Efficacy of Subgrid Models and Scientific Equation Discovery using Neural ODEs and Symbolic Regression
• Systematic selection of surrogate models for nonequilibrium chemistry