Galaxy formation and evolution critically depend on understanding the complex photo-chemical processes that govern the evolution and thermodynamics of the InterStellar Medium (ISM). Computationally, solving chemistry is among the most heavy tasks in cosmological and astrophysical simulations. The evolution of such non-equilibrium photo-chemical network relies on implicit, precise, computationally costly, ordinary differential equations (ODE) solvers. Here, we aim at substituting such procedural solvers with fast, pre-trained, emulators based on neural operators. We emulate a non-equilibrium chemical network up to H$_2$ formation (9 species, 52 reactions) by adopting the DeepONet formalism, i.e. by splitting the ODE solver operator that maps the initial conditions and time evolution into a tensor product of two neural networks. We use $\texttt{KROME}$ to generate a training set spanning $-2\leq \log(n/\mathrm{cm}^{-3}) \leq 3.5$, $\log(20) \leq\log(T/\mathrm{K}) \leq 5.5$, $-6 \leq \log(n_i/n) < 0$, and by adopting an incident radiation field $\textbf{F}$ sampled in 10 energy bins with a continuity prior. We separately train the solver for $T$ and each $n_i$ for $\simeq 4.34\,\rm GPUhrs$. Compared with the reference solutions obtained by $\texttt{KROME}$ for single zone models, the typical precision obtained is of order $10^{-2}$, i.e. the $10 \times$ better with a training that is $40 \times$ less costly with respect to previous emulators which however considered only a fixed $\mathbf{F}$. The present model achieves a speed-up of a factor of $128 \times$ with respect to stiff ODE solvers. Our neural emulator represents a significant leap forward in the modeling of ISM chemistry, offering a good balance of precision, versatility, and computational efficiency.

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.

Predicting of chemical compounds is one of the fundamental tasks in bioinformatics and chemoinformatics, because it contributes to various applications in metabolic engineering and drug discovery. The recent rapid growth of the amount of available data has enabled applications of computational approaches such as statistical modeling and machine learning method. Both a set of chemical interactions and chemical compound structures are represented as graphs, and various graph-based approaches including graph convolutional neural networks have been successfully applied to chemical network prediction. However, there was no efficient method that can consider the two different types of graphs in an end-to-end manner. We give a new formulation of the chemical network prediction problem as a link prediction problem in a graph of graphs (GoG) which can represent the hierarchical structure consisting of compound graphs and an inter-compound graph. We propose a new graph convolutional neural network architecture called dual graph convolutional network that learns compound representations from both the compound graphs and the inter-compound network in an end-to-end manner. Experiments using four chemical networks with different sparsity levels and degree distributions shows that our dual graph convolution approach achieves high prediction performance in relatively dense networks, while the performance becomes inferior on extremely-sparse networks.