# NeuralPDR: Neural Differential Equations as surrogate models for Photodissociation Regions

arXiv: https://arxiv.org/abs/2506.14270 · HTML: https://mlsanity.com/paper/2506.14270/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Builds on (most cited first, 15 of 15)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [Efficient Marginalization of Discrete and Structured Latent Variables via Sparsity](https://mlsanity.com/paper/2007.01919/) (2020)
- [Neural networks: solving the chemistry of the interstellar medium](https://mlsanity.com/paper/2211.15688/) (2022)
- [Speeding up astrochemical reaction networks with autoencoders and neural ODEs](https://mlsanity.com/paper/2312.06015/) (2023)
- [Emulating the interstellar medium chemistry with neural operators](https://mlsanity.com/paper/2402.12435/) (2024)
- [CODES: Benchmarking Coupled ODE Surrogates](https://mlsanity.com/paper/2410.20886/) (2024)
- [3D-PDR Orion dataset and NeuralPDR: Neural Differential Equations for Photodissociation Regions](https://mlsanity.com/paper/2412.00758/) (2024)

## Built on by (most cited first, 1 of 1)

- [Weight-Parameterization in Continuous Time Deep Neural Networks for Surrogate Modeling](https://mlsanity.com/paper/2507.22045/) (2025)

## Abstract (arXiv)

Computational astrochemical models are essential for helping us interpret and understand the observations of different astrophysical environments. In the age of high-resolution telescopes such as JWST and ALMA, the substructure of many objects can be resolved, raising the need for astrochemical modeling at these smaller scales, meaning that the simulations of these objects need to include both the physics and chemistry to accurately model the observations. The computational cost of the simulations coupling both the three-dimensional hydrodynamics and chemistry is enormous, creating an opportunity for surrogate models that can effectively substitute the chemical solver. In this work we present surrogate models that can replace the original chemical code, namely Latent Augmented Neural Ordinary Differential Equations. We train these surrogate architectures on three datasets of increasing physical complexity, with the last dataset derived directly from a three-dimensional simulation of a molecular cloud using a Photodissociation Region (PDR) code, 3D-PDR. We show that these surrogate models can provide speedup and reproduce the original observable column density maps of the dataset. This enables the rapid inference of the chemistry (on the GPU), allowing for the faster statistical inference of observations or increasing the resolution in hydrodynamical simulations of astrophysical environments.