Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian deep learning.

Area of Science:

• Computational physics
• Astrophysics
• Machine learning

Background:

• Generative models struggle with high-dimensional data, limiting their application in complex scientific simulations.
• Physical processes in nature possess inherent symmetries and constraints that are challenging for standard generative models to capture.

Purpose of the Study:

• To develop a scalable generative model for high-dimensional data by incorporating physical constraints.
• To apply this novel approach to cosmological hydrodynamical simulations, learning effective physical laws from data.

Main Methods:

• Introduced Lagrangian deep learning (LDL), a method that models particle displacements as gradients of an effective potential, ensuring physical invariances.
• Integrated LDL with the Fast Particle Mesh (FastPM) N-body solver for cosmological simulations.
• Utilized a small number of layers (around 10) to learn effective theory parameters.

Main Results:

• LDL successfully learned effective physical laws, enabling generative modeling in very high dimensions.
• The LDL-FastPM combination accurately simulated a range of cosmological outputs, including dark matter, stellar, gas density, and temperature maps.
• Achieved computational costs nearly four orders of magnitude lower than full hydrodynamical simulations while outperforming them at equivalent resolutions.

Conclusions:

• Lagrangian deep learning provides a highly efficient and accurate method for simulating complex physical systems like those in cosmology.
• The framework significantly reduces computational cost and time, making it feasible to analyze cosmological observations without massive simulations.
• This approach opens new avenues for integrating generative models with physical laws for scientific discovery.