A Theoretical Framework for Cosmological Field Evolution with Physics-Informed Neural Operators and Geometric Deep Learning
DOI:
https://doi.org/10.65093/aci.v16.n4.2025.44Keywords:
cosmology, neural operators, graph neural networks, dark matterAbstract
The large-scale structure (LSS) of the universe poses formidable computational and theoretical challenges for standard cosmological models. We propose a unified theoretical framework that synthesizes six advanced machine learning paradigms to model the evolution of dark matter fields and the dynamics of the cosmic web. This frame-work integrates (1) Neural Operators (NOs) to learn PDE solvers in the continuous limit, (2) Normalizing Flows (NFs) for simulation-based Bayesian inference with exact likelihoods, (3) topological and geometric methods to characterize the structure of the cosmic web, (4) effective field theories (EFTs) and coarse-graining to model multiscale matter dynamics, (5) causal inference to disentangle systematic effects from underlying physics, and (6) geometric autoencoders to learn symmetry-preserving latent representations. We argue that the hybridization of these approaches offers a promising path toward building high-fidelity, computationally efficient, and physically consistent cosmological emulators, capable of overcoming the limitations of current methods and exploiting the wealth of data from upcoming large-scale surveys.
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