Abstract: Reconstructing the early universe from the evolved present-day cosmic web is a formidable computational challenge. Traditional 3D grid simulations suffer from the "void problem" because cosmic voids occupy approximately 64% of the universe's volume but contain only 16% of its mass, and uniform voxel representations waste billions of floating-point operations processing essentially empty space.

To address these dimensionality and sparsity bottlenecks, we introduce Cosmo3DFlow, a novel generative artificial intelligence framework that powers a practical digital twin of the universe. Cosmo3DFlow overcomes existing simulation limitations through two key innovations: 1) Spatial-to-Spectral Compression: By integrating a 3D Discrete Wavelet Transform (DWT), we address the void problem by translating spatial emptiness into spectral sparsity. This achieves an 8x spatial compression by decoupling high-frequency details from low-frequency structures, ensuring computational density is concentrated solely on mass-dense filaments and halos. 2) Wavelet Flow Matching: Unlike stochastic diffusion models, we formulate generation as solving a deterministic ordinary differential equation (ODE) using flow matching in the wavelet domain. This yields stable, wavelet-space velocity fields that allow ODE solvers to utilize significantly larger step sizes.

At 1283 resolutions, Cosmo3DFlow achieves up to a 50x sampling speedup over state-of-the-art diffusion models. By combining a 10x reduction in integration steps with a 5x lower per-step computational cost, Cosmo3DFlow enables cosmological initial conditions to be sampled in seconds rather than minutes, maintaining rigorous physical accuracy and paving the way for next-generation astrophysical inference.

Bio: Judy Fox is an Associate Professor in the School of Data Science at the University of Virginia. Her expertise spans big data analytics and computer systems, with research focused on innovative AI systems and real-time machine learning for interdisciplinary applications, including biomedical science, graph and network science, and astronomy. She led an Intel Parallel Computing Center (IPCC) site. Her research has been supported by the National Science Foundation (NSF), National Institutes of Health (NIH), Intel, Microsoft, and Google. Dr. Fox received her Ph.D. in Computer Science from Syracuse University in 2005 with the Outstanding Graduate Student Award. She is also a recipient of the NSF CAREER Award and most recently served as Director of the Ph.D. Program in Data Science at the University of Virginia’s School of Data Science.