Dark Quest II: A Wide-Coverage Neural Network Emulator of the Nonlinear Matter Power Spectrum Across Extended Cosmologies

We are witnessing a surge in observations of the cosmic dawn (CD) and epoch of reionisation (EoR), driving an increasing demand for fast and robust theoretical interpretation frameworks. In response, machine learning (ML), and emulation in particular, has emerged as a powerful approach to accelerate and enhance inference pipelines. In this work, we present 21cmEMUv3, an emulator trained on 21cmFASTv3 simulations that model both atomically and molecularly cooling galaxies. 21cmEMUv3 is conditioned on $σ_8$ and ten astrophysical parameters to produce seven summary observables: (i) the cylindrical 21cm power spectrum (PS), emulated for the first time at such high resolution and accuracy across a wide redshift range of $z \sim$ 6--30; (ii) the spherically-averaged 21cm PS; (iii) the mean neutral fraction of the intergalactic medium (IGM); (iv) the mean 21cm spin temperature; (v) the global 21cm signal; (vi) the ultraviolet (UV) luminosity functions (LFs); and (vii) the Thomson scattering optical depth. Notably, the cylindrical 21cm PS is emulated via score-based diffusion, while the remaining six summaries are emulated via long-short term memory (LSTM) networks, all achieving sub-percent median accuracy. We use the emulator to reinterpret current 21cm PS upper limits from HERA, for the first time using state-of-the-art hydrodynamical simulations to inform priors on star formation inside molecularly cooling galaxies. We find that our inferred soft-band X-ray luminosity per unit star formation rate is consistent with extrapolations of high-mass X-ray binaries to the low-metallicity regimes expected in the first galaxies, excluding values below $10^{39.2}$ erg s$^{-1}M^{-1}_\odot \rm{yr}$ at $95\%$ confidence. Finally, we produce forecasts for the detection of the cosmic 21cm PS with the Square Kilometre Array for different array configurations. The 21cmEMU package is publicly available.

Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable. Traditional N-body simulations are accurate but computationally prohibitive for iterative inference, while approximate solvers like Lagrangian Perturbation Theory (LPT) fail to capture the knotty halo-forming dynamics of the cosmic web at late times. We introduce the \textit{Lagrangian Neural Cellular Automaton} (LNCA), a hybrid deep learning framework that can be applied to emulate structure formation as a local, iterative dynamical process on a comoving lattice. Unlike standard Eulerian Convolutional Neural Networks (CNNs) which map fixed density fields, the LNCA operates in the Lagrangian frame, advecting the computational graph itself to follow the flow of mass. By training the network to learn only the \textit{residual} displacement corrections to the Zeldovich approximation, we achieve high-fidelity emulation of the non-linear physics while guaranteeing accuracy at large scales. We further constrain our model to produce complete trajectories, not just final states, by adopting an equivariant cellular automaton architecture, which recurrently iterates on its internal states to yield a dynamic history. The resulting model is strictly local, translationally and rotationally equivariant, and naturally supports continuous time integration, making it a reliable differentiable forward model for reconstructing the initial conditions of the universe from lightcone data. Our trained model supports percent-level precision in the power and cross spectra well into the non-linear regime ($k \lesssim 0.5 \, h \text{Mpc}^{-1}$), while requiring $\sim10^4$ times fewer learned parameters than comparable models which take the form of an interpretable internal dynamic rule set.

Ocean general circulation models (OGCMs) are essential to climate science but computationally expensive, limiting ensemble size and forcing scenarios. Neural emulators promise orders-of-magnitude speedups, yet existing ocean emulators have not combined fine spatial resolution with multi-year autoregressive rollouts. Samudra, the first autoregressive neural ocean emulator to produce multi-decade global rollouts, is limited to $1^\circ$ resolution and exhibits two long-horizon failure modes: \emph{variance collapse}, the loss of temporal variability, and \emph{imprinting artifacts}, in which velocity patterns leak into deep-ocean fields. We present Samudra 2, which introduces a wider U-Net backbone with modified ConvNeXt-style blocks and a reduced block-internal expansion factor, together with a dynamic loss that reweights output channels according to their prediction errors, strengthening gradients for slow-evolving deep-ocean fields. At $1^\circ$, Samudra 2 increases upper-ocean global-mean temperature $R^2$ from 0.56 to 0.87 and reduces deep-ocean temperature error by roughly sevenfold. The same architecture scales to $1/2^\circ$ and $1/4^\circ$ over approximately 8-year autoregressive rollouts, recovering mesoscale eddies and sharp western boundary currents. Running on a single GPU, Samudra 2 enables larger ensembles for sea-level projections, ocean heat uptake, and climate variability studies. All artifacts are publicly available: project page, code, checkpoints, documentation.