BHCast: Unlocking Black Hole Plasma Dynamics from a Single Blurry Image with Long-Term Forecasting

General-relativistic magnetohydrodynamic (GR-MHD) simulations are essential for studying black hole accretion, relativistic jets, and magnetic reconnection, yet their computational cost severely limits systematic parameter exploration. We investigate neural operator surrogates for two astrophysically relevant simulation scenarios produced by the Black Hole Accretion Code (BHAC). First, a Physics Informed Fourier Neural Operator (PINO) is trained on the special-relativistic resistive MHD (SRRMHD) evolution of the Orszag-Tang vortex over a range of resistivities spanning the Sweet-Parker and fast reconnection regimes. By embedding the governing equations as an additional loss term evaluated at finer temporal resolution than the available data supervision, the model learns dynamics at time steps where no simulation data is provided, enabling recovery of plasmoid formation that a data-only baseline trained on the same sparse snapshots fails to reproduce. To our knowledge, the present work is the first application of a physics informed neural operator to special relativistic resistive MHD, and the first to investigate the capability of such models to resolve plasmoid formation in SRRMHD. In a second line of investigation, an OFormer-style Transformer Neural Operator is trained on the evolution of spine-sheath relativistic jets created with BHAC, in special-relativistic MHD (SRMHD). The model is directly applied on the adaptive mesh, highlighting the need for linear attention due to long sequences. The neural surrogate model is capable of capturing most of the major details, especially in early predictions. To our knowledge, this constitutes the first application of a neural operator directly on a high resolution adaptive mesh refinement grid in the context of MHD simulations.

Many challenges in scientific imaging involve solving ill-posed inverse problems, where the goal is to recover spatio-temporal fields from indirect, noisy, and highly sparse measurements - often without access to ground truth data or reliable simulators. To address this challenging scenario, we present NeuralDMD, an interpretable, untrained (per-instance) reconstruction framework that combines neural implicit representations with Dynamic Mode Decomposition (DMD) to reconstruct continuous spatio-temporal dynamics directly from measurements. NeuralDMD parameterizes DMD modes as continuous neural fields, and imposes a low-rank linear dynamics prior with spectral time evolution to enforce temporal continuity. This formulation enables both forecasting under sparsity, and yields interpretable modes and spectra. We find that NeuralDMD outperforms baselines on a wide variety of tasks: from weather data assimilation from sparse station observations to interferometric (Fourier domain) observations of Sagittarius A, the black hole at the center of our galaxy. Moreover, NeuralDMD remains stable when extrapolating into the future. While this framework is most naturally suited to linear dynamics, we show that it can be applied to nonlinear regimes, though with extrapolation performance that degrades with increasing nonlinearity. Together, these results show that NeuralDMD enables interpretable reconstruction and forecasting of spatio-temporal dynamics directly from sparse and indirect measurements without relying on numerical simulators or training data.

Pulsar timing arrays (PTAs) provide a unique window into nanohertz gravitational waves (GWs), but extracting astrophysical parameters from noisy, long-baseline timing residuals remains computationally challenging with traditional Bayesian techniques due to the high dimensionality of the parameter space, complex and correlated noise models, and the cost of repeated likelihood evaluations. We introduce a Transformer with a physics-informed positional-encoding framework for the efficient inference of eccentric binary black holes in relativistic orbits from PTA data. Our approach embeds analytical GW phase evolution directly into the model through structured positional encodings, enabling the network to learn physically meaningful representations from raw PTA timing residuals. We then use generative models, including discrete and continuous conditional normalizing flows, to infer posterior distributions within a simulation-based inference framework. Across a range of signal-to-noise ratios, the proposed method achieves improved accuracy, sharper posteriors, and faster inference compared to physics-agnostic baselines. While presented for deterministic white-noise signals, the modular framework readily generalizes to realistic PTA analyses incorporating red noise and additional components. This work highlights the potential of physics-aware deep learning models as scalable alternatives to conventional inference pipelines for next-generation PTA datasets.