Gianluca Gregori

Abstract:

Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation-the canonical use cases-provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.

Abstract:

<jats:p>Time-resolved neutron information is essential for understanding the dynamics of inertial confinement fusion (ICF) implosions, providing key indicators that distinguish igniting from non-igniting plasmas and revealing the underlying causes of shot-to-shot performance variations. The moments method framework offers a practical pathway to extract such temporally resolved quantities using only a small number of neutron time-of-flight detectors. For example, one only needs four detectors to extract the burn-averaged rate of change of ion temperature, a well-defined physically useful quantity. In this work, we evaluate and validate the moments method across several levels of complexity. We first employ a controlled toy model to test the foundational assumptions and mathematical structure of the approach. We then demonstrate that the method generalizes to realistic one-dimensional simulation data of direct drive implosions with a 25 kJ laser driver that include time-dependent ion temperature evolution and hydrodynamic burn dynamics. Together, these results establish the moments method as an experimentally accessible and robust tool for extracting unique and independent information such as the burn-averaged rates of change of fluid velocity and ion temperature with time from neutron time-of-flight measurements, broadening the diagnostic capability of existing neutron detector systems. Fielding this diagnostic on ICF campaigns would improve our understanding of failure modes, helping to determine causes for improved or reduced performance during implosions, informing future target and laser drive design.</jats:p>

Abstract:

Accurate modeling of heat flux in inertial confinement fusion plasmas requires closures that remain predictive far from local equilibrium and across disparate spatial and temporal resolutions. We develop a resolution-robust machine learning heat flux closure trained on particle-in-cell simulations using a Fourier neural operator. Two nonlocal electron thermal conduction models are trained and tested. When embedded self-consistently into the electron energy equation, the learned closure faithfully reproduces the temperature evolution and shows good temporal extrapolation and generalization capability. Remarkably, models trained on coarse-resolution data accurately predict heat flux when deployed in substantially finer-resolution implicit, iterative solvers of the energy equation, significantly enhancing the practicality of embedding data-driven closures into partial differential equation solvers. These results establish a data-driven closure that bridges kinetic and fluid descriptions and provides a viable pathway for treating machine learning as an iterative solver within the radiation-hydrodynamic simulations of inertial confinement fusion plasma.