Stochastic hierarchical data-driven optimization: application to plasma-surface kinetics

This work introduces a stochastic hierarchical optimization framework inspired by Sloppy Model theory for the efficient calibration of physical models. Central to this method is the use of a reduced Hessian approximation, which identifies and targets the stiff parameter subspace using minimal simulation queries. This strategy enables efficient navigation of highly anisotropic landscapes, avoiding the computational burden of exhaustive sampling. To ensure rigorous inference, we integrate this approach with a probabilistic formulation that derives a principled objective loss function directly from observed data. We validate the framework by applying it to the problem of plasma-surface interactions, where accurate modelling is strictly limited by uncertainties in surface reactivity parameters and the computational cost of kinetic simulations. Comparative analysis demonstrates that our method consistently outperforms baseline optimization techniques in sample efficiency. This approach offers a general and scalable tool for optimizing models of complex reaction systems, ranging from plasma chemistry to biochemical networks.

Conditional Denoising Model as a Physical Surrogate Model

Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a strategy that frequently fails to guarantee strict adherence to the governing equations, or rely on post-processing corrections that do not intrinsically learn the underlying solution geometry. To address these limitations, we introduce the {Conditional Denoising Model (CDM)}, a generative model designed to learn the geometry of the physical manifold itself. By training the network to restore clean states from noisy ones, the model learns a vector field that points continuously towards the valid solution subspace. We introduce a time-independent formulation that transforms inference into a deterministic fixed-point iteration, effectively projecting noisy approximations onto the equilibrium manifold. Validated on a low-temperature plasma physics and chemistry benchmark, the CDM achieves higher parameter and data efficiency than physics-consistent baselines. Crucially, we demonstrate that the denoising objective acts as a powerful implicit regularizer: despite never seeing the governing equations during training, the model adheres to physical constraints more strictly than baselines trained with explicit physics losses.