Fast Amortized Fitting of Scientific Signals Across Time and Ensembles via Transferable Neural Fields

Neural fields, also known as implicit neural representations (INRs), offer a powerful framework for modeling continuous geometry, but their effectiveness in high-dimensional scientific settings is limited by slow convergence and scaling challenges. In this study, we extend INR models to handle spatiotemporal and multivariate signals and show how INR features can be transferred across scientific signals to enable efficient and scalable representation across time and ensemble runs in an amortized fashion. Across controlled transformation regimes (e.g., geometric transformations and localized perturbations of synthetic fields) and high-fidelity scientific domains-including turbulent flows, fluid-material impact dynamics, and astrophysical systems-we show that transferable features improve not only signal fidelity but also the accuracy of derived geometric and physical quantities, including density gradients and vorticity. In particular, transferable features reduce iterations to reach target reconstruction quality by up to an order of magnitude, increase early-stage reconstruction quality by multiple dB (with gains exceeding 10 dB in some cases), and consistently improve gradient-based physical accuracy.

When are Diffusion Priors Helpful in Sparse Reconstruction? A Study with Sparse-view CT

Diffusion models demonstrate state-of-the-art performance on image generation, and are gaining traction for sparse medical image reconstruction tasks. However, compared to classical reconstruction algorithms relying on simple analytical priors, diffusion models have the dangerous property of producing realistic looking results \emph{even when incorrect}, particularly with few observations. We investigate the utility of diffusion models as priors for image reconstruction by varying the number of observations and comparing their performance to classical priors (sparse and Tikhonov regularization) using pixel-based, structural, and downstream metrics. We make comparisons on low-dose chest wall computed tomography (CT) for fat mass quantification. First, we find that classical priors are superior to diffusion priors when the number of projections is ``sufficient''. Second, we find that diffusion priors can capture a large amount of detail with very few observations, significantly outperforming classical priors. However, they fall short of capturing all details, even with many observations. Finally, we find that the performance of diffusion priors plateau after extremely few ($\approx$10-15) projections. Ultimately, our work highlights potential issues with diffusion-based sparse reconstruction and underscores the importance of further investigation, particularly in high-stakes clinical settings.