Many of the smooth functions that matter most in physics are precisely the ones that standard neural network methods struggle to fit accurately. Here we present NestyNet, a coupled model-and-optimizer framework capable of fitting such targets to high accuracy while also delivering their gradients, Hessians, Laplacians, and antiderivatives analytically and at low cost. This makes it a natural substrate for scientific machine learning tasks. The model is a deterministic segmented analytic surrogate, and its optimizer is a second-order Levenberg--Marquardt scheme whose damping and linear solves are tailored to the stiff, strongly correlated parameter geometries induced by multiscale and sharply structured targets typical in physics and other scientific applications. On the AI Feynman benchmark of 120 physics equations, NestyNet achieves median improvement factors of $2\,100\times$ for function values, $1\,400\times$ for first derivatives, and $780\times$ for second derivatives relative to standard neural networks trained with first-order optimization (Adam). Even after refining those fits with quasi-Newton (L-BFGS) optimization, the corresponding improvements are $540\times$, $450\times$, and $250\times$. Owing to the analytic design it is up to $\approx 44\times$ faster than vectorized automatic-differentiation (autograd) baselines, with a margin growing with model size. The same analytic-derivative framework also supports vector- and complex-valued targets, measurement uncertainties in both inputs and outputs, and constraints, and its modules can be composed flexibly to build scientifically useful model architectures, all without reverting to autograd. Together, these components provide a practical modular framework for fitting difficult scientific surrogates while delivering accurate differential operators for subsequent analysis.
Astronomers classify galaxy morphology to investigate cosmic evolution. While deep foundation models are increasingly utilized in Galaxy Morphology Classification (GMC), little work has been done on evaluating the uncertainty of GMC results. Uncertainty evaluation is important because astronomical data are inherently noisy due to instrumental and environmental limitations. Also, the continuous evolution of galaxies creates intrinsic morphological ambiguity. However, current foundation models operate as deterministic point estimators, failing to quantify the uncertainty. To overcome this limitation, we propose UEGMC, a post-hoc framework of Uncertainty Estimation for Galaxy Morphology Classification. It categorizes uncertainty in GMC into distinct types by model parameters, astronomical data, reference standards, or intrinsic physical ambiguities, thereby facilitating better classification. Our framework can directly predict uncertainties from representations extracted from the frozen backbones of foundation models, without computationally expensive sampling, therefore enabling fine-grained uncertainty evaluations. Our experimental results demonstrate that UEGMC provides competitive uncertainty quantification performance compared with previous methods.
The Lunar Reconnaissance Orbiter (LRO) has been collecting high-resolution images (at around 0.5-2 meters per pixel linearly with its Narrow Angle Camera) of the Moon since 2009, amassing a large dataset of images and offering researchers the opportunity to study the surface of the Moon at unprecedented scale. Here, we aim to test the abilities of the Beta-Variational Autoencoder (VAE) created by Lesnikowski et al. (2024), an unsupervised learning model which identifies anomalous features across the Moon's surface, locating not only scientifically useful geologic formations such as rockfall deposits, fresh impact craters, irregular mare patches, or volcanic pits/collapsed lava tubes, but also artificial objects such as landed spacecraft. This investigation further gauged the model's ability to locate anomalous surface features, successfully recovering two places of interest (Plaskett Crater and Paracelsus C Crater) and numerous landed technological assets at a statistically significant rate.