Differentiable programming has emerged as an important tool for gradient-based inverse problems and end-to-end hybrid physics–machine learning in computational fluid dynamics. Existing differentiable CFD platforms predominantly rely on structured Cartesian grids, limiting their direct application to geometrically complex domains where body-conforming unstructured discretizations are essential. We present DiFVM, the first GPU-native, end-to-end differentiable finite-volume (FV) CFD solver for incompressible flow on unstructured polyhedral meshes. The central methodological contribution is a graph-based computational reformulation of the complete unstructured FV/PISO solution procedure: by expressing FV operators as static scatter/gather primitives on the mesh connectivity graph, DiFVM transforms irregular unstructured connectivity into a GPU-compatible computational representation. All operations are implemented in JAX/XLA, providing just-in-time compilation, operator fusion, and automatic differentiation through the complete simulation pipeline. Differentiable Windkessel outlet boundary conditions are provided for cardiovascular applications, and DiFVM accepts standard OpenFOAM case directories without modification for seamless adoption in existing workflows. Forward accuracy is assessed through analytical and canonical benchmark problems, comparisons with published reference data, and independent solver comparisons, while end-to-end differentiability is demonstrated through proof-of-concept inverse modeling examples. DiFVM provides a differentiable CFD framework for gradient-based optimization, inverse modeling and future physics-integrated machine learning on complex unstructured geometries.
Modeling and predicting neurodegenerative disease progression from medical images remains a major challenge in medical AI, with significant implications for early diagnosis, disease monitoring, and treatment planning. However, most longitudinal neuroimaging datasets are temporally sparse, with substantial gaps and missing follow-up scans for individual subjects. This makes it difficult to learn and accurately capture the continuous anatomical changes associated with disease progression at the level of individual subjects. To address this problem, we propose a novel model named 4DLoG, a full 4D (3DxT) Longitudinal Generative framework that effectively models and synthesizes follow-up brain anatomy over time, conditioned on available clinical and demographic variables. In contrast to previous approaches, our 4DLoG features two main contributions. First, it introduces a full 4D generative diffusion framework that jointly models spatial and temporal dependencies across complete longitudinal sequences through dedicated spatiotemporal attention, with robust spatial patch extraction and temporal alignment. Second, it explicitly learns the distribution of topology-preserving spatiotemporal deformations, which captures realistic geometric changes in brain structures over time. These new components enable a better generation of anatomically plausible future states from an imaging scan at any time point, providing greater flexibility for modeling individual longitudinal brain trajectories. We validate our model through both synthetic sequence generation and downstream longitudinal disease classification, as well as brain segmentation. Experiments on two large-scale longitudinal neuroimage datasets demonstrate that our method outperforms state-of-the-art baselines in generating anatomically accurate, temporally consistent, and clinically meaningful brain trajectories. Our code is available on Github
Accurate quantification of terrestrial gross primary production (GPP) is fundamental to understanding plant productivity, ecosystem function, and carbon-climate feedbacks. Existing approaches typically rely on meteorological, soil, and other ancillary inputs, which introduce substantial uncertainties at regional to global scales. NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, carrying the Ocean Color Instrument (OCI), provides the first contiguous global hyperspectral observations from space. Using 122 spectral bands from PACE, we developed a data-driven framework based on partial least squares regression to generate an 8-day global GPP product. The model achieves a robust performance (R2 = 0.71, RMSE = 1.93 gC m−2 d−1), comparable to models that incorporate meteorological drivers, and outperforms approaches based on broadband reflectance or vegetation indices. PACE-derived GPP showed broad spatial correspondence with solar-induced fluorescence (SIF), including hotspots across high productivity regions such as the U.S. Corn Belt, the Amazon and Congo basins, and the Indo-Gangetic and North China Plains. This strong spatial coherence supports the physiological relevance of the PACE retrievals. Our results demonstrate that hyperspectral observations provide a direct, observation-driven framework for estimating plant productivity at the global scale, opening new opportunities for monitoring vegetation responses to environmental change.
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We derive an irreversibility condition for fracture in the inverse-deformation approach using the second law of thermodynamics. We consider the problem of brittle failure in one-dimensional, homogeneous, elastic bars undergoing quasistatic motion. Despite the presence of a non-zero interfacial/surface energy, the third derivative of the inverse deformation is discontinuous at crack faces. This is due to the inequality constraint allowing fracture while ensuring that the orientation of matter is preserved. We show that any change in the location of open cracks in their reference configuration results in negative entropy production. We disallow these changes according to the second law of thermodynamics, fixing the location of cracks in their reference domain. The inequality constraint and the irreversibility condition limit the space of admissible variations. We prove second-order conditions for local stability incorporating these restrictions. Their numerical implementation shows that all broken equilibria of the elastic bar under hard loading are locally stable.
