arXiv:2507. 03094v2 Announce Type: replace-cross Abstract: Many challenges in scientific imaging involve solving ill-posed inverse problems, where the goal is to recover spatio-temporal fields from indirect, noisy, and highly sparse measurements - often without access to ground truth data or reliable simulators.
arXiv:2603. 12676v3 Announce Type: replace Abstract: Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable.
arXiv:2608. 14744v1 Announce Type: new Abstract: Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation.
arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.
arXiv:2601. 17074v4 Announce Type: replace-cross Abstract: Accurate estimation in time-varying inverse problems under limited and sparse observations remains a fundamental challenge across scientific domains.
arXiv:2601. 17074v5 Announce Type: replace-cross Abstract: Accurate estimation of unobserved quantities in time-varying inverse problems remains challenging when observations are sparse and only indirectly related to the target variable.
arXiv:2605. 14285v2 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science.
arXiv:2509. 21751v2 Announce Type: replace Abstract: Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, yet it remains computationally intensive and sensitive to initialization due to the non-convexity of its objective function.
arXiv:2607. 14937v1 Announce Type: cross Abstract: Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts.
arXiv:2605. 27527v2 Announce Type: replace-cross Abstract: Astrophysical observations from Earth are subject to weather, environmental, and scientific constraints that lead to sparse, irregular light curves.
arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.
arXiv:2605. 27756v2 Announce Type: replace-cross Abstract: Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span.
arXiv:2607. 20970v1 Announce Type: new Abstract: Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time.