AdaKoop introduces an efficient streaming algorithm that models complex nonlinear dynamics from nonstationary data streams by leveraging the Koopman operator theory, achieving state-of-the-art accurac…

This paper introduces a local information-operator framework to analyze spatial identifiability in inverse problems where spatially varying fields are inferred from heterogeneous observations.

The paper introduces Strong Stochastic Flow Maps (SSFMs), a novel framework that directly learns the strong solution map of additive-noise Stochastic Differential Equations (SDEs), enabling few-step s…

The paper introduces a history-aware adaptive Reduced-Order Model (ROM) framework using incremental Singular Value Decomposition (iSVD) that maintains accuracy for online dynamics far beyond the initi…

The paper introduces Multifidelity Proper Orthogonal Decomposition (MFPOD), a method that significantly reduces the computational cost of dimension reduction by intelligently combining data from cheap…

The paper develops a quantitative framework to analyze and improve flow distillation in diffusion models, providing stability guarantees and suggesting non-uniform time scheduling to reduce approximat…

The paper reformulates nonreversible perturbations of Fokker--Planck dynamics as gauge fields, providing a unified operator viewpoint to analyze relaxation processes and develop methods for learning o…

The paper introduces hybrid neural world models that provide fast, multi-horizon predictions for complex physical dynamics, implicitly handling sharp events like shocks and contacts without explicit t…

The paper introduces Robust Prior Update (RPU), a module that improves the faithfulness of diffusion-based inverse solvers by stabilizing the prior update step, thereby reducing measurement-conditione…

The paper introduces the Computation-Aware State-Space Model (CASSM), a novel framework that extends Bayesian methods to handle model selection and large state-spaces, achieving competitive performanc…

Low-Pass Flow Matching introduces a spectral bias into the flow matching process, allowing it to better model natural data by transitioning from a standard source spectrum to a frequency-decaying bias…

This paper develops a perturbation theory for spherical Hellinger-Kantorovich (SHK) gradient flows, providing explicit, time-dependent bounds on divergence metrics to guarantee differential privacy fo…

This paper establishes an exact mathematical correspondence between training and inference in deep learning and the solution of Hamilton-Jacobi partial differential equations, unifying multiple theore…

The paper introduces a Jacobian-based spectral audit to evaluate neural operators, demonstrating that standard prediction error metrics fail to capture crucial local dynamical structures and operator…

The paper introduces STEP, a self-supervised method that learns interpretable, structured embeddings for progressive time series, allowing the state progression and active mode to be read out using po…

The paper proposes a measurement-geometry framework to quantify how well fixed measurement operators can distinguish between images generated by a prior, thereby guiding the design of more trustworthy…

The paper introduces a novel diffusion posterior sampling method that stabilizes and accelerates data-consistent sampling by replacing hand-tuned guidance weights with a per-noise-level, curvature-gui…