The paper introduces Kinematic Interpolants (KI), a new framework that extends stochastic interpolants to infer nonlinear dynamics from multiple snapshots in phase space, incorporating both position and velocity measurements. KI addresses the ambiguity in dynamics inference from real-world data and is scalable without simulation or unnecessary approximations. Experiments on various scientific datasets show that KI reconstructs underlying dynamics more accurately than existing baselines while requiring significantly less training time.
arXiv:2608.21070v1 Announce Type: cross Abstract: Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics. While Optimal T...
arXiv:2608. 03916v1 Announce Type: new Abstract: Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories that best resemble and interpolate the data.
arXiv:2601. 22123v4 Announce Type: replace Abstract: Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration.
The paper introduces Double‑Stitch, a simulation‑free method for learning population dynamics in Wasserstein space. It penalizes the residual of the equation of motion along a learned path, derived from a Clebsch variational principle that avoids gradient velocities. Experiments on synthetic, single‑cell, and ocean vortex data show that Double‑Stitch matches or surpasses gradient‑flow and simulation‑based methods while training 4–14 times faster.
The paper presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.
arXiv:2606. 26769v1 Announce Type: new Abstract: The adoption of powerful diffusion models is hindered by their significant inference latency.
arXiv:2602.23188v2 Announce Type: replace Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
PACE is a trajectory inference framework that reconstructs continuous transport dynamics from destructive single‑cell time‑course snapshots. It uses a state‑ and time‑dependent anisotropic Riemannian metric to guide transport along tangent directions, alternates between refining cross‑time couplings and fitting neural bridges, and distills the learned dynamics into a global velocity field. Across multiple datasets, PACE outperforms existing methods, reducing key distance metrics by an average of 23.7% and improving RNA‑velocity alignment by 15.4%.
arXiv:2510.01159v3 Announce Type: replace Abstract: Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applicat...
The adoption of powerful diffusion models is hindered by their significant inference latency. Recent ``cache-then-forecast'' schemes alleviate this issue by accelerating DiTs using derivative-based polynomials, but they suffer from severe quality degradation at high acceleration ratios.
The paper introduces Finsler Flow Matching (FFM), a method for learning continuous stochastic dynamics from discrete Markov transition graphs in single‑cell snapshot data. FFM constructs a Finsler geometry using first and second local moments, learns directed geodesics via neural networks, and employs these to build geometry‑aware stochastic paths that can be simulated without explicit score or flow matching. Benchmark tests show that FFM better recovers intermediate cellular states, especially when dynamics are directional or anisotropic.
arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.