By using neural networks to regress the acceleration field, TracingFlow provides an exact, efficient solution to the Dynamical Optimal Acceleration Transport (DOAT) problem and recovers dynamical structures that are both mathematically optimal and biologically plausible.
Abstract
Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics. While Optimal Transport (OT) is popular, existing frameworks are largely restricted to first-order dynamics, assuming memoryless velocity fields. This limits expressiveness, as first-order systems fail to account for regulatory momentum and time-delayed responses inherent in processes like cell differentiation. Here, we introduce TracingFlow, a simulation-free Flow Matching framework generalizing to second-order dynamics. By using neural networks to regress the acceleration field, TracingFlow provides an exact, efficient solution to the Dynamical Optimal Acceleration Transport (DOAT) problem. Unlike first-order methods yielding over-smoothed trajectories, our second-order formulation captures high-curvature transitions and nonlinear evolutions by learning the underlying force fields. Evaluated on complex synthetic and large-scale scRNA-seq datasets, TracingFlow achieves superior accuracy in distributional reconstruction and trajectory faithfulness. Moreover, by integrating lineage tracing priors, it recovers dynamical structures that are both mathematically optimal and biologically plausible.
While stochastic diffusion samplers such as DDPM better preserve the enstrophy spectrum during rollouts in the stochastic setting, deterministic samplers such as DDIM and DPM-2 show better spectral preservation in the deterministic setting.
S. Pfister, Benjamin J. Holzschuh, Nils Thürey· 0 citations
This work exploits the affine state update to obtain the exact one-step conditional-mean sensitivity by differentiating normalized reaction propensities, and defines the propensity straight-through (PST) estimator, a temperature- and Gumbel-free path to scalable gradient-based learning through exact stochastic trajectories.
HyperODE is introduced, a surrogate capable of operating across an entire class of approximately mass-conserving compartmental models without retraining, by mapping the structure of ordinary differential equations into directed hypergraphs, which decouples the functional form of system interactions from the neural network architecture.
We develop a Bayesian framework for model comparison of second-order Langevin dynamics from position-only trajectories. While approximate increment likelihoods for nonlinear position-only inference have been formulated previously, a unified evidence-based framework for comparing multiple second-order models under positional observation has remained lacking. Here we address this problem by combining exact increment likelihoods for linear Gaussian models with a previously proposed approximate likelihood for nonlinear dynamics. Synthetic-data benchmarks show reliable recovery of the generating model at fine sampling intervals and progressive loss of identifiability under coarse temporal sampling. Application to Dictyostelium discoideum trajectories demonstrates that the statistically supported model depends strongly on temporal resolution. Moreover, the selected models reproduce key statistical properties of the experimental trajectories, providing additional support for the model-comparison results. Our framework therefore offers a practical approach to evidence-based comparison of partially observed stochastic dynamics.
Yusuke Kato, Jan Albrecht, T. Moldenhawer et al.· 0 citations
Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among existing deep learning?based approaches for solving PDEs, neural operators typically rely on extensive trajectory data, whereas physics-informed meth?ods often exhibit limited stability during long-time extrapolation. For a well-posed autonomous PDE, long-time trajectories can be generated by repeated composition of a fixed-step evolution operator; hence, long-time extrapolation depends on controlling the approximation error of this operator and the propagation of that error under recursive composition. Accordingly, we propose a numerical-prior-guided, physics-constrained method trained without ground-truth trajectory supervision: a low-cost numerical prior reduces the difficulty of approximating the one?step evolution operator, while a weak-form PDE residual provides a computable proxy for the one-step error term in the error?propagation bound. We validate the method on five benchmark cases spanning four PDE classes and compare it with ten physics?informed learning methods under a unified protocol that excludes ground-truth trajectories from training and model selection. The results indicate that, in all five cases, the proposed method reduces long-time extrapolation error relative to the numerical prior and outperforms the best competing baseline in each case, thereby improving long-time simulation accuracy across different PDEs without ground-truth trajectory supervision. The source code developed for this paper will be made publicly available upon acceptance of the manuscript.
Maqun Zhang, Feng Gao, Wankun Chen et al.· 0 citations
This work proposes Teacher Rollout Extension (TREX), a knowledge distillation framework that transfers the predictive capability of a pretrained foundation model into a compact and efficient student that can match or surpass the teacher's accuracy while reducing the number of parameters by several orders of magnitude and achieving more than an order-of-magnitude speedup in inference.
Daniel Musekamp, Boshra Ariguib, Andrei Manolache et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
