Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity

Ruifeng Shang; Shu Liu; Yuhua Zhu

Home/Archive/arXiv

arXiv · 2609.32026

Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity

Ruifeng Shang·Shu Liu·Yuhua Zhu

View original source ↗Read source document ↗Export metadata ↓

Abstract

Physical systems evolve continuously in time, yet their states are typically observed only at discrete times. Generating trajectories consistent with their probability densities from such observations therefore requires capturing the continuous-time evolution rather than only learning transition mappings between consecutive observations. We propose PhiBE-Flow, a framework that directly estimates the probability velocity field induced by the stochastic differential equation (SDE) which governs this continuous-time distributional evolution. PhiBE-Flow learns from discrete observations using a model-free approach requiring neither known SDE coefficients nor score estimation. We establish convergence guarantees for the method, accounting for both time-discretization and finite-sample errors. We evaluate PhiBE-Flow on systems of increasing complexity, from controlled stochastic numerical systems to Navier--Stokes dynamics and real-world videos. Our results show that PhiBE-Flow accurately recovers probability flows of stochastic dynamics, preserves multiscale physical statistics, and improves video generation performance over representative baselines. The code is available at https://github.com/R1fe/PhiBE-Flow.

Explore related subjects

stat.ML cs.LG math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ruifeng Shang, Shu Liu, Yuhua Zhu. 2026-09-25. Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity. https://arxiv.org/abs/2609.32026

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Adaptively Truncated Signature-based Logistic Regression for Semi-parametric Functional Classification

Modern sensing technologies routinely generate multi-dimensional functional data, often accompanied by scalar covariates, motivating statistical methods that can jointly accommodate nonlinear functional effects, complex cross-component dependencies, and irregular sampling patterns. Existing functional logistic regression approaches rely on basis expansions whose performance is critically sensitive to the choice of basis, smoothing parameters, and sampling design; meanwhile, current signature-based methods require heuristic selection of the signature truncation order. We propose Adaptively Truncated Signature-based Logistic Regression (ATSLR), a semi-parametric classification framework that integrates path-signature representations with a data-driven procedure for selecting the signature truncation order via penalized empirical risk minimization. Our method is supported by rigorous theoretical guarantees, including the existence of an optimal truncation order, consistency of its adaptive estimator, convergence rates for the classifier risk, a finite and computable search bound, and a general error-propagation analysis for irregular sampling. Experiments on synthetic and real-world datasets demonstrate that our framework consistently outperforms traditional functional classifiers and fixed-order signature baselines in accuracy, robustness, and interpretability. Our results highlight the practical and theoretical value of integrating rough path theory with adaptive model complexity control.

stat.ML↗

arXiv2026

Design of Experiment for Discovering Directed Mixed Graph

We study the design of interventions for causal discovery in simple structural causal models whose causal graphs are directed mixed graphs (DMGs) that may contain directed cycles and bidirected edges representing latent confounding. In such case, observational conditional-independence (CI) information may not identify even the graph skeleton, while CI alone cannot generally detect a bidirected edge coexisting with a directed edge. To this end, we propose a stage-wise framework based on tailored separating systems. Separating-system interventions first recover descendant relations and strongly connected components (SCCs). The SCCs are then ordered by ancestry, and an SCC-Anc separating system recovers the directed subgraph. Given this subgraph, further systems use CI tests interpreted through $d$- or $σ$-separation to recover non-adjacent bidirected edges, whose endpoints share no directed edge, and do-see comparisons to recover those coexisting with exactly one directed edge. Under our assumptions, the framework recovers the directed subgraph and every bidirected edge except double-adjacent ones, whose endpoints are connected by a directed edge in each direction. We develop algorithms for unrestricted and $M$-bounded settings, with each experiment targeting at most $M$ variables in the latter. For recovering the directed subgraph and non-adjacent bidirected edges, our upper bounds on the number and maximum size of experiments match corresponding worst-case lower bounds up to logarithmic factors.

stat.ML↗

arXiv2026

Synthetic data for ratemaking: imputation-based methods vs adversarial networks and autoencoders

Actuarial ratemaking depends on high-quality data, yet access to such data is often limited by the cost of obtaining new data, privacy concerns, etc. In this paper, we explore synthetic-data generation as a potential solution to these issues. In addition to generative methods previously studied in the actuarial literature, we explore and benchmark another class of approaches based on Multivariate Imputation by Chained Equations (MICE). In a comparative study using an open-source dataset, MICE-based models are evaluated against other generative models like Variational Autoencoders and Conditional Tabular Generative Adversarial Networks. We assess how well synthetic data preserves the original marginal distributions of variables as well as the multivariate relationships among covariates. The consistency between Generalized Linear Models (GLMs) trained on synthetic data with GLMs trained on the original data is also investigated. Furthermore, we assess the ease of use of each generative approach and study the impact of generically augmenting original data with synthetic data on the estimation of GLMs for predicting claim counts. Our results highlight the potential of MICE-based methods in creating high-fidelity tabular data while offering lower implementation complexity compared to deep generative models.

stat.ML↗