action-conditioned dynamics modeling

How can piecewise-linear trajectory tracking be achieved for unknown nonlinear systems with time-varying dynamics—without prior system knowledge—while ensuring robustness against abrupt dynamic changes? Method: We propose a data-driven online control framework that (i) identifies local system dynamics in real time via small-perturbation excitation and local system identification; (ii) analytically derives the state reachable set without model assumptions, leveraging an upper bound on the local growth rate; and (iii) synthesizes a receding-horizon closed-loop controller based on reachable-set prediction. Contribution/Results: The approach avoids global modeling and parametric structural assumptions, enabling rapid adaptation to sudden dynamic shifts. Experimental validation across multiple unknown nonlinear systems demonstrates stable waypoint-sequence tracking, confirming strong robustness and generalization capability under unmodeled dynamics and disturbances.

This study addresses the challenge of translating stability trends into verifiable predictions for early warning of critical transitions in nonlinear systems. Departing from conventional signal detection paradigms, this work proposes an innovative framework that integrates decision consequence analysis with finite-horizon extrapolation. By quantifying false alarm costs, defining bounded prediction horizons, and explicitly formalizing extrapolation assumptions, the proposed approach is systematically validated through the coupling of nonlinear dynamics with risk assessment models. This research bridges the gap between trend identification and actionable forecasting, significantly enhancing predictive skill metrics for critical events. Ultimately, it provides a robust and practically viable early warning methodology for the risk management of complex systems.

This study addresses the frequent failure of time-series foundation models in predictive control due to their inability to accurately model responses to intervention actions. Using heat pump control as a representative scenario, we conduct closed-loop experiments integrating model predictive control with zero-shot forecasting. Our findings reveal a critical insight: low prediction error does not necessarily translate to effective control performance. Furthermore, we establish contextual excitation as a fundamental prerequisite for achieving model controllability. Specifically, sufficient contextual excitation is essential for recovering input-response relationships and ensuring system controllability. Preliminary closed-loop evaluations further demonstrate the practical potential of short context windows in real-world control applications.

This work addresses the challenge of generating dynamically feasible control trajectories in complex environments. We propose a novel framework that implicitly embeds system dynamics into the denoising process of diffusion models. Methodologically, we design a temporal-aware physical projection mechanism that aligns denoising steps with the noise schedule and enforces kinematic or dynamic constraints at each iteration—without requiring explicit dynamical priors—enabling recovery of linear feedback controller trajectories directly from expert demonstrations. Our key contributions are: (i) the first diffusion-based trajectory generation method ensuring dynamical consistency under maximum-likelihood estimation; and (ii) the integration of implicit dynamics learning with projection-based constraint optimization. Evaluated on standard control benchmarks and non-convex optimal control tasks involving obstacle avoidance and path tracking, our approach significantly improves trajectory feasibility and task success rates, demonstrating strong potential for real-world deployment.

This work proposes a unified mathematical framework grounded in dynamic information flow for constructing structurally rigorous models of future prediction. By integrating filtering theory, regular conditional probabilities, Markov semigroups, infinitesimal generators, and multiple information geometries—including Hilbert, Fisher–Rao, and Wasserstein—the approach conceptualizes prediction as the construction of conditional distributions governed by informational, geometric, and modeling constraints. The framework elucidates deep connections among classical results such as the tower property and semigroup laws, as well as Itô’s formula and backward equations. Explicit transition laws, spectral decompositions, term structures, and asymptotic behaviors are derived within canonical models like Ornstein–Uhlenbeck and Cox–Ingersoll–Ross, thereby establishing a compact mathematical mapping from idealized theoretical constructs to empirical forecasting.

针对世界建模中数据分布错位和因果关系缺失问题，提出OnlineWM框架，通过主动在线学习和因果意识微调来提高模型预测的准确性和鲁棒性。

This study addresses error accumulation and sequence bottlenecks caused by autoregressive rollout in long-horizon world models by proposing a parallel predictive world model. We introduce a novel parallel causal trajectory prediction paradigm that decouples temporal causal dependencies from state-recursive outputs, thereby eliminating the decoding feedback loop. By integrating causal action-prefix conditioning with future representation interaction mechanisms, our approach enables efficient parallel trajectory generation. Experiments demonstrate that the proposed method achieves the lowest prediction error on visual control tasks, accelerates cross-entropy method (CEM) planning by over 3×, and significantly outperforms existing baselines in success rate, delivering simultaneous breakthroughs in both accuracy and efficiency.

This work addresses a critical limitation in existing latent-variable world models, which rely on average prediction error over training data for training and selection—a metric that fails to reflect actual controller performance due to a mismatch between the evaluation distribution and the distribution queried by the planner. The authors propose instead to center model assessment on the discrepancy between predicted and true costs over states reachable by the planner. They establish, for the first time, a rigorous theoretical link between this discrepancy and control suboptimality, proving it provides a valid upper bound on performance loss, whereas conventional prediction errors neither bound nor track performance. Leveraging control theory, spectral analysis, and non-normal operator theory, they decompose the discrepancy into an intrinsic manifold residual and an off-manifold divergence term, and introduce a fidelity score to quantify alignment of the planner’s reachable distribution. Experiments on synthetic systems and model predictive control confirm that the proposed metric reliably tracks control performance, while single-step prediction error shows virtually no correlation.

This study addresses the computational bottleneck associated with dynamically constrained sampling of state spaces in feedback control and planning. To overcome this challenge, the work reformulates control as a dynamically constrained sampling problem, establishing a mapping framework that bridges controllability, optimal control theory, and generative modeling. Specifically, it integrates flow matching, normalizing flows, and denoising diffusion techniques to guide system evolution toward target states or distributions. The proposed approach enables efficient reachable set sampling and precise trajectory planning while unifying control-theoretic and generative-modeling paradigms. Furthermore, the authors provide an accessible open-source tutorial to facilitate practical adoption by the research community.

This study addresses the challenges of modeling long-term dependencies and probability distributions in continuous time series forecasting by proposing a state transition reconstruction framework based on incremental dynamics. The core innovations include the introduction of a "derivative fingerprint" state definition and a history-anchored inversion mechanism, which reformulate continuous forecasting as transition distribution prediction, thereby effectively bridging statistical inference and probabilistic forecasting. Furthermore, efficient computation is achieved through the integration of trailing convolutions, orthogonal decomposition, sparse dynamic models, and Monte Carlo sampling. Experimental results demonstrate that the proposed method significantly outperforms fourteen baseline models across nine benchmarks, reducing energy errors by 24%–56% in Aizawa attractor trajectory experiments.