A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data distribution but not \emph{away} from it. In this work, we investigate this phenomenon of \emph{robustness of the support} by taking a dynamical systems approach on the generating stochastic/deterministic process. Our perturbation analysis of the probability flow reveals that infinitesimal learning errors cause the predicted density to be different from the target density only on the data manifold for a wide class of generative models. Further, what is the dynamical mechanism that leads to the robustness of the support? We show that the alignment of the top Lyapunov vectors (most sensitive infinitesimal perturbation directions) with the tangent spaces along the boundary of the data manifold leads to robustness and prove a sufficient condition on the dynamics of the generating process to achieve this alignment. Moreover, the alignment condition is efficient to compute and, in practice, for robust generative models, automatically leads to accurate estimates of the tangent bundle of the data manifold. Using a finite-time linear perturbation analysis on samples paths as well as probability flows, our work complements and extends existing works on obtaining theoretical guarantees for generative models from a stochastic analysis, statistical learning and uncertainty quantification points of view. Our results apply across different dynamical generative models, such as conditional flow-matching and score-based generative models, and for different target distributions that may or may not satisfy the manifold hypothesis.

This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment evolution, we design a two-stage method to recover the pseudo-potential and rotation in the pointwise orthogonal decomposition of a class of non-gradient drifts in generalized diffusions. Our two-stage method is applied to complex generalized diffusion processes including dissipation-rotation dynamics, rough pseudo-potentials and noisy data. Representative numerical experiments demonstrate the effectiveness of our approach for learning physical laws in non-gradient generalized diffusions.

With increasing wastewater rates, achieving energy-neutral purification is challenging. We introduce a coral-reef-inspired Swarm Interaction Network for carbon-neutral wastewater treatment, combining morphogenetic abstraction with multi-task carbon awareness. Scalability stems from linear token complexity, mitigating the energy-removal problem. Compared with seven baselines, our approach achieves 96.7\% removal efficiency, 0.31~kWh~m$^{-3}$ energy consumption, and 14.2~g~m$^{-3}$ CO$_2$ emissions. Variance analysis demonstrates robustness under sensor drift. Field scenarios--insular lagoons, brewery spikes, and desert greenhouses--show potential diesel savings of up to 22\%. However, data-science staffing remains an impediment. Future work will integrate AutoML wrappers within the project scope, although governance restrictions pose interpretability challenges that require further visual analytics.

Motion capture (MoCap) data from wearable Inertial Measurement Units (IMUs) is vital for applications in sports science, but its utility is often compromised by missing data. Despite numerous imputation techniques, a systematic performance evaluation for IMU-derived MoCap time-series data is lacking. We address this gap by conducting a comprehensive comparative analysis of statistical, machine learning, and deep learning imputation methods. Our evaluation considers three distinct contexts: univariate time-series, multivariate across subjects, and multivariate across kinematic angles. To facilitate this benchmark, we introduce the first publicly available MoCap dataset designed specifically for imputation, featuring data from 53 karate practitioners. We simulate three controlled missingness mechanisms: missing completely at random (MCAR), block missingness, and a novel value-dependent pattern at signal transition points. Our experiments, conducted on 39 kinematic variables across all subjects, reveal that multivariate imputation frameworks consistently outperform univariate approaches, particularly for complex missingness. For instance, multivariate methods achieve up to a 50% mean absolute error reduction (MAE from 10.8 to 5.8) compared to univariate techniques for transition point missingness. Advanced models like Generative Adversarial Imputation Networks (GAIN) and Iterative Imputers demonstrate the highest accuracy in these challenging scenarios. This work provides a critical baseline for future research and offers practical recommendations for improving the integrity and robustness of Mo-Cap data analysis.

Simulating the dynamic characteristics of a PN junction at the microscopic level requires solving the Poisson's equation at every time step. Solving at every time step is a necessary but time-consuming process when using the traditional finite difference (FDM) approach. Deep learning is a powerful technique to fit complex functions. In this work, deep learning is utilized to accelerate solving Poisson's equation in a PN junction. The role of the boundary condition is emphasized in the loss function to ensure a better fitting. The resulting I-V curve for the PN junction, using the deep learning solver presented in this work, shows a perfect match to the I-V curve obtained using the finite difference method, with the advantage of being 10 times faster at every time step.

Reconstructing the position of an interaction for any dual-phase time projection chamber (TPC) with the best precision is key to directly detect Dark Matter. Using the likelihood-free framework, a new algorithm to reconstruct the 2-D (x; y) position and the size of the charge signal (e) of an interaction is presented. The algorithm uses the charge signal (S2) light distribution obtained by simulating events using a waveform generator. To deal with the computational effort required by the likelihood-free approach, we employ the Bayesian Optimization for Likelihood-Free Inference (BOLFI) algorithm. Together with BOLFI, prior distributions for the parameters of interest (x; y; e) and highly informative discrepancy measures to perform the analyses are introduced. We evaluate the quality of the proposed algorithm by a comparison against the currently existing alternative methods using a large-scale simulation study. BOLFI provides a natural probabilistic uncertainty measure for the reconstruction and it improved the accuracy of the reconstruction over the next best algorithm by up to 15% when focusing on events over a large radii (R > 30 cm). In addition, BOLFI provides the smallest uncertainties among all the tested methods.