Wentao Tang

Wentao Tang

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear ones, promoting the use of operator theory, which ``universally'' represents a nonlinear system by a nonparametric operator. On the other hand, interpretability requires by a ``non-universal'', parametric nonlinear model family satisfying first principles; these constraints tend to complicate the learning procedure. This paper considers hybrid modeling by formulating convex learning problems that account for interpretability systematically and give surrogate models efficiently. Three settings are discussed -- (i) regularization around a particular ``reference model'', (ii) restriction on an ``interpretable subspace'', and more generally, (iii) restriction on a ``interpretable manifold'' that is nonlinearly parameterized. In the more general setting, by introducing an operator-theoretic technique to re-parameterize models in the ``lifted'' parameters (``canonical features'', potentially infinite-dimensional), the system is regarded as a kernel-based mixture of interpretable models. Application to both static and dynamic models are exemplified in numerical studies.

Yizhi Li, Xiaohan Chen, Miao Jiang et al.

With the explosive growth of digital entertainment, automated video summarization has become indispensable for applications such as content indexing, personalized recommendation, and efficient media archiving. Automatic synopsis generation for long-form videos, such as movies and TV series, presents a significant challenge for existing Vision-Language Models (VLMs). While proficient at single-image captioning, these general-purpose models often exhibit critical failures in long-duration contexts, primarily a lack of ID-consistent character identification and a fractured narrative coherence. To overcome these limitations, we propose MovieTeller, a novel framework for generating movie synopses via tool-augmented progressive abstraction. Our core contribution is a training-free, tool-augmented, fact-grounded generation process. Instead of requiring costly model fine-tuning, our framework directly leverages off-the-shelf models in a plug-and-play manner. We first invoke a specialized face recognition model as an external "tool" to establish Factual Groundings--precise character identities and their corresponding bounding boxes. These groundings are then injected into the prompt to steer the VLM's reasoning, ensuring the generated scene descriptions are anchored to verifiable facts. Furthermore, our progressive abstraction pipeline decomposes the summarization of a full-length movie into a multi-stage process, effectively mitigating the context length limitations of current VLMs. Experiments demonstrate that our approach yields significant improvements in factual accuracy, character consistency, and overall narrative coherence compared to end-to-end baselines.

Moritz Woelk, Jarod Morris, Wentao Tang

This work proposes a method for model-free synthesis of a state observer for nonlinear systems with manipulated inputs, where the observer is trained offline using a historical or simulation dataset of state measurements. We use the structure of the Kazantzis-Kravaris/Luenberger (KKL) observer, extended to nonautonomous systems by adding an additional input-affine term to the linear time-invariant (LTI) observer-state dynamics, which determines a nonlinear injective mapping of the true states. Both this input-affine term and the nonlinear mapping from the observer states to the system states are learned from data using fully connected feedforward multi-layer perceptron neural networks. Furthermore, we theoretically prove that trained neural networks, when given new input-output data, can be used to observe the states with a guaranteed error bound. To validate the proposed observer synthesis method, case studies are performed on a bioreactor and a Williams-Otto reactor.

Xiuzhen Ye, Wentao Tang

This paper presents a data-driven approach for designing state observers for continuous-time nonlinear systems, where an extended dynamic mode decomposition (EDMD) procedure is used to identify an approximate linear lifted model. Since such a model on a finite-dimensional space spanned by the dictionary functions has an inevitable mismatch, we first establish, based on our theory of reproducing kernel Hilbert space with a linear-radial kernel, that the nonlinear error magnitude in the approximate linear model is sectorially bounded by the lifted state. The sector bound comprises a deterministic part due to the finite dictionary and a stochastic part due to the random data samples, and the observer design needs to account for both of these errors in a robust formulation. Hence, the observer synthesis is performed using linear matrix inequalities (LMIs), specified by the desired exponential decay rate of the observation error (when the system is asymptotically stable) or the L2-gain from the modeling error to the observation error. Numerical studies demonstrate the effectiveness and flexibility of the proposed method. As such, this work entails an explicit elementary use of linear systems theory for nonlinear state observation in a Koopman operator-theoretic framework.

Xiuzhen Ye, Wentao Tang

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system on a reproducing kernel Hilbert space (RKHS), the storage function and supply rate functions are expressed as kernel quadratic forms, through which the dissipative inequality is expressed as a linear operator inequality. The RKHS is specified by a linear--radial kernel, which inherently encode the information of equilibrium point, thus ensuring that all functions in the RKHS are locally at least linear around the origin and that kernel quadratic forms are locally at least quadratic, which expressively generalize conventional quadratic forms including sum-of-squares polynomials. Based on the kernel matrices of the sampled data, the dissipativity estimation can be posed as a finite-dimensional convex optimization problem, and a statistical learning bound can be derived on the kernel quadratic form for the probabilistic approximate correctness of dissipativity estimation.