Na Li

Philip K. Hopke, Maggie Leung, Na Li et al.

The ambient particulate chemical composition data with three particle diameter sizes (2.5mm<D< 1.15mm, 1.15mm<D<0.34mm and 0.34mm<D<0.1mm) collected at a major industrial center in Allen Park in Detroit, MI is examined. Standard multiway (tensor) methods like PARAFAC and Tucker tensor decompositions have been applied extensively to many chemical data. However, for multiple particle sizes, the source apportionment analysis calls for a novel multiway factor analysis. We apply the regularized block tensor decomposition to the collected air sample data. In particular, we use the Block Term Decomposition (BTD) in rank-(L;L;1) form to identify nine pollution sources (Fe+Zn, Sulfur with Dust, Road Dust, two types of Metal Works, Road Salt, Local Sulfate, and Homogeneous and Cloud Sulfate).

Michael Brazell, Na Li, Carmeliza Navasca et al.

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we derived new tensor decompositions which we have shown to be related to the well-known canonical polyadic decomposition and multilinear SVD. Moreover, within this group structure framework, multilinear systems are derived, specifically, for solving high dimensional PDEs and large discrete quantum models. We also address multilinear systems which do not fit the framework in the least-squares sense, that is, when the tensor has an odd number of modes or when the tensor has distinct dimensions in each modes. With the notion of tensor inversion, multilinear systems are solvable. Numerically we solve multilinear systems using iterative techniques, namely biconjugate gradient and Jacobi methods in tensor format.

Amit Jena, Na Li, Le Xie

System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as stability and typically assume stationary dynamics, limiting their applicability under distribution shifts. Existing approaches generally address either stability or adaptability in isolation, lacking a unified framework that ensures both. We propose LILAD (Learning In-Context Lyapunov-stable Adaptive Dynamics), a novel framework for system identification that jointly guarantees adaptability and stability. LILAD simultaneously learns a dynamics model and a Lyapunov function through in-context learning (ICL), explicitly accounting for parametric uncertainty. Trained across a diverse set of tasks, LILAD produces a stability-aware, adaptive dynamics model alongside an adaptive Lyapunov certificate. At test time, both components adapt to a new system instance using a short trajectory prompt, which enables fast generalization. To rigorously ensure stability, LILAD also computes a state-dependent attenuator that enforces a sufficient decrease condition on the Lyapunov function for any state in the new system instance. This mechanism extends stability guarantees even under out-of-distribution and out-of-task scenarios. We evaluate LILAD on benchmark autonomous systems and demonstrate that it outperforms adaptive, robust, and non-adaptive baselines in predictive accuracy.