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Matthew Huynh

Publications and source records attributed to Matthew Huynh.

3 recordsLinked to original sources

Information-Guided Safe Reinforcement Learning for Autonomous Gas Source Localization using sUAS

The autonomous localization of fugitive gas emissions using small Unmanned Aircraft Systems (sUAS) constitutes a fundamentally ill-posed inverse problem. In turbulent atmospheric boundary layers, highly intermittent scalar concentration fields violate the assumptions of classical gradient-based navigation, causing data-driven estimators to suffer from severe noise and spurious local minima. To address these challenges, we introduce an Information-Guided Safe Reinforcement Learning framework evaluated within a custom, GPU-accelerated 3D simulation environment coupling an Eulerian wind solver with a Lagrangian puff dispersion model. We identify a critical vulnerability in deterministic information-seeking planners - a Gramian bias where agents act greedily upon flawed early estimates, starving the estimator of spatial diversity. To systematically break this degeneracy, our architecture integrates a classical empirical observability Gramian (EMGR) planner with a learned Soft Actor-Critic (SAC) exploratory policy. A deterministic meta-supervisor actively monitors estimator reliability via Kullback-Leibler (KL) divergence, dynamically blending deterministic exploitation with learned exploration to steer the sUAS into high-information zones. Trained via a progressive curriculum and safeguarded by a strictly enforced Robust Control Barrier Function (RCBF), our RL framework achieves nearly 80% localization success on complex, mobile sources - drastically outperforming classical baselines (~30%) - while ensuring zero safety violations.

cs.RO

The Hitchin morphism for certain surfaces fibered over a curve

The Chen-Ng\^o Conjecture predicts that the Hitchin morphism from the moduli stack of $G$-Higgs bundles on a smooth projective variety surjects onto the space of spectral data. The conjecture is known to hold for the group $GL_n$ and any surface, and for the group $GL_2$ and any smooth projective variety. We prove the Chen-Ng\^o Conjecture for any reductive group when the variety is a ruled surface or (a blowup of) a nonisotrivial elliptic fibration with reduced fibers. Furthermore, if the group is a classical group, i.e. $G \in \{SL_n,SO_n,Sp_{2n}\}$, then we prove the Hitchin morphism restricted to the Dolbeault moduli space of semiharmonic $G$-Higgs bundles surjects onto the space of spectral data.

math.AG

Complex algebraic stacks and morphisms of intersection complexes

We generalize a construction of Barthel-Brasselet-Fieseler-Gabber-Kaup in the setting of complex varieties to the setting of finite type, complex algebraic stacks. Given two such stacks $\mathcal{X},\mathcal{Y}$ with affine stabilizers, and a morphism between them, we construct a morphism from the pullback of the intersection complex of $\mathcal{Y}$ to the intersection complex of $\mathcal{X}$. As an application, we show that the Borel-Moore fundamental class of a closed substack $\mathcal{Z}$ in a Deligne-Mumford stack $\mathcal{X}$ lifts to a class in the intersection cohomology of $\mathcal{X}$.

math.AG