arXiv subjects

Minh-Nhat Phung

Publications and source records attributed to Minh-Nhat Phung.

7 recordsLinked to original sources

arXiv2026

Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control

We establish a finite-sample learning-to-control theory for geometrically supervised latent models of nonlinear deterministic systems. Geometric supervision is used only during training: simulator state, proprioception, or state estimates with independently validated metric and directional error bounds supply observable-state distances and tangent directions, while deployment remains observation- and action-conditioned. We introduce an encoder-only local--global metric hinge that enforces directional resolution and separated-state discrimination. Under regular observable-factor, coverage, finite-capacity approximation, and uniform $C^{1,1}$ hypotheses, a computable one-sided regularization regime has a strong selection property: with high probability, every approximate empirical minimizer is simultaneously pointwise co-Lipschitz and uniformly approximately semiconjugate to the controlled dynamics. Approximation, sampling, and optimization errors remain explicit and separate. Norm-constrained tensor-product B-spline classes constructively realize the approximation hypotheses, and the interpolation exponent converting mean residual control into a uniform bound is sharp. A modular deterministic corollary transfers the learned certificates to trajectory, finite-horizon cost, learned-cost-head, and optimizer guarantees, while a validated finite-net result enables sharper model-specific certification. Controlled experiments isolate collapse and folding, quantify the analytic certificate's reserve, and demonstrate the control benefit of restored metric resolution. The principal contribution is a complete finite-sample implication from approximate empirical optimization to metric faithfulness, uniform controlled dynamics, and reliable planning for the same learned model.

math.OC↗

arXiv2026

Computational Control of Nonlinear Partial Differential Equations Using Machine Learning

The numerical reconstruction of controls for nonlinear partial differential equations (PDEs) remains a challenging and relatively underdeveloped problem, despite the extensive literature on controllability theory. In this work, we introduce an operator-decomposed physics-informed neural network framework, called WeightedPINN, for approximating controls in nonlinear PDE settings. The method is designed for both internal and bilinear control problems and incorporates the governing equation, boundary and initial conditions, and terminal control constraints directly into the training objective. The main feature of WeightedPINN is that the different components of the controlled PDE residual are weighted separately. In particular, the time derivative, directional diffusion terms, nonlinear response, and control term are assigned independent adaptive space--time weights, and the same weighted formulation is applied to the boundary, initial, and terminal constraints. This produces a control-aware residual metric that is more sensitive to operator-level imbalance and to the mechanism through which the unknown control enters the equation. We provide a convergence analysis for the proposed method and present numerical experiments for semilinear heat and wave equations with internal and bilinear controls. The high-dimensional experiments demonstrate improved residual-based testing errors compared with the standard PINN baseline, while lower-dimensional manufactured-solution benchmarks show improved direct reconstruction errors for both the state and the control against several adaptive and control-oriented PINN methods. The results suggest that WeightedPINN is particularly effective in regimes where componentwise residual imbalance, anisotropy, variable coefficients, or control-identification sensitivity play a significant role.

math.OC↗

arXiv2026

Control, Optimal Transport and Neural Differential Equations in Supervised Learning

We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal transport (UOT) in the continuum using Neural ODEs. By generalizing a discrete UOT problem with Pearson divergence, we constructively design vector fields for Neural ODEs that converge to the true UOT dynamics, thereby advancing the mathematical foundations of computational transport and machine learning. To this end, we design a numerical scheme inspired by the Sinkhorn algorithm to solve the corresponding minimization problem and rigorously prove its convergence, providing explicit error estimates. From the obtained numerical solutions, we derive vector fields defining the transport dynamics and construct the corresponding transport equation. Finally, from the numerically obtained transport equation, we construct a neural differential equation whose flow converges to the true transport dynamics in an appropriate limiting regime.

math.NA↗

arXiv2025

A Relative Ignorability Framework for Decision-Relevant Observability in Control Theory and Reinforcement Learning

Sequential decision-making systems routinely operate with missing or incomplete data. Classical reinforcement learning theory, which is commonly used to solve sequential decision problems, assumes Markovian observability, which may not hold under partial observability. Causal inference paradigms formalise ignorability of missingness. We show these views can be unified and generalized in order to guarantee Q-learning convergence even when the Markov property fails. To do so, we introduce the concept of relative ignorability. Relative ignorability is a graphical-causal criterion which refines the requirements for accurate decision-making based on incomplete data. Theoretical results and simulations both reveal that non-Markovian stochastic processes whose missingness is relatively ignorable with respect to causal estimands can still be optimized using standard Reinforcement Learning algorithms. These results expand the theoretical foundations of safe, data-efficient AI to real-world environments where complete information is unattainable.

cs.LG↗

arXiv2024

Internal Control of The Transition Kernel for Stochastic Lattice Dynamics

In [5], we have designed impulsive and feedback controls for harmonic chains with a point thermostat. In this work, we study the internal control for stochastic lattice dynamics, with the goal of controlling the transition kernel of the kinetic equation in the limit. A major novelty of the work is the introduction of a new geometric combinatorial argument, used to establish paths for the controls.

math.OC↗

arXiv2024

Algebraic and topological properties of Riordan groups over finite fields

In this paper, we investigate algebraic and topological properties of the Riordan groups over finite fields. These groups provide a new class of topologically finitely generated profinite groups with finite width. We also introduce, characterize index-subgroups of our Riordan groups, and finally we show exactly the range of Hausdorff dimensions of these groups. The latter results are analogous to the work of Barnea and Klopsch for the Nottingham groups.

math.GR↗

arXiv2020

Barycenters in the Hellinger-Kantorovich space

Recently, Liero, Mielke and Savaré introduced Hellinger-Kantorovich distance on the space of nonnegative Radon measures of a metric space $X$ [19,20]. We prove that Hellinger-Kantorovich barycenters always exist for a class of metric spaces containing of compact spaces, and Polish $CAT(1)$ spaces; and if we assume further some conditions on starting measures, such barycenters are unique. We also introduce homogeneous multimarginal problems and illustrate some relations between their solutions with Hellinger-Kantorovich barycenters. Our results are analogous to the work of Agueh and Carlier [1] for Wassertein barycenters.

math.OC↗