arXiv subjects

Ruimeng Hu

Publications and source records attributed to Ruimeng Hu.

At least 19 recordsLinked to original sources

arXiv2026

Strategic Inference of Adversarial Navigation Objectives for Unmanned Underwater Vehicles

We study destination inference for adversarial unmanned underwater navigation in a spatially varying current field. The red vehicle is modeled as approximately following a Hamilton-Jacobi (HJ) time-optimal path toward an unknown destination, while a blue vehicle observes a noisy realization of that trajectory. We derive a continuous-time likelihood model for this problem and obtain a closed-form local maximum likelihood estimator, a constant-memory multi-period estimator, and an asymptotic Cram\'er-Rao efficiency result. The Fisher information is governed by a combined score kernel with two additive components, a policy-mean sensitivity and a reference-path sensitivity, and a multiplicative drift sensitivity whose leading geometric contribution is a contraction of the current Hessian with the Jacobi field of the HJ characteristic flow. All three sensitivities are induced by that Jacobi field, yielding a computable link between current-field geometry and destination identifiability. We further extend the framework to a sweep-dependent observation model and formulate an active sweep-design problem for the blue team. Numerical experiments in vortex and channel-shear currents validate the Cram\'er-Rao prediction and illustrate how current geometry determines which destinations can be reliably inferred.

math.OC↗

arXiv2026

Current-Sheet Formation in Electron Magnetohydrodynamics with Split Fractional Dissipation

Thin current sheets are central small-scale structures in electron magnetohydrodynamics (EMHD), closely associated with energy dissipation and fast magnetic reconnection at electron scales. We study their formation numerically in a $2\frac{1}{2}$-dimensional EMHD system on a periodic domain with split fractional dissipation, where the magnetic potential and the vertical magnetic component are damped separately. The local theory is governed by a symmetric combined damping balance, but the numerical onset of small-scale growth need not follow this symmetry. A scaling analysis identifies the out-of-plane current as the primary concentration observable, since it is regularized only through the magnetic-potential equation. Using a validated Fourier pseudospectral exponential time-differencing solver with resolution-controlled diagnostics, we find a clear decay/concentration dichotomy. The onset boundary is markedly asymmetric: current-sheet formation appears to be controlled mainly by damping of the magnetic potential, rather than by the combined damping strength. The analyticity strip collapses to the grid scale, the concentration sharpens under grid refinement, and the observed growth is consistent with an energy-critical self-similar rate, with exponent near three. These experiments indicate that magnetic-potential damping is the apparent binding constraint for current-sheet concentration, refining the symmetric sum picture.

physics.plasm-ph↗

arXiv2026

Onsager-Type Energy Equality and Prodi--Serrin Uniqueness for Nernst--Planck Fluid Systems

We study weak solutions of electrodiffusion systems coupling the Nernst--Planck equations with fluid models. First, for the three-dimensional Nernst--Planck--Euler system, we establish an Onsager-type criterion for the validity of the coupled kinetic-electrostatic energy balance. The energy equality is shown to hold for weak solutions whose velocity satisfies critical Besov regularity and a vanishing dyadic flux condition. Furthermore, assuming the corresponding Onsager-type regularity for the ionic concentrations, we also prove parabolic regularity, preservation of non-negativity of the concentrations, and the associated charge-density energy identity. Second, for the three-dimensional Nernst--Planck--Navier--Stokes system, we prove a Prodi--Serrin-type uniqueness criterion for Leray--Hopf solutions: uniqueness in the Leray--Hopf class holds whenever the velocity field lies in the Ladyzhenskaya--Prodi--Serrin class $L^p_tL^q_x$ with $2/p+3/q=1$ and $q>3$. These results extend energy-equality and weak--strong uniqueness principles from incompressible fluid dynamics to electrodiffusion models involving convection, diffusion, and self-consistent electrostatic forcing.

math.AP↗

arXiv2026

Deep Learning for Reflected BSDEs: Regularization and Error Analysis

Reflected backward stochastic differential equations (RBSDEs) provide a probabilistic formulation for obstacle constrained problems, but existing deep learning methods for their high dimensional solution remain limited. In this paper, we propose two deep learning schemes for RBSDEs, a deep forward scheme (DFS) and a deep backward scheme (DBS), by first reducing the reflected problem to a family of regularized BSDEs. Our main theoretical contribution concerns the DBS: we establish an explicit error bound showing that, for each fixed regularization parameter $\varepsilon>0$, the approximation error between the DBS solution and the solution to the regularized BSDE is controlled by the associated training loss. We prove that this training loss can be controlled by the universal approximation capability of neural networks. Together, these results yield a theoretical foundation for the deep learning-based solution and complement existing analysis for forward type methods. We illustrate the framework on high dimensional American option pricing, where the reflected formulation allows us to address the continuous time exercise feature directly rather than through a Bermudan approximation. Numerical experiments demonstrate that both DFS and DBS deliver accurate solutions in high dimensions.

q-fin.CP↗

arXiv2026

Endogenous Reinsurance Pricing in Large Competitive Insurance Markets: Finite-Player and Mean Field Analysis

We study endogenous reinsurance pricing in a competitive insurance market with one strategic reinsurer and many heterogeneous insurers. The reinsurer acts as a Stackelberg leader by choosing a common premium rate and an investment strategy, while insurers decide how much risk to retain and how to invest, taking into account their own performance, their performance relative to the insurer population, and common insurance-claim and financial-market noise. This creates a feedback loop absent from standard reinsurance models with exogenous premiums: a premium change affects insurers directly through the cost of reinsurance, and indirectly through the population's aggregate exposure to common insurance-claim risk. For a fixed premium, we characterize the insurers' equilibrium retention through a scalar fixed point and establish its monotone premium response. This characterization reveals a spillover mechanism generated by relative performance concerns and leads to a threshold structure in which insurers move from full cession to partial retention and then to full retention as the premium increases. Using this structure, we reduce the reinsurer's premium problem to a one-dimensional optimization over a compact premium interval and characterize Stackelberg equilibria in both finite-player and mean field models. In the finite-player case, we develop an efficient threshold continuation procedure that determines equilibrium premiums without enumerating all retention configurations. We also prove convergence from finite-player equilibria to mean field equilibria without requiring the mean field equilibrium premium to be unique. Numerical illustrations show how relative performance concerns amplify spillover effects and can induce retention even when reinsurance remains actuarially favorable. They also demonstrate that Stackelberg equilibria need not be unique in either setting.

q-fin.RM↗

arXiv2026

A Gradient Recovery Method for Electron Magnetohydrodynamics with Fractional Dissipation

We propose and analyze a structure-preserving numerical method for the $2\tfrac{1}{2}$-dimensional (2.5D) electron magnetohydrodynamics system with fractional dissipation on the periodic torus. The method works directly with the magnetic field components and combines this component formulation with the gradient recovery operator of [T. Chu, H. Guo, and Z. Zhang, SIAM J. Numer. Anal., 63 (2025), pp. 23--53]. We establish discrete energy stability for a semi-implicit structure-preserving formulation and use an explicit-Hall integrating-factor implementation for efficient computation on periodic grids. The fractional dissipation is treated exactly in Fourier space, and the in-plane divergence constraint is enforced by a spectral Hodge projection. Numerical experiments demonstrate second-order spatial convergence and stable Hall-driven dynamics across several benchmark tests.

math.NA↗

arXiv2026

Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach

We study the optimal design of stealthy attacks against partially observed linear control systems. We first propose a novel likelihood-based detection mechanism derived from the innovation process, based on which we quantify stealthiness and formulate an attack design problem that trades off performance degradation and detectability. We develop a tractable control-theoretic framework for optimal stealthy attacks under two information structures: deterministic attacks fixed prior to system evolution, and adaptive attacks constructed from available observations. In the adaptive setting, the attacker's partial observation leads to a stochastic control problem with an endogenous information structure. We address this challenge through a hierarchical optimization framework combined with the separation principle, reducing the problem to a Markovian control formulation and yielding semi-explicit optimal attacks. We further establish well-posedness of the resulting systems and illustrate through numerical experiments how information constraints shape the trade-off between attack effectiveness and stealthiness.

math.OC↗

arXiv2026

Modeling Stochastic Multi-Agent Interaction in Intraday Battery Energy Storage Dispatch with Market Power

We develop a stochastic game-theoretic model for intraday dispatch of grid-scale battery energy storage systems (BESSs). We assume that each BESS operator competitively manages her state-of-charge to maximize energy arbitrage revenues, driven by the endogenized electricity price that depends on the sum of the charging rates. We characterize the Nash equilibrium of the resulting finite-player linear-quadratic differential game with a shared stochastic driver, obtaining semi-explicit representations of equilibrium feedback controls and equilibrium prices both in the general heterogeneous and the simplified homogeneous BESS setting, via a system of Riccati equations. We then analyze competitive effects, including the marginal externality of additional BESS entering the market, the benefit of coordination and the corresponding market power of large operators, and supply effects from hybrid-type BESSs. We further study the asymptotic regime as the number of agents grows large. Our model provides a quantitative testbed to study the impact of decentralized BESS deployment on the grid and the resulting reduction in daily price spreads.

math.OC↗

arXiv2026

The Three-Dimensional Stochastic EMHD System: Local Well-Posedness and Maximal Pathwise Solutions

We study the three-dimensional stochastic electron magnetohydrodynamics (EMHD) system with fractional dissipation on the torus, driven by Stratonovich transport noise acting through divergence-free first-order operators. The noise generates an It\^o correction while preserving the transport structure of the Hall nonlinearity. Since the Hall term contains one more derivative, in the stochastic setting it must be controlled together with commutators arising from the transport operators. We develop a high-order Sobolev energy method based on Littlewood--Paley analysis and refined commutator estimates, which yields uniform bounds for Galerkin approximations in $H^s$ with $s > \tfrac{5}{2}$ together with suitable time regularity. Using stochastic compactness and identification of limits, we construct martingale solutions for initial data in $L^2(\Omega; H^s)$. Pathwise uniqueness follows from cancellations in the Hall term combined with a stochastic Gr\"onwall argument. An application of a Yamada--Watanabe type result then yields local pathwise well-posedness and the existence of maximal pathwise solutions.

math.PR↗

arXiv2026

An Actor-Critic Framework for Continuous-Time Jump-Diffusion Controls with Normalizing Flows

Continuous-time stochastic control with time-inhomogeneous jump-diffusion dynamics is central in finance and economics, but computing optimal policies is difficult under explicit time dependence, discontinuous shocks, and high dimensionality. We propose an actor-critic framework that serves as a mesh-free solver for entropy-regularized control problems and stochastic games with jumps. The approach is built on a time-inhomogeneous little q-function and an appropriate occupation measure, yielding a policy-gradient representation that accommodates time-dependent drift, volatility, and jump terms. To represent expressive stochastic policies in continuous-action spaces, we parameterize the actor using conditional normalizing flows, enabling flexible non-Gaussian policies while retaining exact likelihood evaluation for entropy regularization and policy optimization. We validate the method on time-inhomogeneous linear-quadratic control, Merton portfolio optimization, and a multi-agent portfolio game, using explicit solutions or high-accuracy benchmarks. Numerical results demonstrate stable learning under jump discontinuities, accurate approximation of optimal stochastic policies, and favorable scaling with respect to dimension and number of agents.

math.OC↗

arXiv2026

Deception in Linear-Quadratic Control

Systems operating in adversarial environments may inadvertently leak sensitive information to adversaries. To address this challenge, we revisit the linear-quadratic control framework and introduce deception to actively mislead adversaries. Specifically, we consider a blue-team agent, observed by a red-team agent, that seeks to minimize a quadratic cost while introducing perturbations to its trajectories over time. These perturbations are designed to corrupt the red team's observations and, consequently, any downstream inferences, while remaining undetected by a red team using sequential hypothesis testing. We implement this idea by augmenting the blue team's quadratic cost with a likelihood ratio statistic. Under this augmented control problem, we derive a semi-explicit solution for the optimal deceptive control law and establish corresponding well-posedness results. In addition, we provide both numerical approximations and analytical bounds for the probability that the red team detects the blue team's deceptive strategies. Numerical results demonstrate the effectiveness of the proposed framework in deceiving the red team while remaining undetected with probability near 1.

math.OC↗

arXiv2026

Information Revelation and Alignment Faking in Stochastic Differential Games

In competitive games with private objectives, actions can reveal information about hidden parameters. However, quantifying such information revelation is nontrivial, since it depends not only on the opponent's hidden parameter but also on the opponent's model of the game. We study this problem via a two-player linear-quadratic stochastic differential game under partial information, in which each player knows its own coupling parameter and models the opponent's hidden parameter through a prior. Starting from the full-information game, we characterize the Nash equilibrium by coupled Riccati equations. We then define baseline implementable controls by averaging the equilibrium under each player's prior. Building on this baseline, we formulate an alignment faking control problem in which one player trades off fidelity to its implementable policy against information acquisition about the opponent's hidden parameter. The information incentive is constructed from a proxy Fisher information matrix based only on the player's available model. This leads to a tractable saddle-point formulation with semi-explicit control characterization through Riccati systems. Numerical illustrations show that alignment faking can substantially improve information gain over baseline play when the faker's model is accurate, but often at the cost of greater detectability. They also show that the proxy Fisher information can systematically differ from the true information under model misspecification.

math.OC↗

arXiv2026

Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains

We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity constraints, and standard neural network approximations do not naturally enforce the associated spectral boundary conditions. To address this challenge, we introduce a spectrally-defined mollification strategy that preserves the structure of the nonlocal operator while ensuring boundary compatibility. This enables the derivation of rigorous energy estimates in Sobolev spaces. Our results rely on analytical tools from PDE theory, highlighting the compatibility of PINN approximations with classical energy estimates for nonlocal equations. We prove convergence of the PINN approximation in any space-time Sobolev norm $H^k$ (with $k \in \N)$. The analysis highlights the role of mollified residuals in enabling theoretical guarantees for neural-network-based solvers of nonlocal PDEs.

math.NA↗

arXiv2025

Deep Signature Approach for McKean-Vlasov FBSDEs in a Random Environment

Mean-field games with common noise provide a powerful framework for modeling the collective behavior of large populations subject to shared randomness, such as systemic risk in finance or environmental shocks in economics. These problems can be reformulated as McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) in a random environment, where the coefficients depend on the conditional law of the state given the common noise. Existing numerical methods, however, are largely limited to cases where interactions depend only on expectations or low-order moments, and therefore cannot address the general setting of full distributional dependence. In this work, we introduce a deep learning-based algorithm for solving MV-FBSDEs with common noise and general mean-field interactions. Building on fictitious play, our method iteratively solves conditional FBSDEs with fixed distributions, where the conditional law is efficiently represented using signatures, and then updates the distribution through supervised learning. Deep neural networks are employed both to solve the conditional FBSDEs and to approximate the distribution-dependent coefficients, enabling scalability to high-dimensional problems. Under suitable assumptions, we establish convergence in terms of the fictitious play iterations, with error controlled by the supervised learning step. Numerical experiments, including a distribution-dependent mean-field game with common noise, demonstrate the effectiveness of the proposed approach.

math.OC↗

arXiv2025

Learning Mean-Field Games through Mean-Field Actor-Critic Flow

We propose the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), combining techniques from reinforcement learning and optimal transport. The MFAC framework jointly evolves the control (actor), value function (critic), and distribution components through coupled gradient-based updates governed by partial differential equations (PDEs). A central innovation is the Optimal Transport Geodesic Picard (OTGP) flow, which drives the distribution toward equilibrium along Wasserstein-2 geodesics. We conduct a rigorous convergence analysis using Lyapunov functionals and establish global exponential convergence of the MFAC flow under a suitable timescale. Our results highlight the algorithmic interplay among actor, critic, and distribution components. Numerical experiments illustrate the theoretical findings and demonstrate the effectiveness of the MFAC framework in computing MFG equilibria.

math.OC↗

arXiv2025

Strategic Inference in Stackelberg Games: Optimal Control for Revealing Adversary Intent

We study a continuous-time stochastic Stackelberg game in which a leader seeks to accomplish a primary objective while inferring a hidden parameter of a rational follower. The follower solves an entropy-regularized tracking problem and responds to the leader's trajectory with a randomized policy. Anticipating this response, the leader designs informative controls to maximize the estimation efficiency for the follower's latent intent, through maximum likelihood estimation. Unlike prior work on discrete-time or finite-candidate inverse learning, our framework enables continuous parameter inference without prior assumptions and endogenizes the information source through the follower's strategic feedback. We derive semi-explicit solutions, prove well-posedness, and develop recurrent neural network algorithms to approximate the leader's path-dependent control. Numerical experiments demonstrate how the leader balances task performance and information gain, highlighting the practical value of our approach for adversarial strategic inference.

math.OC↗

arXiv2025

Well-posedness of the relaxed Electron MHD equations with random diffusion

We investigate a three-dimensional active-vector relaxation of the electron magnetohydrodynamics (EMHD) equations without resistivity. The relaxation replaces the electron current by a generalized current defined through a fractional power of the Laplacian. We drive the system by multiplicative pseudo-differential noise and apply an exponential transformation that removes the stochastic differential term and produces an effective fractional damping. For deterministic divergence-free, mean-zero initial data, we prove local well-posedness up to a stopping time in suitable Gevrey spaces. Under a smallness condition, we further establish global well-posedness with high explicit probability.

math.AP↗

arXiv2025

Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architectures

We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs. These games model a broad class of graph-structured multi-agent systems arising in finance, robotics, energy, and social dynamics, where agents interact locally under uncertainty. The NTM architecture imposes a graph-guided sparsification on feedforward neural networks, embedding fixed, non-trainable components aligned with the underlying graph topology. This design enhances interpretability and stability, while significantly reducing the number of trainable parameters in large-scale, sparse settings. We theoretically establish a universal approximation property for NTM in static games on graphs and numerically validate its expressivity and robustness through supervised learning tasks. Building on this foundation, we incorporate NTM into two state-of-the-art game solvers, Direct Parameterization and Deep BSDE (backward stochastic differential equation), yielding their sparse variants (NTM-DP and NTM-DBSDE). Numerical experiments on three SDGs across various graph structures demonstrate that NTM-based methods achieve performance comparable to their fully trainable counterparts, while offering improved computational efficiency.

cs.LG↗