SearcharxivSearch

arXiv subjects

Jie Xiong

Publications and source records attributed to Jie Xiong.

At least 19 recordsLinked to original sources

Extinction behaviour for mutually enhancing continuous-state population dynamics

In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and spectrally positive $α$-stable random measures. Such a SDE system can be identified as a continuous-state Lotka-Volterra type population model. Extinction properties of the populations are studied for different choices of the coefficients involved in the SDEs.

math.PR

Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients

We study pathwise uniqueness for cyclic catalytic stochastic differential equations whose state-dependent square-root diffusion coefficients are non-Lipschitz and degenerate on the boundary. The approach is the direct construction of a strong solution using a Malliavin compactness criterion. The key is the development of a new family of boundary-sensitive weighted Malliavin estimates for the tangent processes of the smooth approximations. Pathwise uniqueness then follows from the dual Yamada-Watanabe argument together with the weak uniqueness available in the literature.

math.PR

Continuous-time q-learning for Markov regime switching system under Tsallis entropy

This paper studies continuous-time q-learning (the continuous-time counterpart of Q-learning) for a Markov regime-switching system under Tsallis entropy regularization. The Tsallis entropy regularization yields an optimal policy distribution that may not necessarily be a Gibbs measure, thereby complicating algorithm design. Furthermore, to address the limited universality of current continuous-time regime-switching reinforcement learning algorithms (often restricted to the exploratory mean-variance framework), this study focuses on continuous-time q-learning for Markov regime-switching systems based on Tsallis entropy, aiming for a more universally applicable continuous-time reinforcement learning method. We establish the martingale characterization of the q-function under Tsallis entropy for continuous-time Markov regime-switching systems. We further design two q-learning algorithms that differ based on whether the Lagrange multiplier can be explicitly derived. We apply these algorithms to the continuous-time exploratory mean-variance portfolio optimization problem in a regime-switching market. Numerical experiments demonstrate the satisfactory performance of our q-learning algorithms.

math.OC

Extinction and extinguishment properties for a nonlinear predator-prey branching model

We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populations are subject to nonlinear self-regulation and a mixed-sign predator--prey interaction: the second promotes the first, whereas the first suppresses the second. Two complementary structures are developed. An exact power--logarithmic cancellation functional removes the interaction drifts and yields stochastic Lyapunov estimates, nonexplosion, and boundary criteria. In the multiplicative regimes, integrating-factor identities and geometric Lévy factorizations express extinction through weighted exposure clocks and reduce the long-time analysis to effective decay rates. These methods yield almost-sure extinction criteria and identify a regime in which finite-time extinction and nonextinction coexist. On nonextinction, both populations remain positive at all finite times and converge jointly to zero, exhibiting joint extinguishment rather than positive persistence.

math.PR

Saturation-Aware Predictive Quantization for Low-Power ECG Acquisition: A Benchmark of Taylor, Adaptive-Order, Kalman, and LSTM Predictors

Wearable electrocardiogram (ECG) monitors require energy-efficient analog-to-digital converters (ADCs), yet conventional successive-approximation-register (SAR) ADCs repeatedly resolve slowly varying most significant bits. Predictive quantization (PQ) instead estimates the next sample and quantizes only the residual, thereby reducing the required conversion depth. Its principal failure mode is residual saturation, which occurs when prediction error exceeds the residual ADC range and is irreversibly clipped. We compared four one-step-ahead predictors under a common 10-bit, saturation-aware PQ model with residual widths from 2 to 8 bits. The benchmark included first-order Taylor extrapolation, an adaptive-order predictor, a constant-velocity Kalman filter, and a two-layer long short-term memory (LSTM) network. We used an open-loop protocol in which all predictors received past original samples. This protocol isolates intrinsic prediction performance from recursive reconstruction-error propagation. Saturation rate (SR) was the primary metric, complemented by overflow energy ratio (OER), which weights each event by its squared overflow depth. On a 5,317-sample excerpt from MIT-BIH Arrhythmia Database Record 101, the Kalman predictor performed best at Br=6. It achieved 30.88 dB SNR, 2.16% SR, and 12.93% OER, compared with 28.39 dB, 2.69%, and 25.29% for Taylor extrapolation. The adaptive-order predictor achieved 29.61 dB SNR and 2.44% SR using three registers, two comparators, and no multiplier. The LSTM reached 29.28 dB SNR and did not outperform the model-based predictors on this limited-data benchmark. Under the evaluated excerpt and open-loop protocol, Br=6 provided a favorable balance between reconstruction fidelity and conversion depth. Closed-loop, multi-subject, and hardware validation are required before system-level energy or deployment claims can be made.

eess.SP

Closed-loop solvability of infinite-horizon stochastic linear-quadratic problem for Markov regime-switching jump-diffusion system

This paper investigates a class of stochastic linear-quadratic (SLQ) control problems over an infinite horizon for Markov regime-switching jump-diffusion systems. Unlike classical diffusion models modulated by a Markov chain, we assume that the state process undergoes abrupt jumps that are synchronous with the regime switches of the Markov chain. In contrast to conventional Poisson jump-diffusion models, the jumps in the state process are entirely induced by the state transitions of the Markov chain, which can be interpreted as losses or gains of state process incurred during regime changes. Under this formulation, we thoroughly discuss the closed-loop solvability of the SLQ control problem and provide a feedback representation of the optimal control via the stabilizing solution of a system of coupled algebraic Riccati equations (CAREs). Finally, we further apply our results to a lifetime wealth tracking problem and derive the corresponding optimal investment strategy.

math.OC

Constrained Zero-Sum Stochastic Linear-Quadratic Differential Game for Jump-Diffusion Systems with Random Coefficients

This paper studies a two-player zero-sum stochastic linear-quadratic (SLQ) differential game for controlled jump-diffusion systems with random coefficients, where the controls of both players are constrained to nonempty closed convex cones. Under a uniform convexity--concavity condition, we establish the existence and uniqueness of an open-loop saddle point and characterize it by a forward--backward stochastic differential equation with jumps (FBSDEJ) together with cone-type variational inequalities. Assuming the existence of positive bounded solutions to the associated system of indefinite extended stochastic Riccati equations with jumps (IESREJs), we derive a feedback-form representation of the unique open-loop saddle point by constructing predictable minimax selectors and combining the Meyer--Itô formula with jumps, and the FBSDEJ characterization. Finally, under additional structural conditions, we prove the existence of positive bounded solutions to the IESREJs by a double-truncation approximation and a multidimensional BSDEJ comparison theorem.

math.OC

Indefinite Stochastic Linear-Quadratic Optimal Control Problems with Random Coefficients and Poisson Jumps: Closed-Loop Representation of Open-Loop Optimal Controls

This paper is concerned with stochastic linear-quadratic (SLQ) optimal control problems with random coefficients and Poisson jumps. The weighting matrices are allowed to be random and indefinite. Under the uniform convexity condition, the global fundamental matrix representation $P=\mathbf Y\mathbf X^{-1}$, used in the diffusion case, is generally unavailable because Poisson jumps may cause the optimal state fundamental matrix $\mathbf X$ to become singular. We construct the process $P$ directly from the stochastic value flow and prove that the associated stochastic Riccati equation with jumps (SRE-J) admits a unique maximal strongly regular solution, which gives a closed-loop representation of the unique open-loop optimal control. We also give sufficient conditions for uniform convexity and present indefinite SLQ examples with jumps.

math.OC

A Kalman Filter-Assisted Data-Predictive SAR ADC With Reduced Switching Energy for Low-Power Applications

The proliferation of Internet of Things (IoT) devices and wearable health monitors has created an urgent demand for ultra-low-power analog-to-digital converters (ADCs). Successive approximation register (SAR) ADCs are widely used in such applications, yet their energy efficiency remains constrained by the sequential bit-by-bit switching of the capacitive DAC (CDAC). The high-weight most significant bit (MSB) transitions dominate the total switching energy, and the rigid N -cycle conversion flow imposes a hard lower bound on latency per sample.This paper presents a Kalman filter-assisted data-predictive SAR ADC that replaces the first four comparator-driven decisions with a recursive state estimator. The Kalman filter predicts the 4 MSBs from the complete conversion history before each cycle begins, enabling simultaneous parallel switching of the MSB capacitors. This eliminates redundant CDAC transitions, shortens the quantization cycle by four clock periods, and reduces switching energy by approximately 50%. An optimized 4-bit MSB switching scheme further suppresses residual switching at the hardware level. The ADC, designed in a 180-nm CMOS process, supports configurable dual-mode operation, toggling between a conventional mode and the Kalman-driven predictive mode for robustness under erratic inputs. At 20 MS/s and a 1.8-V supply, the predictive mode reduces total power consumption by 50.3% (from 1.96 mW to 0.975 mW), with a measured SNR/SFDR of 57.88/74.51 dB at 504 kHz, confirming its suitability for energy-constrained wireless sensor networks.

eess.SP

Strong uniqueness and large deviation principle for mutually catalytic super Markov chains

In this paper, we study the strong uniqueness problem for the mutually catalytic super-Markov chain, which is a two-dimensional degenerate stochastic differential equation with Hölder continuous coefficients. The key step is to find a process which is a function of two coupled processes and satisfies an autonomous one-dimensional stochastic differential equation; uniqueness for this equation follows from a Yamada-Watanabe argument. A large deviation principle is then established, in the irreducible two-state case, by applying the weak-convergence approach of Budhiraja, Dupuis and Maroulas to the controlled equations.

math.PR

Bgolearn: a Unified Bayesian Optimization Framework for Accelerating Materials Discovery

Efficient exploration of vast compositional and processing spaces remains a major challenge in accelerated materials discovery. Bayesian optimization (BO) provides a principled approach to identify optimal materials with minimal experimentation, but its adoption has been limited by implementation complexity and a lack of domain-specific tools. Here, we present Bgolearn, a versatile Python framework that brings BO to materials research through intuitive interfaces, robust algorithms, and materials-focused workflows. Bgolearn supports single- and multi-objective optimization, multiple acquisition strategies, diverse surrogate models, and uncertainty quantification, enabling effective navigation of complex design spaces. Benchmark studies show that Bgolearn reduces experimental effort by 40-60\% compared with random search, grid search, and genetic algorithms, while achieving comparable or superior solution quality. Its effectiveness is demonstrated across case studies, including the discovery of maximum-elastic-modulus triply periodic minimal surface structures, ultra-high-hardness high-entropy alloys, and high-strength, high-ductility medium-Mn steels, and is further supported by numerous publications. With a modular architecture that integrates seamlessly into existing materials workflows and a graphical interface (BgoFace) that removes programming barriers, Bgolearn establishes a practical, reliable platform for Bayesian optimization in materials science. The software is openly available at https://github.com/Bin-Cao/Bgolearn.

cond-mat.mtrl-sci

A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations

This paper studies a partially observed stochastic control problem for jump-diffusion state processes observed through multivariate counting processes with state-dependent intensities. In contrast to diffusion observations or observation jumps with state-independent intensities, each observation jump carries information about the latent state and enters the likelihood-ratio dynamics, producing a coupled variational structure involving both the state perturbation and the likelihood-ratio perturbation. By introducing a reference probability measure and augmenting the state with the counting-process likelihood ratio, we derive a stochastic maximum principle for the resulting partially observed control problem. The necessary optimality condition is expressed as a conditional Hamiltonian stationarity relation with respect to the observation filtration. As an illustration, we apply the result to a linear-quadratic execution model and obtain a Riccati-type feedback driven by the conditional mean of the latent state. The resulting feedback is illustrated numerically by a particle-filter implementation under nonlinear point-process filtering.

math.OC

Stochastic Mean-Field LQ Stackelberg Differential Games with Random Coefficients: Theory and a Deep FBSDE Picard Solver

This paper studies a stochastic mean-field linear-quadratic Stackelberg differential game with random coefficients. The interaction between mean-field terms and random coefficients precludes the direct use of conventional decoupling techniques. We apply an extended Lagrange multiplier method to derive an affine operator representation of the follower's optimal response. The induced leader problem is then formulated as a generalized stochastic LQ control problem with operator-valued coefficients, and the Stackelberg optimal control is characterized through a Riccati-free coupled FBSDE system. We further develop a Deep FBSDE Picard Solver that preserves the Stackelberg order through follower-response learning, response-sensitivity extraction, leader optimization, and neural augmented Lagrangian enforcement of mean-field consistency constraints. Numerical studies covering convergence diagnostics, discretization sensitivity, Riccati calibration, ablation tests, stability under control perturbations, Stackelberg--Nash comparisons, and a financial application support the effectiveness of the proposed framework.

math.OC

Physics-informed operator learning for transferable energy-dissipative microstructure dynamics

Phase-field simulations provide mechanistic descriptions of microstructure evolution, but repeated high-fidelity integration over long horizons and broad parameter spaces remains computationally expensive. We present PFNet, a physics-informed neural operator framework that advances microstructural states by learning conditional evolution operators rather than direct correlations. PFNet combines a diffusion-inspired U-Net with periodic padding, entropy-based state conditioning and thermodynamic-parameter modulation to encode boundary consistency, instantaneous ordering state and changes in the free-energy landscape. For Cahn-Hilliard coarsening, PFNet achieves accurate one-step prediction and stable autoregressive rollouts across composition, gradient-energy coefficient, coarsening stage and morphology class, with errors concentrated near diffuse interfaces and topology-changing regions. The same framework extends to a four-channel martensitic-transformation benchmark without martensite-specific redesign. These results indicate that physics-informed operator learning can provide transferable surrogates for phase-field dynamics and broader energy-dissipative dynamical systems.

cond-mat.mtrl-sci

Equilibrium Strategies for the N-agent Mean-Variance Investment Problem over a Random Horizon

We study equilibrium feedback strategies for a family of dynamic mean-variance problems with competition among a large group of agents. We assume that the time horizon is random and each agent's risk aversion depends dynamically on the current wealth. We consider both the finite population game and the corresponding mean-field one. Each agent can invest in a risk-free asset and a specific individual stock, which is correlated with other stocks by a common noise. By applying stochastic control theory, we derive the extended Hamilton-Jacobi-Bellman (HJB) system of equations for both $n$-agent and mean-field games. Under an exponentially distributed random horizon, in each case, we explicitly obtain the equilibrium feedback strategies and the value function. Our results show that the agent's equilibrium feedback strategy depends not only on his/her current wealth but also on the wealth of other competitors. Moreover, when the risk aversion is state-independent and the risk-free interest rate is zero, the equilibrium strategies degenerate to constants, which is identical to the unique equilibrium obtained in \citet{lacker2019mean} with exponential risk preferences; when the competition parameter goes to zero and the risk aversion equals some specific value, the equilibrium strategies coincide with the ones derived in \citet{landriault2018equilibrium}.

math.OC

Full waveform inversion method based on diffusion model

Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process getting trapped in local minima. In recent years, generative diffusion models have provided a way to regularize full-waveform inversion by learning implicit prior distributions. However, existing methods mostly use unconditional diffusion processes, ignoring the inherent physical coupling relationship between velocity and density and other physical properties. This paper proposes a full-waveform inversion method based on conditional diffusion model regularization. By improving the backbone network structure of the diffusion model, two-dimensional density information is introduced as a conditional input into the U-Net network. Experimental results show that the full-waveform inversion method based on the conditional diffusion model significantly improves the resolution and structural fidelity of the inversion results, and exhibits stronger stability and robustness when dealing with complex situations. This method effectively utilizes density information to constrain the inversion and has good practical application value. Keywords: Deep learning; Diffusion model; Full waveform inversion.

cs.LG

High-Fidelity Compression of Seismic Velocity Models via SIREN Auto-Decoders

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing continuous signals independently of grid resolution. In this paper, we propose a high-fidelity neural compression framework based on a SIREN (Sinusoidal Representation Networks) auto-decoder to represent multi-structural seismic velocity models from the OpenFWI benchmark. Our method compresses each 70x70 velocity map (4,900 points) into a compact 256-dimensional latent vector, achieving a compression ratio of 19:1. We evaluate the framework on 1,000 samples across five diverse geological families: FlatVel, CurveVel, FlatFault, CurveFault, and Style. Experimental results demonstrate an average PSNR of 32.47 dB and SSIM of 0.956, indicating high-quality reconstruction. Furthermore, we showcase two key advantages of our implicit representation: (1) smooth latent space interpolation that generates plausible intermediate velocity structures, and (2) zero-shot super-resolution capability that reconstructs velocity fields at arbitrary resolutions up to 280x280 without additional training. The results highlight the potential of INR-based auto-decoders for efficient storage, multi-scale analysis, and downstream geophysical applications such as full waveform inversion.

cs.LG

Seismic full-waveform inversion based on a physics-driven generative adversarial network

Objectives: Full-waveform inversion (FWI) is a high-resolution geophysical imaging technique that reconstructs subsurface velocity models by iteratively minimizing the misfit between predicted and observed seismic data. However, under complex geological conditions, conventional FWI suffers from strong dependence on the initial model and tends to produce unstable results when the data are sparse or contaminated by noise. Methods: To address these limitations, this paper proposes a physics-driven generative adversarial network-based full-waveform inversion method. The proposed approach integrates the data-driven capability of deep neural networks with the physical constraints imposed by the seismic wave equation, and employs adversarial training through a discriminator to enhance the stability and robustness of the inversion results. Results: Experimental results on two representative benchmark geological models demonstrate that the proposed method can effectively recover complex velocity structures and achieves superior performance in terms of structural similarity (SSIM) and signal-to-noise ratio (SNR). Conclusions: This method provides a promising solution for alleviating the initial-model dependence in full-waveform inversion and shows strong potential for practical applications.

cs.LG