arXiv subjects

Chengyang Huang

Publications and source records attributed to Chengyang Huang.

3 recordsLinked to original sources

arXiv2026

Learning Population-Level Dynamics through a Latent Fokker--Planck Model and Discrepancy Transport Maps

Many scientific and engineering systems are observed as time-indexed probability distributions whose governing dynamics are unknown and whose individual trajectories are unavailable. These settings challenge conventional system-identification approaches that rely on trajectory correspondence or prescribed evolution equations. This work presents a population-level inference framework that recovers latent stochastic dynamics directly from snapshot probability distributions by decomposing the observed evolution into an intrinsic latent stochastic process and a discrepancy transport map that captures geometric deformation between the latent and observed probability spaces. The latent dynamics are modeled using an Ornstein--Uhlenbeck process, providing a closed-form solution to the associated Fokker--Planck equation, while the discrepancy transport map is parameterized through the Knothe--Rosenblatt rearrangement with monotone neural networks. To mitigate the non-uniqueness inherent in the latent--transport decomposition, the transport map is regularized using a deformation energy motivated by hyperelasticity, promoting smooth, physically interpretable deformations while reducing unnecessary complexity. The latent stochastic model and discrepancy transport map are learned jointly through a unified optimization problem defined over probability distributions. Numerical examples involving nonlinear and multimodal distributional dynamics demonstrate that the proposed framework accurately reconstructs complex probability evolution while preserving a compact and analytically tractable latent representation. The proposed formulation provides a general framework for population-level dynamical inference and establishes a foundation for extending latent stochastic models and transport-based learning to more general and higher-dimensional systems.

cs.CE↗

arXiv2026

Bayesian Variational System Identification with Weak-Form Residual Likelihoods

We consider system identification for discovering parameterized operators in governing partial differential equations (PDEs) from noisy spatiotemporal data. Building on variational system identification (VSI), which identifies PDEs through Galerkin weak-form residuals, we develop a Bayesian VSI (B-VSI) framework for operator selection, parameter estimation, and uncertainty quantification. The central idea is to define the likelihood directly in weak-form residual space by propagating observation uncertainty through the weak-form residual map. The resulting likelihood captures heteroscedastic and correlated residual errors while avoiding repeated forward PDE solves during inference. For efficient computation, we use lagged-covariance updates that yield generalized least-squares estimates and conjugate posterior approximations when applicable, together with gradient-based and particle-based methods for more general priors and posterior structures. Model-form uncertainty is handled through sequential operator elimination guided by a residual-space Bayesian information criterion. We demonstrate the framework on state-linear and nonlinear PDEs, including the Fokker--Planck equation and a two-field Cahn--Hilliard equation. The results show that B-VSI accurately recovers active operators and coefficients from noisy data, improves robustness relative to classical VSI, and provides posterior uncertainty estimates for coefficients and derived physical quantities.

cs.CE↗

arXiv2023

FP-IRL: Fokker--Planck Inverse Reinforcement Learning -- A Physics-Constrained Approach to Markov Decision Processes

Inverse reinforcement learning (IRL) is a powerful paradigm for uncovering the incentive structure that drives agent behavior, by inferring an unknown reward function from observed trajectories within a Markov decision process (MDP). However, most existing IRL methods require access to the transition function, either prescribed or estimated \textit{a priori}, which poses significant challenges when the underlying dynamics are unknown, unobservable, or not easily sampled. We propose Fokker--Planck inverse reinforcement learning (FP-IRL), a novel physics-constrained IRL framework tailored for systems that can be described by Fokker--Planck (FP) dynamics. FP-IRL simultaneously infers both the reward and transition functions directly from trajectory data, without requiring access to sampled transitions. Our method leverages a correspondence between MDPs and the FP equation, linking reward maximization in MDPs with free energy minimization in FP dynamics. This connection enables inference of the FP potential function using our inference approach of variational system identification, from which the full set of MDP components -- reward, transition, and policy -- can be recovered using analytic expressions. We demonstrate the effectiveness of FP-IRL through experiments on synthetic benchmarks and a modified version of the Mountain Car problem. Our results show that FP-IRL achieves accurate recovery of agent incentives while preserving computational efficiency and physical interpretability.

cs.LG↗