Jinwei Liu

Jinwei Liu, Lu Ren, Wang Yao et al.

Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria, yet ensuring mathematically consistent density-coupled evolution remains a major challenge. This paper proposes the NF-MKV Net, a neural network approach that integrates process-regularized normalizing flow (NF) with state-policy-connected time-series neural networks to solve MKV FBSDEs and their associated fixed-point formulations of MFG equilibria. The method first reformulates MFG equilibria as MKV FBSDEs, embedding density evolution into equation coefficients within a probabilistic framework. Neural networks are then employed to approximate value functions and their gradients. To enforce volumetric invariance and temporal continuity, NF architectures impose loss constraints on each density transfer function.

Jinwei Liu, Wang Yao, Xiao Zhang

Neural network-based methods are effective for solving equilibria in Mean-Field Games (MFGs), particularly in high-dimensional settings. However, solving the coupled partial differential equations (PDEs) in MFGs limits their applicability since solving coupled PDEs is computationally expensive. Additionally, modifying boundary conditions, such as the initial state distribution or terminal value function, necessitates extensive retraining, reducing scalability. To address these challenges, we propose a generalized framework, PIONM (Physics-Informed Neural Operator NF-MKV Net), which leverages physics-informed neural operators to solve MFGs equations. PIONM utilizes neural operators to compute MFGs equilibria for arbitrary boundary conditions. The method encodes boundary conditions as input features and trains the model to align them with density evolution, modeled using discrete-time normalizing flows. Once trained, the algorithm efficiently computes the density distribution at any time step for modified boundary condition, ensuring efficient adaptation to different boundary conditions in MFGs equilibria. Unlike traditional MFGs methods constrained by fixed coefficients, PIONM efficiently computes equilibria under varying boundary conditions, including obstacles, diffusion coefficients, initial densities, and terminal functions. PIONM can adapt to modified conditions while preserving density distribution constraints, demonstrating superior scalability and generalization capabilities compared to existing methods.

Feng Zhang, Jinwei Liu, Xiatian Zhu et al.

Pose distillation is widely adopted to reduce model size in human pose estimation. However, existing methods primarily emphasize the transfer of teacher knowledge while often neglecting the performance degradation resulted from the curse of capacity gap between teacher and student. To address this issue, we propose AgentPose, a novel pose distillation method that integrates a feature agent to model the distribution of teacher features and progressively aligns the distribution of student features with that of the teacher feature, effectively overcoming the capacity gap and enhancing the ability of knowledge transfer. Our comprehensive experiments conducted on the COCO dataset substantiate the effectiveness of our method in knowledge transfer, particularly in scenarios with a high capacity gap.