线性扩散方程解的随机变分公式

A variational characterization of the risk-sensitive average reward for controlled diffusions on $\mathbb{R}^d$

We address the variational formulation of the risk-sensitive reward problem for non-degenerate diffusions on $\mathbb{R}^d$ controlled through the drift. We establish a variational formula on the whole space and also show that the risk-sensitive value equals the generalized principal eigenvalue of the semilinear operator. This can be viewed as a controlled version of the variational formulas for principal eigenvalues of diffusion operators arising in large deviations. We also revisit the average risk-sensitive minimization problem and by employing a gradient estimate developed in this paper, w…

A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$

We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula for potentials that vanish at infinity under minimal hypotheses, and also for general potentials under blanket geometric ergodicity assumptions. We also present associated results having the flavor of a refined maximum principle.

cDVAE：由变分自编码器潜空间嵌入引导的多模态生成式条件扩散，用于虚拟6D相空间诊断

cDVAE: Multimodal Generative Conditional Diffusion Guided by Variational Autoencoder Latent Embedding for Virtual 6D Phase Space Diagnostics

针对加速器无法单次测量束流6D相空间的问题，提出cDVAE条件扩散虚拟诊断方法，利用VAE将标量参数和图像编码为潜向量进行引导，并在HiRES上准确重建全部15个独立2D投影。

隐扩散过程路径估计与参数推断的变分方法

A variational approach to path estimation and parameter inference of hidden diffusion processes

本文提出一种变分方法，用于估计隐扩散过程的路径并推断参数，通过高效推理方案提升对随机微分方程参数的估计精度。

用于聚集-扩散方程的变分神经传输

Variational neural transport for aggregation-diffusion equations

该研究针对趋化性等领域的聚集-扩散方程，基于Onsager变分原理构建神经传输框架，将方程转化为最优控制问题，通过神经网络参数化速度场并结合欧拉法求解，经误差分析和数值实验验证了方法的准确性与有效性。

变分时间隐式格式的高阶空间离散：Wasserstein梯度流与反应-扩散系统

High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems

本文为广义最优传输空间中的梯度流构造一阶时间隐式广义JKO变分格式，结合ALG2与高阶有限元实现稳定迭代求解，并通过多类二维PDE验证有效性。

A variational formula for risk-sensitive reward

We derive a variational formula for the optimal growth rate of reward in the infinite horizon risk-sensitive control problem for discrete time Markov decision processes with compact metric state and action spaces, extending a formula of Donsker and Varadhan for the Perron-Frobenius eigenvalue of a positive operator. This leads to a concave maximization formulation of the problem of determining this optimal growth rate.