Neural Operator Approximation Dataset

该数据集是为了训练和测试神经算子对反应-扩散偏微分方程自适应控制中的增益核的近似而构建的。它包含了从有限差分求解器模拟得到的估计反应系数与增益核的配对数据。此外，该数据集包括10个随机抽取的λ值，其中γ在(8.5, 9.5)范围内均匀采样。使用Nvidia RTX 3090Ti显卡模拟10个植物的轨迹耗时超过1小时。数据集规模为5000对(λ̂, k̅)，用于训练和测试，任务旨在训练神经算子近似，以应用于反应-扩散偏微分方程的自适应控制。

This dataset is constructed for training and testing neural operator approximations of the gain kernel in adaptive control of reaction-diffusion partial differential equations (PDEs). It contains paired data of estimated reaction coefficients and gain kernels generated via finite difference solver simulations. Additionally, the dataset includes 10 randomly sampled λ values, with γ uniformly sampled within the interval (8.5, 9.5). Simulating 10 plant trajectories using an NVIDIA RTX 3090Ti graphics card took over one hour. The dataset comprises 5000 paired (λ̂, k̅) samples for training and testing, with the core goal of training neural operator approximations for application in adaptive control of reaction-diffusion PDEs.