Electroencephalography (EEG) provides a non-invasive insight into the brain's cognitive and emotional dynamics. However, modeling how these states evolve in real time and quantifying the energy required for such transitions remains a major challenge. The Schrödinger Bridge Problem (SBP) offers a principled probabilistic framework to model the most efficient evolution between the brain states, interpreted as a measure of cognitive energy cost. While generative models such as GANs have been widely used to augment EEG data, it remains unclear whether synthetic EEG preserves the underlying dynamical structure required for transition-based analysis. In this work, we address this gap by using SBP-derived transport cost as a metric to evaluate whether GAN-generated EEG retains the distributional geometry necessary for energy-based modeling of cognitive state transitions. We compare transition energies derived from real and synthetic EEG collected during Stroop tasks and demonstrate strong agreement across group and participant-level analyses. These results indicate that synthetic EEG preserves the transition structure required for SBP-based modeling, enabling its use in data-efficient neuroadaptive systems. We further present a framework in which SBP-derived cognitive energy serves as a control signal for adaptive human-machine systems, supporting real-time adjustment of system behavior in response to user cognitive and affective state.

翻译：脑电图（EEG）能够以非侵入方式洞察大脑的认知与情感动态。然而，如何实时建模这些状态的演变过程，并量化此类转变所需的能量，仍然是一个重大挑战。薛定谔桥问题（SBP）提供了一种严谨的概率框架，用于建模大脑状态间最有效的演变过程，并被解读为认知能量消耗的度量。尽管生成对抗网络（GAN）等生成模型已被广泛用于扩充脑电数据，但合成脑电数据是否保留进行基于状态转变分析所需的底层动态结构仍不明确。在本研究中，我们通过将SBP导出的传输成本作为度量指标来填补这一空白，以评估GAN生成的脑电数据是否保留进行认知状态转变能量建模所需的条件分布几何结构。我们比较了在斯特鲁普任务中采集的真实与合成脑电数据推导出的转变能量，并在群体和个体受试者层面分析中均显示出高度一致性。这些结果表明，合成脑电数据保留了基于SBP建模所需的转变结构，从而能够将其应用于数据高效的神经自适应系统中。我们进一步提出一个框架，在该框架中，SBP推导出的认知能量作为自适应人机系统的控制信号，支撑系统根据用户认知与情感状态实现实时行为调整。