ABRIDGED. The analysis of spectral energy distributions (SEDs) of protoplanetary disks to determine their physical properties is known to be highly degenerate. Hence, a Bayesian analysis is required to obtain parameter uncertainties and degeneracies. The challenge here is computational speed, as one radiative transfer model requires a couple of minutes to compute. We performed a Bayesian analysis for 30 well-known protoplanetary disks to determine their physical disk properties, including uncertainties and degeneracies. To circumvent the computational cost problem, we created neural networks (NNs) to emulate the SED generation process. We created two sets of radiative transfer disk models to train and test two NNs that predict SEDs for continuous and discontinuous disks. A Bayesian analysis was then performed on 30 protoplanetary disks with SED data collected by the DIANA project to determine the posterior distributions of all parameters. We ran this analysis twice, (i) with old distances and additional parameter constraints as used in a previous study, to compare results, and (ii) with updated distances and free choice of parameters to obtain homogeneous and unbiased model parameters. We evaluated the uncertainties in the determination of physical disk parameters from SED analysis, and detected and quantified the strongest degeneracies. The NNs are able to predict SEDs within 1ms with uncertainties of about 5% compared to the true SEDs obtained by the radiative transfer code. We find parameter values and uncertainties that are significantly different from previous values obtained by $\chi^2$ fitting. Comparing the global evidence for continuous and discontinuous disks, we find that 26 out of 30 objects are better described by disks that have two distinct radial zones. Also, we created an interactive tool that instantly returns the SED predicted by our NNs for any parameter combination.

翻译：摘要（精简版）。通过分析原行星盘的能谱分布（SEDs）来确定其物理性质，已知存在高度简并性问题。因此，需要采用贝叶斯分析来获取参数的不确定度和简并性。挑战在于计算速度，因为单个辐射传输模型需要数分钟才能完成计算。我们对30个已知的原行星盘进行了贝叶斯分析，以确定其物理盘性质，包括不确定度和简并性。为规避计算成本问题，我们创建了神经网络（NNs）来模拟SED生成过程。我们建立了两组辐射传输盘模型，用于训练和测试两个分别预测连续盘和不连续盘SED的神经网络。随后，使用DIANA项目收集的SED数据对30个原行星盘进行贝叶斯分析，以确定所有参数的后验分布。我们进行了两次分析：（i）使用先前的距离和额外参数约束（与之前研究相同），以比较结果；（ii）使用更新后的距离并自由选择参数，以获得均匀且无偏的模型参数。我们评估了从SED分析中确定物理盘参数时的不确定度，并检测和量化了最强的简并性。神经网络能在1毫秒内预测SED，与辐射传输代码获得的真实SED相比，不确定度约为5%。我们发现参数值和不确定度与先前通过$\chi^2$拟合获得的值存在显著差异。比较连续盘和不连续盘的整体证据，发现30个目标中有26个更适合用具有两个不同径向区域的盘来描述。此外，我们创建了一个交互式工具，可即时返回神经网络针对任何参数组合预测的SED。