AI 中文总结
研究针对非均质多孔介质反应性输运反问题，提出CoDe-BPINN框架，可同时重构浓度场、估计参数及量化不确定性，经实验验证其能准确再现输运动力学并揭示参数关联。
AI 中文摘要
我们针对非均质多孔介质中的反应性输运反问题，该问题需从稀疏实验观测中推断未知模型参数。强非线性、空间非均质性及有限数据可用性使该问题复杂化。我们提出了Conditioned-on-Design贝叶斯物理信息神经网络（CoDe-BPINN），其结合了域分解PINN求解器与贝叶斯推理网络，该网络学习给定实验设计变量时模型参数的条件分布。该框架通过最大化物理信息证据下界（ELBO）进行训练，可同时重构时空浓度场、进行概率参数估计及不确定性量化。我们通过含碘造影剂的多层多孔柱中污染物输运的实验室实验验证该方法，模型准确再现了穿透动力学，同时揭示了参数对流动条件的系统依赖性。特别地，其识别出有效吸附容量随流速和孔隙率增加呈非线性下降，这与动力学限制及吸附剂质量减少一致。贝叶斯公式还揭示了吸附亲和力与吸附容量间的强负相关，量化了该反问题的固有不可识别性。CoDe-BPINN为数据稀缺的反应性输运问题中的参数推理及不确定性量化提供了鲁棒框架。
英文摘要
We address the inverse problem of reactive transport in heterogeneous porous media, where unknown model parameters must be inferred from sparse experimental observations. The problem is complicated by strong nonlinearities, spatial heterogeneity, and limited data availability. We propose a Conditioned-on-Design Bayesian Physics-Informed Neural Network (CoDe-BPINN), which combines a domain-decomposed PINN solver with a Bayesian inference network that learns the conditional distribution of model parameters given experimental design variables. The framework is trained by maximizing a physics-informed Evidence Lower Bound (ELBO), enabling simultaneous reconstruction of spatiotemporal concentration fields, probabilistic parameter estimation, and uncertainty quantification. We demonstrate the approach using laboratory experiments on contaminant transport through a multilayer porous column with an iodinated contrast medium. The model accurately reproduces breakthrough dynamics while revealing systematic parameter dependence on flow conditions. In particular, it identifies a nonlinear decrease in effective sorption capacity with increasing flow rate and porosity, consistent with kinetic limitations and reduced adsorbent mass. The Bayesian formulation also uncovers a strong negative correlation between sorption affinity and sorption capacity, quantifying the intrinsic non-identifiability of the inverse problem. CoDe-BPINN provides a robust framework for parameter inference and uncertainty quantification in data-scarce reactive transport problems.
Comments27 pages, 9 figures
