用持续学习的神经算子替代电磁反演中的正演求解，实现秒级大规模反演。
Continually learning neural-operator surrogate for three-dimensional airborne electromagnetic Bayesian inversion
- 基于麦克斯韦方程不变性，通过持续学习多地质先验构建神经算子代理模型。
- 在西澳2013年测深数据上，两百万个测点反演仅需数秒，可信区间误差小于2.6%。
- 适合需要实时矿产系统靶区定位的地球物理勘探团队使用。
三维时域航空电磁（AEM）数据的概率反演受限于正演求解的成本。尽管单次模拟仅需数十秒，但对包含数百万个测点的调查进行贝叶斯反演需约 $10^{10}$ 次正演计算。为此，我们开发了一种持续学习的三维AEM正演算子神经算子代理模型，用于替代贝叶斯反演中的求解器。我们从一个基本观点出发：无论设定何种地质先验，麦克斯韦定律始终保持不变。其次，通过在连续先验上进行持续学习，避免了单一先验的局限性，使代理模型随未来案例应用而不断丰富，可由作者或科学界共同迭代。我们引入基于集合分歧的验证机制，将超出训练范围的测量数据导向原始求解器。在相同马尔可夫链蒙特卡洛采样器驱动下，代理模型重现了全求解器后验分布，其可信区间与真实值偏差不超过2.6个百分点。应用于西澳2013年Capricorn TEMPEST调查，代理模型在数秒内完成超过两百万个测点的反演，这一计算对原始求解器而言不可行。对整个调查的地质先验检验耗时仅几分钟。该框架实现了调查尺度上的不确定性量化电导率成像，我们认为这对实现近实时的矿产系统靶区定位至关重要。
原文摘要 · Abstract (English)
Three-dimensional probabilistic inversion of time-domain airborne electromagnetic (AEM) data is limited by the cost of the forward solve. Even though one simulation takes only tens of seconds, a Bayesian inversion of a survey of millions of soundings requires of order $10^{10}$ forward evaluations. To address this, we develop a continually learning neural-operator surrogate of the three-dimensional AEM forward operator that replaces the solver inside the Bayesian inversion. We start from the point of view that regardless of what geological prior is specified, Maxwell's laws remain invariant. Secondly, we avoid the limitation of learning on a single prior by continual learning on consecutive priors, which means our surrogate becomes richer as it is applied in future case studies, either by the authors, or by the scientific community. We use a validity check built on ensemble disagreement to divert cases with measurements outside the training range to the solver. Driven by the surrogate, the identical Markov chain Monte Carlo sampler reproduces the full-solver posterior, and its credible intervals cover the truth within 2.6 percentage points. Applied to the 2013 Capricorn TEMPEST survey in Western Australia, the surrogate inverts over two million soundings in seconds, a computation infeasible for the solver. Testing the geological prior against the entire survey costs minutes. The framework delivers uncertainty-quantified conductivity imaging at survey scale, which we believe is essential to perform near real-time mineral-systems targeting with geophysics.
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