Probabilistic inversions of electrical resistivity tomography data with a machine learning?based forward operator

Casting a geophysical inverse problem into Bayesian setting is often discouraged by the computational workload needed to run many forward modelling evaluations. Here we present probabilistic inversions of electrical resistivity tomography data in which operator replaced trained residual neural network that learns non-linear mapping between model and apparent values. The use this specific architecture can provide some advantages over standard convolutional networks as it mitigates vanishing gradient might affect deep networks. error introduced approximation properly taken account propagated onto estimated uncertainties. One crucial aspect any machine learning application definition an appropriate training set. We draw models forming validation sets from previously defined prior distributions, while finite element code provides associated datasets. apply approach two inversion frameworks: A Markov chain Monte Carlo algorithm applied synthetic data, ensemble-based employed for field measurements. For both tests, outcomes proposed method are benchmarked against predictions obtained when constitutes operator. Our experiments illustrate effectively approximate even relatively small set created. strategy three orders magnitude faster than accurate but computationally expensive code. also yields most likely solutions uncertainty quantifications comparable those employed. presented allows solving with reasonable cost limited hardware resources.