# The Neuro-Physical Inverter: A Modular Framework for Magnetotelluric Inversion Coupling Ensemble Conditioning with Residual Learning

arXiv: https://arxiv.org/abs/2610.03225 · HTML: https://mlsanity.com/paper/2610.03225/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 84 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond](https://mlsanity.com/paper/2103.10689/) (2021)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Deep learning electromagnetic inversion with convolutional neural networks](https://mlsanity.com/paper/1812.10247/) (2018)
- [Informative Neural Ensemble Kalman Learning](https://mlsanity.com/paper/2008.09915/) (2020)
- [Inversion of 1D frequency- and time-domain electromagnetic data with convolutional neural networks](https://mlsanity.com/paper/1912.00612/) (2019)
- [Physically Guided Deep Unsupervised Inversion for 1D Magnetotelluric Models](https://mlsanity.com/paper/2410.15274/) (2024)
- [PreAdaptFWI: Pretrained-Based Adaptive Residual Learning for Full-Waveform Inversion Without Dataset Dependency](https://mlsanity.com/paper/2502.11913/) (2025)
- [Enhanced 3D Gravity Inversion Using ResU-Net with Density Logging Constraints: A Dual-Phase Training Approach](https://mlsanity.com/paper/2601.02890/) (2026)
- [Ensemble-Conditional Gaussian Processes (Ens-CGP): Representation, Geometry, and Inference](https://mlsanity.com/paper/2602.13871/) (2026)

## Abstract (arXiv)

We present the Neuro-Physical Inverter (NPI), a modular, uncertainty-aware framework for geophysical inversion that couples ensemble-based conditioning with constrained residual learning, demonstrated in the 1D magnetotelluric (MT) setting as a controlled testbed. The framework operates in two stages. An Ensemble-Conditional Gaussian Process (EnsCGP) conditions a prior ensemble of resistivity models on the observed response, producing a physically admissible reference ensemble. A residual-learning neural network then predicts targeted corrections to this reference, trained on synthetic data and fine-tuned per station for field application through a physics-coupled objective. Because an ensemble is conditioned, refined, and propagated through both stages, every estimate carries an associated ensemble spread. Synthetic experiments show that NPI systematically reduces ensemble-mean error without destabilizing the ensemble. Applied to broadband MT data from the Gabbs Valley geothermal region (Nevada, USA), NPI reduces the across-station mean misfit over the mid-period band while retaining comparable ensemble spread. The propagated ensemble yields a factor of uncertainty that serves as an operational measure of constraint within the assumed model class. Both stages are dimension-agnostic in formulation, and the design principles established here are intended to scale to higher-dimensional parameterizations.