# DualTCN: A Physics-Constrained Temporal Convolutional Network for 2 Time-Domain Marine CSEM Inversion

arXiv: https://arxiv.org/abs/2605.04997 · HTML: https://mlsanity.com/paper/2605.04997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 7 of 7)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Deep learning electromagnetic inversion with convolutional neural networks](https://mlsanity.com/paper/1812.10247/) (2018)
- [Inversion of 1D frequency- and time-domain electromagnetic data with convolutional neural networks](https://mlsanity.com/paper/1912.00612/) (2019)

## Abstract (arXiv)

DualTCN is the first deep-learning framework for inverting time-domain marine controlled-source electromagnetic (MCSEM) transient data. Moving away from traditional subsurface discretization, the framework regresses four earth-model parameters -- σ1, σ2, d1, d2 -- and reconstructs conductivity-depth profiles using a differentiable soft-step decoder. The optimized architecture (379K parameters) features a Temporal Convolutional Network (TCN) encoder paired with a late-time branch and an auxiliary seafloor-depth head. This design achieves a 25.3% loss reduction over baseline models, with high predictive accuracy (R2 = 0.898 for σ2) and an inversion speed of 3.5~ms per sample on an A100 GPU. The framework demonstrates high robustness to noise through curriculum-based amplitude augmentation, maintaining a mean barR2 of 0.858 at ±2% random amplitude error, compared to 0.363 without augmentation. DualTCN generalizes effectively to three-layer extensions (seawater/resistive layer/basement), accurately resolving basement conductivity (R2 ≈ 0.88), though thin-layer resolution remains a physical limitation (R2 ≈ 0.23). In comparative benchmarks, DualTCN significantly outperforms traditional local optimization methods like Levenberg-Marquardt and L-BFGS-B, yielding a mean barR2 = 0.877 versus 0.129-0.439 for multi-start baselines, while operating at up to 21,000× lower computational cost. Finally, the framework incorporates uncertainty quantification via Monte Carlo (MC) Dropout. While well-calibrated for σ1 (PICP90 = 0.944), inherent signal limitations at short offsets (200m) lead to under-coverage for d2 (PICP90 = 0.572), which can be mitigated through post-hoc temperature scaling or split conformal prediction.