# Learned multiphysics inversion with differentiable programming and machine learning

arXiv: https://arxiv.org/abs/2304.05592 · HTML: https://mlsanity.com/paper/2304.05592/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 90 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)
- [Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operators](https://mlsanity.com/paper/2210.17051/) (2022)
- [Don't Unroll Adjoint: Differentiating SSA-Form Programs](https://mlsanity.com/paper/1810.07951/) (2018)
- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [Preconditioned training of normalizing flows for variational inference in inverse problems](https://mlsanity.com/paper/2101.03709/) (2021)
- [Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs](https://mlsanity.com/paper/2204.01205/) (2022)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization](https://mlsanity.com/paper/2004.07871/) (2020)
- [Learning by example: fast reliability-aware seismic imaging with normalizing flows](https://mlsanity.com/paper/2104.06255/) (2021)
- [A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification](https://mlsanity.com/paper/2001.04567/) (2020)
- [Learned imaging with constraints and uncertainty quantification](https://mlsanity.com/paper/1909.06473/) (2019)
- [Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantification](https://mlsanity.com/paper/2303.03478/) (2023)
- [Uncertainty quantification in imaging and automatic horizon tracking: a Bayesian deep-prior based approach](https://mlsanity.com/paper/2004.00227/) (2020)
- [Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators](https://mlsanity.com/paper/2203.14396/) (2022)
- [Weak deep priors for seismic imaging](https://mlsanity.com/paper/2004.06835/) (2020)
- [De-risking geological carbon storage from high resolution time-lapse seismic to explainable leakage detection](https://mlsanity.com/paper/2211.03527/) (2022)
- [A Linear Algebraic Approach to Model Parallelism in Deep Learning](https://mlsanity.com/paper/2006.03108/) (2020)
- [Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems](https://mlsanity.com/paper/1902.09699/) (2019)
- [Time-domain sparsity promoting least-squares reverse time migration with source estimation](https://mlsanity.com/paper/2003.01159/) (2020)
- [Extended source imaging, a unifying framework for seismic & medical imaging](https://mlsanity.com/paper/2004.07389/) (2020)
- [SciAI4Industry -- Solving PDEs for industry-scale problems with deep learning](https://mlsanity.com/paper/2211.12709/) (2022)

## Built on by (most cited first, 7 of 7)

- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [Solving multiphysics-based inverse problems with learned surrogates and constraints](https://mlsanity.com/paper/2307.11099/) (2023)
- [InvertibleNetworks.jl: A Julia package for scalable normalizing flows](https://mlsanity.com/paper/2312.13480/) (2023)
- [Inference of CO2 flow patterns -- a feasibility study](https://mlsanity.com/paper/2311.00290/) (2023)
- [Conditional neural control variates for variance reduction in Bayesian inverse problems](https://mlsanity.com/paper/2602.21357/) (2026)
- [Dual-space posterior sampling for Bayesian inference in constrained inverse problems](https://mlsanity.com/paper/2603.00393/) (2026)
- [Diffusion-based subsurface CO2 multiphysics monitoring and forecasting](https://mlsanity.com/paper/2407.18426/) (2024)

## Abstract (arXiv)

We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, our software is designed to be both readable and scalable. This allows researchers to easily formulate their problems in an abstract fashion while exploiting the latest developments in high-performance computing. We illustrate and demonstrate our design principles and their benefits by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which aside from coupling of wave physics and multiphase flow, involves machine learning.