# Overview of Physics-Informed Machine Learning Inversion of Geophysical Data

arXiv: https://arxiv.org/abs/2310.08109 · HTML: https://mlsanity.com/paper/2310.08109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [Active Importance Sampling for Variational Objectives Dominated by Rare Events: Consequences for Optimization and Generalization](https://mlsanity.com/paper/2008.06334/) (2020)
- [Making Invisible Visible: Data-Driven Seismic Inversion with Spatio-temporally Constrained Data Augmentation](https://mlsanity.com/paper/2106.11892/) (2021)

## Abstract (arXiv)

We review four types of algorithms for physics-informed machine learning (PIML) inversion of geophysical data. The unifying equation is given by the joint objective function ε: begineqnarray ε||-PIML&=&λ1 overbrace||bf WML(bf H_bf w bf dobs-bf m)||2NN + λ2 overbrace||bf WFWI(bf L bf m-bf dobs)||2FWI ~+ nonumber nonumber && + ~~Regularizer, labelPIML.eq120 endeqnarraywhere the optimal model bf m^* and weights bf w^* minimize ε. Here, The matrix weights are given by the boldface symbol bf W, and full waveform inversion (FWI) is typically computed using a finite-difference solution of the wave equation, where bf L represents the forward modeling operation of the wave equation as a function of the model bf m. Also, a fully-connected neural network (NN) is used to compute the model bf Hwbf dobs ≈ bf m from the observed input data bf dobs. The selection of weights λi and the NN operations determine one of four different PIML algorithms. PIML offers potential advantages over standard FWI through its enhanced ability to avoid local minima and the option to locally train the inversion operator, minimizing the requirement for extensive training data for global applicability. However, the effectiveness of PIML relies on the similarity between the test and trained data. Nevertheless, a possible strategy to overcome this limitation involves initial pretraining of a PIML architecture with data from a broader region, followed by fine-tuning for specific data-a method reminiscent of the way large language models are pretrained and adapted for various tasks.