# PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems

arXiv: https://arxiv.org/abs/2305.11056 · HTML: https://mlsanity.com/paper/2305.11056/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 18 May 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [HUMUS-Net: Hybrid unrolled multi-scale network architecture for accelerated MRI reconstruction](https://mlsanity.com/paper/2203.08213/) (2022)
- [Benchmarking deep inverse models over time, and the neural-adjoint method](https://mlsanity.com/paper/2009.12919/) (2020)
- [Learning to Invert: Signal Recovery via Deep Convolutional Networks](https://mlsanity.com/paper/1701.03891/) (2017)
- [Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solvers](https://mlsanity.com/paper/2203.02821/) (2022)
- [Loop Unrolled Shallow Equilibrium Regularizer (LUSER) -- A Memory-Efficient Inverse Problem Solver](https://mlsanity.com/paper/2210.04987/) (2022)
- [ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing](https://mlsanity.com/paper/1706.07929/) (2017)

## Built on by (most cited first, 1 of 1)

- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)

## Abstract (arXiv)

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear forward model can be computationally expensive, as it often involves computing and inverting a linearization at a series of estimates. Rather than inverting the physics-based model, we instead train a surrogate forward model (emulator) and leverage modern auto-grad libraries to solve for the input within a classical optimization framework. Current methods to train emulators are done in a black box supervised machine learning fashion and fail to take advantage of any existing knowledge of the forward model. In this article, we propose a simple learned weighted average model that embeds linearizations of the forward model around various reference points into the model itself, explicitly incorporating known physics. Grounding the learned model with physics based linearizations improves the forward modeling accuracy and provides richer physics based gradient information during the inversion process leading to more accurate signal recovery. We demonstrate the efficacy on an ocean acoustic tomography (OAT) example that aims to recover ocean sound speed profile (SSP) variations from acoustic observations (e.g. eigenray arrival times) within simulation of ocean dynamics in the Gulf of Mexico.