# SimPINNs: Simulation-Driven Physics-Informed Neural Networks for Enhanced Performance in Nonlinear Inverse Problems

arXiv: https://arxiv.org/abs/2309.16729 · HTML: https://mlsanity.com/paper/2309.16729/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [SIMBA: Scalable Inversion in Optical Tomography using Deep Denoising Priors](https://mlsanity.com/paper/1911.13241/) (2019)
- [Deep S3PR: Simultaneous Source Separation and Phase Retrieval Using Deep Generative Models](https://mlsanity.com/paper/2002.05856/) (2020)

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

- [Neutrino Oscillation Parameter Estimation Using Structured Hierarchical Transformers](https://mlsanity.com/paper/2603.22342/) (2026)

## Abstract (arXiv)

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the underlying forward model demonstrates pronounced nonlinear behaviour, and where the dimensionality of the unknown parameter space is substantially smaller than that of the observations. Our proposed method builds upon physics-informed neural networks (PINNs) trained with a hybrid loss function that combines observed data with simulated data generated by a known (approximate) physical model. Experimental results on an orbit restitution problem demonstrate that our approach surpasses the performance of standard PINNs, providing improved accuracy and robustness.