# Benchmarking deep inverse models over time, and the neural-adjoint method

arXiv: https://arxiv.org/abs/2009.12919 · HTML: https://mlsanity.com/paper/2009.12919/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2020.

## Built on by (most cited first, 28 of 28)

- [Solving PDE-constrained Control Problems Using Operator Learning](https://mlsanity.com/paper/2111.04941/) (2021)
- [PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations](https://mlsanity.com/paper/2505.24717/) (2025)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)
- [Autoinverse: Uncertainty Aware Inversion of Neural Networks](https://mlsanity.com/paper/2208.13780/) (2022)
- [Invertible Rescaling Network and Its Extensions](https://mlsanity.com/paper/2210.04188/) (2022)
- [Do Deepfake Detectors Work in Reality?](https://mlsanity.com/paper/2502.10920/) (2025)
- [Inverse deep learning methods and benchmarks for artificial electromagnetic material design](https://mlsanity.com/paper/2112.10254/) (2021)
- [An Agentic Framework for Autonomous Metamaterial Modeling and Inverse Design](https://mlsanity.com/paper/2506.06935/) (2025)
- [Reverse Engineering Breast MRIs: Predicting Acquisition Parameters Directly from Images](https://mlsanity.com/paper/2303.04911/) (2023)
- [Manifold Learning for Knowledge Discovery and Intelligent Inverse Design of Photonic Nanostructures: Breaking the Geometric Complexity](https://mlsanity.com/paper/2102.04454/) (2021)
- [Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solvers](https://mlsanity.com/paper/2203.02821/) (2022)
- [Mixed Integer Neural Inverse Design](https://mlsanity.com/paper/2109.12888/) (2021)
- [RID-Noise: Towards Robust Inverse Design under Noisy Environments](https://mlsanity.com/paper/2112.03912/) (2021)
- [LUCID: Exposing Algorithmic Bias through Inverse Design](https://mlsanity.com/paper/2208.12786/) (2022)
- [Accelerating Inverse Learning via Intelligent Localization with Exploratory Sampling](https://mlsanity.com/paper/2212.01016/) (2022)
- [ISR: Invertible Symbolic Regression](https://mlsanity.com/paper/2405.06848/) (2024)
- [Meta-simulation for the Automated Design of Synthetic Overhead Imagery](https://mlsanity.com/paper/2209.08685/) (2022)
- [Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling](https://mlsanity.com/paper/2211.14366/) (2022)
- [Does Deep Active Learning Work in the Wild?](https://mlsanity.com/paper/2302.00098/) (2023)
- [Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates](https://mlsanity.com/paper/2304.13860/) (2023)
- [PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems](https://mlsanity.com/paper/2305.11056/) (2023)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Fast ABC with joint generative modelling and subset simulation](https://mlsanity.com/paper/2104.08156/) (2021)
- [Towards Robust Deep Active Learning for Scientific Computing](https://mlsanity.com/paper/2201.12632/) (2022)
- [IDToolkit: A Toolkit for Benchmarking and Developing Inverse Design Algorithms in Nanophotonics](https://mlsanity.com/paper/2305.18978/) (2023)
- [Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems](https://mlsanity.com/paper/2501.16573/) (2025)
- [Interpretable inverse design of optical multilayer thin films based on extended neural adjoint and regression activation mapping](https://mlsanity.com/paper/2507.18644/) (2025)

## Abstract (arXiv)

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning have arisen generating impressive results. We conceptualize these models as different schemes for efficiently, but randomly, exploring the space of possible inverse solutions. As a result, the accuracy of each approach should be evaluated as a function of time rather than a single estimated solution, as is often done now. Using this metric, we compare several state-of-the-art inverse modeling approaches on four benchmark tasks: two existing tasks, one simple task for visualization and one new task from metamaterial design. Finally, inspired by our conception of the inverse problem, we explore a solution that uses a deep learning model to approximate the forward model, and then uses backpropagation to search for good inverse solutions. This approach, termed the neural-adjoint, achieves the best performance in many scenarios.