# Mixed Integer Neural Inverse Design

arXiv: https://arxiv.org/abs/2109.12888 · HTML: https://mlsanity.com/paper/2109.12888/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 52 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Benchmarking deep inverse models over time, and the neural-adjoint method](https://mlsanity.com/paper/2009.12919/) (2020)
- [Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures](https://mlsanity.com/paper/1902.03865/) (2019)
- [Amortized Synthesis of Constrained Configurations Using a Differentiable Surrogate](https://mlsanity.com/paper/2106.09019/) (2021)
- [Computational Design of Cold Bent Glass Faccades](https://mlsanity.com/paper/2009.03667/) (2020)

## Built on by (most cited first, 3 of 3)

- [Autoinverse: Uncertainty Aware Inversion of Neural Networks](https://mlsanity.com/paper/2208.13780/) (2022)
- [Large-Batch, Iteration-Efficient Neural Bayesian Design Optimization](https://mlsanity.com/paper/2306.01095/) (2023)
- [Characterizing the Discrete Geometry of ReLU Networks](https://mlsanity.com/paper/2606.07728/) (2026)

## Abstract (arXiv)

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired target performance? Here, we show that the piecewise linear property, very common in everyday neural networks, allows for an inverse design formulation based on mixed-integer linear programming. Our mixed-integer inverse design uncovers globally optimal or near optimal solutions in a principled manner. Furthermore, our method significantly facilitates emerging, but challenging, combinatorial inverse design tasks, such as material selection. For problems where finding the optimal solution is not desirable or tractable, we develop an efficient yet near-optimal hybrid optimization. Eventually, our method is able to find solutions provably robust to possible fabrication perturbations among multiple designs with similar performances.