# A Straightforward Gradient-Based Approach for High-Tc Superconductor Design: Leveraging Domain Knowledge via Adaptive Constraints

arXiv: https://arxiv.org/abs/2403.13627 · HTML: https://mlsanity.com/paper/2403.13627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 20 Mar 2024.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Solving PDE-constrained Control Problems Using Operator Learning](https://mlsanity.com/paper/2111.04941/) (2021)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [Machine learning modeling of superconducting critical temperature](https://mlsanity.com/paper/1709.02727/) (2017)
- [Critical Temperature Prediction for a Superconductor: A Variational Bayesian Neural Network Approach](https://mlsanity.com/paper/2002.04977/) (2020)
- [Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates](https://mlsanity.com/paper/2304.13860/) (2023)

## Abstract (arXiv)

Materials design aims to discover novel compounds with desired properties. However, prevailing strategies face critical trade-offs. Conventional element-substitution approaches readily and adaptively incorporate various domain knowledge but remain confined to a narrow search space. In contrast, deep generative models efficiently explore vast compositional landscapes, yet they struggle to flexibly integrate domain knowledge. To address these trade-offs, we propose a gradient-based material design framework that combines these strengths, offering both efficiency and adaptability. In our method, chemical compositions are optimised to achieve target properties by using property prediction models and their gradients. In order to seamlessly enforce diverse constraints, including those reflecting domain insights such as oxidation states, discretised compositional ratios, types of elements, and their abundance, we apply masks and employ a special loss function, namely the integer loss. Furthermore, we initialise the optimisation using promising candidates from existing dataset, effectively guiding the search away from unfavourable regions and thus helping to avoid poor solutions. Our approach demonstrates a more efficient exploration of superconductor candidates, uncovering candidate materials with higher critical temperature than conventional element-substitution and generative models. Importantly, it could propose new compositions beyond those found in existing databases, including new hydride superconductors absent from the training dataset but which share compositional similarities with materials found in literature. This synergy of domain knowledge and machine-learning-based scalability provides a robust foundation for rapid, adaptive, and comprehensive materials design for superconductors and beyond.