# Teacher-Student Guided Inverse Modeling for Steel Final Hardness Estimation

arXiv: https://arxiv.org/abs/2510.05402 · HTML: https://mlsanity.com/paper/2510.05402/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 4 of 4)

- [mustGAN: Multi-Stream Generative Adversarial Networks for MR Image Synthesis](https://mlsanity.com/paper/1909.11504/) (2019)
- [M2ORT: Many-To-One Regression Transformer for Spatial Transcriptomics Prediction from Histopathology Images](https://mlsanity.com/paper/2401.10608/) (2024)
- [Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps](https://mlsanity.com/paper/2110.06983/) (2021)
- [DistanceNet: Estimating Traveled Distance from Monocular Images using a Recurrent Convolutional Neural Network](https://mlsanity.com/paper/1904.08105/) (2019)

## Abstract (arXiv)

Predicting the final hardness of steel after heat treatment is a challenging regression task due to the many-to-one nature of the process -- different combinations of input parameters (such as temperature, duration, and chemical composition) can result in the same hardness value. This ambiguity makes the inverse problem, estimating input parameters from a desired hardness, particularly difficult. In this work, we propose a novel solution using a Teacher-Student learning framework. First, a forward model (Teacher) is trained to predict final hardness from 13 metallurgical input features. Then, a backward model (Student) is trained to infer plausible input configurations from a target hardness value. The Student is optimized by leveraging feedback from the Teacher in an iterative, supervised loop. We evaluate our method on a publicly available tempered steel dataset and compare it against baseline regression and reinforcement learning models. Results show that our Teacher-Student framework not only achieves higher inverse prediction accuracy but also requires significantly less computational time, demonstrating its effectiveness and efficiency for inverse process modeling in materials science.