# Data-Driven Forward and Inverse Modeling of V-Beam Thermal Sensors

arXiv: https://arxiv.org/abs/2607.09752 · HTML: https://mlsanity.com/paper/2607.09752/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 4 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [A Survey of Optimization Methods from a Machine Learning Perspective](https://mlsanity.com/paper/1906.06821/) (2019)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences -- Version 1](https://mlsanity.com/paper/2106.09757/) (2021)

## Abstract (arXiv)

This paper presents a machine learning framework for data-driven inverse design of V-beam thermal sensors. The goal is to determine the optimal sensor geometry: beam inclination angle, beam length and beam width that achieves a target displacement under a given temperature. The design should also provide the geometry with minimum structure volume and minimum mechanical stress the sensor must support. This problem is ill-posed as for a given displacement there are multiple possible geometric configurations, causing direct regression methods to fail. We document a series of five exploratory trials that progressively revealed the nature of the problem culminating in a two-phase solution: a neural network forward model trained to map geometry and material constants to sensor responses, a gradient-descent inverse optimization over the frozen forward model, minimizing stress and volume simultaneously. The proposed pipeline utilizes a 3000-sample dataset and achieves a MAPE of 4.76% for predicting the displacement, more than 70% of predictions having MAPE of under 5%.