用机器学习反推热传感器最优结构，兼顾精度与低应力。
Data-Driven Forward and Inverse Modeling of V-Beam Thermal Sensors
- 先建正向模型预测几何参数对应的位移响应
- 再用梯度下降优化，同时最小化体积和应力
- 在3000样本上预测误差低于5%的占70%以上
本文提出一种数据驱动的V型梁热传感器逆向设计机器学习框架。目标是确定在给定温度下实现目标位移的最优传感器几何结构：梁倾斜角、梁长和梁宽，同时使结构体积和机械应力最小。由于相同位移对应多种可能的几何配置，直接回归方法失效，该问题为病态问题。通过五轮探索性实验逐步揭示问题本质，最终提出两阶段解决方案：首先训练神经网络正向模型，将几何参数与材料常数映射为传感器响应；其次基于冻结的正向模型进行梯度下降逆向优化，联合最小化应力与体积。该方法使用3000样本数据集，位移预测的MAPE为4.76%，超过70%的预测结果MAPE低于5%。
原文摘要 · Abstract (English)
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%.
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