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

Jul 16, 2026

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A machine learning framework enables data-driven inverse design of V-beam thermal sensors by selecting beam inclination angle, beam length, and beam width to achieve a target displacement under a specified temperature. The design objective also minimizes structural volume and mechanical stress. The inverse problem is ill-posed because multiple geometries can yield the same displacement, causing direct regression to underperform. Five exploratory trials lead to a two-phase pipeline: a neural forward model mapping geometry and material constants to sensor responses, followed by gradient-descent inverse optimization that freezes the forward model while jointly minimizing stress and volume using a 3000-sample dataset.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

Introduction

V-beam thermal sensor background

Motivation for machine learning

Dataset Description

Dataset overview and features

Intended use and limitations

Data-Driven Forward and Inverse Modeling of V-Beam Thermal Sensors Tudor Bartha, Adrian Groza Artificial Intelligence Research Institute (AIRi@UTCN ), Technical University of Cluj-Napoca Radu Chiorean Faculty of Mechanical Engineering Technical University of Cluj-Napoca arXiv :2607 .09752v1 [ ee ss . SP] 4 Jul 2026 Abstract—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 achievesa MAPE of 4.76% for predicting the displacement, more than 70% of predictions having MAPE of under 5%. I. INTRODUCTION The V-beam thermal sensor, often referred to in MEMS literature as a V-shaped or chevron electrothermal microstructure, is a compact microelectromechanical structure that converts thermal energy into mechanical displacement or actuation force. It typically consists of inclined microbeams anchored at both ends and connected to a central shuttle. When Joule heating or an external thermal field increases the temperature of the beams, thermal expansion occurs; because the beams are geometrically constrained, this expansion is redirected into inplane motion. This configuration provides high force density, relatively large displacement, and efficient use of chip area compared with many electrostatic MEMS structures [1] . V-beam MEMS structures are important because they combine electrical, thermal, and mechanical domains in a single miniaturized device. Their performance depends on beam geometry, temperature distribution, material properties and heat transfer to the surrounding environment. Furthermore, they are useful not only as actuators but also as thermal-sensitive structures in sensing and characterization platforms. Thermal MEMS devices have been widely studied for automotive systems, defense technologies, health-care systems, optical switches and nano-positioning applications [2] . The V-beam structure is especially suitable for studies involving machine learning models applied to mechanical structures because of their multiphysics problem and nonlinear dependency on the defining geometrical parameters. Recent research shows that V-shaped electrothermal MEMS devices are used in micro motors, micro robots, optical lens scanners, microgrippers and rotary or linear micromotors [3]–[5] . Machine learning has also been introduced to improve modelling accuracy; for example, a BP neural-network-based modelling approach reduced the error between ANSYS simulation and experimental results for a V-shaped electrothermal MEMS actuator to less than 1%[3] . Therefore, the V-beam thermal MEMS sensor represents a strong candidate structure for data-driven prediction of displacement, temperature, stress, reliability, and coupled electro-thermo-mechanical behavior. Figure 1 shown below illustrates the V-beam thermal sensor response and the geometrical parameters we have chosen to define the structure for the purpose of this study. The displacement is obtained using FEA simulation in ANSYS Workbench. A uniform thermal condition is applied to the structure corresponding to a sensing application with slow temperature variations.

FAQs

What sensor geometry parameters does the inverse design target?

The method optimizes the beam inclination angle, beam length, and beam width to meet a target displacement under a given temperature load.

Why do direct regression methods fail for this inverse problem?

For the same displacement, multiple geometric configurations are possible, making the problem ill-posed and reducing regression accuracy.

How does the proposed two-phase solution work?

It first trains a neural network forward model to predict sensor responses from geometry and material constants, then performs gradient-descent inverse optimization over the frozen forward model while minimizing stress and volume simultaneously.

Jul 16, 2026

Upload by Skyler