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

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%.

Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing. By mapping infinite-dimensional function spaces, this approach provides an efficient surrogate modeling framework for high-dimensional partial differential equations (PDEs). Compared to traditional numerical solvers, it achieves a superior trade-off between computational complexity and approximation accuracy, demonstrating significant advantages in many-query tasks such as real-time prediction and parameter sweeps. Given the stringent accuracy requirements of both forward simulation and inverse inference, as well as the precision bottlenecks of existing operator learning methods in handling complex boundaries or long-term evolution, we propose the Starter-Iterator Neural Operator (SINO). Our framework reinterprets the initialization strategies and iterative formats of traditional iterative methods through neural networks, establishing an efficient approach for spectral-spatiotemporal collaborative modeling. Specifically, the frequency-domain initialization module captures globally stable low-frequency features, while the time-domain learning module focuses on optimizing local solution residuals, thereby effectively overcoming the inherent limitations of conventional single-domain modeling approaches. Extensive experiments on typical dynamical systems such as the Navier-Stokes equations and acoustic wave equations, as well as practical applications including super-resolution imaging and weather forecasting, demonstrate that SINO achieves outstanding performance in numerical accuracy, generalization capability, and robustness.