When we attached vibration sensors and measured the resonance and natural frequencies of the large structures that support our society, such as bridges and buildings, we were amazed to find that these measurements aligned with computer simulation results. This experience became the foundation of our research. I was able to understand the characteristics of the bridges I routinely crossed without much thought after taking a linear algebra class in university. It was then that I sensed the connection between mathematics and the real world. Despite the measurements and simulation results aligning, we found that they do not perfectly coincide. When we consider the cause, we can see that these discrepancies emerge from the unpredictability of real-world phenomena, such as the effects of the natural environment. We are working on data assimilation research to create simulations that capture real-world phenomena through state-of-the-art sensors and machine learning. This allows us to effectively mitigate these uncertainties and provide reliable and well-designed infrastructure.