Numerical algorithms for simulating continua have long been based on the idea that high resolution and high accuracy go hand-in-hand. While engineering and computational mechanics have pushed resolution limits in pursuit of simulation fidelity, computer graphics has often gone the other way, sacrificing resolution and accuracy for performance. However, what if we want both high-performance and predictive accuracy ? In this talk I will discuss how to avoid this seeming fundamental trade-off using measurement-based and data-driven simulation techniques as well as some examples of these methods applied to both forward and inverse problems in graphics and 3D printing. I will conclude with some thoughts on where these methods might take us in the future.