<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>?</mml:mi><mml:mtext>?</mml:mtext><mml:mi>?</mml:mi></mml:math> phase transition of zirconium predicted by on-the-fly machine-learned force field

The accurate prediction of solid-solid structural phase transitions at finite temperature is a challenging task, since the dynamics so slow that direct simulations by first-principles (FP) methods are typically not possible. Here, we study $\alpha$-$\beta$ transition Zr ambient pressure means on-the-fly machine-learned force fields. These automatically generated during FP molecular (MD) without need human intervention, while retaining almost accuracy. Our MD successfully reproduce first-order displacive nature transition, which manifested an abrupt jump volume and cooperative displacement atoms temperature. further identified simulated x-ray powder diffraction, predicted in reasonable agreement with experiment. Furthermore, show using singular value decomposition pseudo inversion design matrix generally improves field compared to usual squared regularized Bayesian regression.