  The rapid degradation of the functional properties of many Ti-based alloys is
due to the precipitation of the $\omega$ phase. In the conventional
high-temperature shape memory alloy Ti-Ta the formation of this phase
compromises completely the shape memory effect and high (>100{\deg}C)
transformation temperatures cannot be mantained during cycling. A solution to
this problem is the addition of other elements to form Ti-Ta-X alloys, which
often modifies the transformation temperatures; due to the largely unexplored
space of possible compositions, very few elements are known to stabilize the
shape memory effect without decreasing the transformation temperatures below
100{\deg}C. In this study we use transparent descriptors derived from first
principles calculations to search for new ternary Ti-Ta-X alloys that combine
stability and high temperatures. We suggest four new alloys with these
properties, namely Ti-Ta-Sb, Ti-Ta-Bi, Ti-Ta-In, and Ti-Ta-Sc. Our predictions
for the most promising of these alloys, Ti-Ta-Sc, are subsequently fully
validated by experimental investigations, the new alloy Ti-Ta-Sc showing no
traces of $\omega$ phase after cycling. Our computational strategy is
immediately transferable to other materials and may contribute to suppress
$\omega$ phase formation in a large class of alloys.
