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%20predict%20the%20stable%20crystal%20structure%20of%20a%20known%20composition%20of%20elements%20and%20(b)%20propose%20novel%20compositions%20along%20with%20their%20stable%20structures.%20We%20present%20FlowMM%2C%20a%20pair%20of%20generative%20models%20that%20achieve%20state-of-the-art%20performance%20on%20both%20tasks%20while%20being%20more%20efficient%20and%20more%20flexible%20than%20competing%20methods.%20We%20generalize%20Riemannian%20Flow%20Matching%20to%20suit%20the%20symmetries%20inherent%20to%20crystals:%20translation%2C%20rotation%2C%20permutation%2C%20and%20periodic%20boundary%20conditions.%20Our%20framework%20enables%20the%20freedom%20to%20choose%20the%20flow%20base%20distributions%2C%20drastically%20simplifying%20the%20problem%20of%20learning%20crystal%20structures%20compared%20with%20diffusion%20models.%20In%20addition%20to%20standard%20benchmarks%2C%20we%20validate%20FlowMM's%20generated%20structures%20with%20quantum%20chemistry%20calculations%2C%20demonstrating%20that%20it%20is%20about%203x%20more%20efficient%2C%20in%20terms%20of%20integration%20steps%2C%20at%20finding%20stable%20materials%20compared%20to%20previous%20open%20methods.)
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