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When a batch of magma reaches Earth's surface, it forms a vent from which volcanic products are erupted. At many volcanoes, successive batches may open vents far away from previous ones, resulting in scattered, sometimes seemingly random spatial distributions. This exposes vast areas to volcanic hazards and makes forecasting difficult. Here, we show that magma pathways and thus future vent locations may be forecast by combining the physics of magma transport with a Monte Carlo inversion scheme for the volcano stress history. We validate our approach on a densely populated active volcanic field, Campi Flegrei (Italy), where we forecast future vents on an onshore semiannular belt located between 2.3 and 4.2 km from the caldera center. Our approach offers a mechanical explanation for the vent migration over time at Campi Flegrei and at many calderas worldwide and may be applicable to volcanoes of any type.