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Thick sedimentary fills in intermontane valleys are common in formerly glaciated mountain ranges but difficult to quantify. Yet knowledge of the fill thickness distribution could help to estimate sediment budgets of mountain belts and to decipher the role of stored material in modulating sediment flux from the orogen to the foreland. Here we present a new approach to estimate valley fill thickness and bedrock topography based on the geometric properties of a landscape using artificial neural networks. We test the potential of this approach following a four-tiered procedure. First, experiments with synthetic, idealized landscapes show that increasing variability in surface slopes requires successively more complex network configurations. Second, in experiments with artificially filled natural landscapes, we find that fill volumes can be estimated with an error below 20%. Third, in natural examples with valley fill surfaces that have steeply inclined slopes, such as the Unteraar and the Rhone Glaciers in the Swiss Alps, for example, the average deviation of cross-sectional area between the measured and the modeled valley fill is 26% and 27%, respectively. Finally, application of the method to the Rhone Valley, an overdeepened glacial valley in the Swiss Alps, yields a total estimated sediment volume of 9711km(3) and an average deviation of cross-sectional area between measurements and model estimates of 21.5%. Our new method allows for rapid assessment of sediment volumes in intermontane valleys while eliminating most of the subjectivity that is typically inherent in other methods where bedrock reconstructions are based on digital elevation models.